![Object-Oriented Python. Copyright © 2022 by Irv Kalb.
All rights reserved. No part of this work may be reproduced or transmitted in any form or by any
means, electronic or mechanical, including photocopying, recording, or by any information storage or
retrieval system, without the prior written permission of the copyright owner and the publisher.
First printing
25 24 23 22 21 1 2 3 4 5 6 7 8 9
ISBN-13: 978-1-7185-0206-2 (print)
ISBN-13: 978-1-7185-0207-9 (ebook)
Publisher: William Pollock
Managing Editor: Jill Franklin
Production Manager: Rachel Monaghan
Production Editor: Kate Kaminski
Developmental Editor: Liz Chadwick
Cover Illustrator: James L. Barry
Interior Design: Octopod Studios
Technical Reviewer: Monte Davidoff
Copyeditor: Rachel Head
Compositor: Maureen Forys, Happenstance Type-O-Rama
Proofreader: Paula L. Fleming
Indexer: Valerie Haynes Perry
The following images are reproduced with permission:
Figure 2-1, photo by David Benbennick, printed under the Creative Commons Attribution-Share
Alike 3.0 Unported license, https://creativecommons.org/licenses/by-sa/3.0/deed.en.
For information on book distributors or translations, please contact No Starch Press, Inc. directly:
No Starch Press, Inc.
245 8th Street, San Francisco, CA 94103
phone: 1.415.863.9900; info@nostarch.com
www.nostarch.com
Library of Congress Cataloging-in-Publication Data
Names: Kalb, Irv, author.
Title: Object-oriented Python: master OOP by building games and GUIs / Irv Kalb.
Description: San Francisco : No Starch Press, [2021] | Includes index. |
Identifiers: LCCN 2021044174 (print) | LCCN 2021044175 (ebook) | ISBN
9781718502062 (print) | ISBN 9781718502079 (ebook)
Subjects: LCSH: Object-oriented programming (Computer science) | Python
(Computer program language)
Classification: LCC QA76.64 .K3563 2021 (print) | LCC QA76.64 (ebook) |
DDC 005.1/17--dc23
LC record available at https://lccn.loc.gov/2021044174
LC ebook record available at https://lccn.loc.gov/2021044175
No Starch Press and the No Starch Press logo are registered trademarks of No Starch Press, Inc.
Other product and company names mentioned herein may be the trademarks of their respective
owners. Rather than use a trademark symbol with every occurrence of a trademarked name, we are
using the names only in an editorial fashion and to the benefit of the trademark owner, with no
intention of infringement of the trademark.](https://image.slidesharecdn.com/28089-250322025241-2640f1b9/85/Object-Oriented-Python-1st-Edition-Irv-Kalb-18-320.jpg)
![ACKNOWLEDGMENTS
I would like to thank the following people, who helped make this book
possible:
Al Sweigart, for getting me started in the use of pygame (especially with his
“Pygbutton” code) and for allowing me to use the concept of his “Dodger”
game.
Monte Davidoff, who was instrumental in helping me get the source code
and documentation of that code to build correctly through the use of
GitHub, Sphinx, and ReadTheDocs. He worked miracles using a myriad of
tools to wrestle the appropriate files into submission.
Monte Davidoff (yes, the same guy), for being an outstanding technical
reviewer. Monte made excellent technical and writing suggestions
throughout the book, and many of the code examples are more Pythonic and
more OOP-ish because of his comments.
Tep Sathya Khieu, who did a stellar job of drawing all the original diagrams
for this book. I am not an artist (I don’t even play one on TV). Tep was able
to take my primitive pencil sketches and turn them into clear, consistent
pieces of art.
Harrison Yung, Kevin Ly, and Emily Allis, for their contributions of
artwork in some of the game art.
The early reviewers, Illya Katsyuk, Jamie Kalb, Gergana Angelova, and Joe
Langmuir, who found and corrected many typos and made excellent
suggestions for modifications and clarifications.
All the editors who worked on this book: Liz Chadwick (developmental
editor), Rachel Head (copyeditor), and Kate Kaminski (production editor).
They all made huge contributions by questioning and often rewording and
reorganizing some of my explanations of concepts. They were also
extremely helpful in adding and removing commas [do I need one here?]](https://image.slidesharecdn.com/28089-250322025241-2640f1b9/85/Object-Oriented-Python-1st-Edition-Irv-Kalb-22-320.jpg)
![deckListOut = deckListIn.copy() # make a copy of the
starting deck
random.shuffle(deckListOut)
return deckListOut
# Main code
print('Welcome to Higher or Lower.')
print('You have to choose whether the next card to be shown
will be higher or lower than the current card.')
print('Getting it right adds 20 points; get it wrong and you
lose 15 points.')
print('You have 50 points to start.')
print()
startingDeckList = []
1 for suit in SUIT_TUPLE:
for thisValue, rank in enumerate(RANK_TUPLE):
cardDict = {'rank':rank, 'suit':suit,
'value':thisValue + 1}
startingDeckList.append(cardDict)
score = 50
while True: # play multiple games
print()
gameDeckList = shuffle(startingDeckList)
2 currentCardDict = getCard(gameDeckList)
currentCardRank = currentCardDict['rank']
currentCardValue = currentCardDict['value']
currentCardSuit = currentCardDict['suit']
print('Starting card is:', currentCardRank + ' of ' +
currentCardSuit)
print()
3 for cardNumber in range(0, NCARDS): # play one game of
this many cards
answer = input('Will the next card be higher or lower
than the ' +
currentCardRank + ' of ' +
currentCardSuit + '? (enter h or l):
')
answer = answer.casefold() # force lowercase
4 nextCardDict = getCard(gameDeckList)
nextCardRank = nextCardDict['rank']
nextCardSuit = nextCardDict['suit']
nextCardValue = nextCardDict['value']](https://image.slidesharecdn.com/28089-250322025241-2640f1b9/85/Object-Oriented-Python-1st-Edition-Irv-Kalb-37-320.jpg)
![# Non-OOP
# Bank Version 1
# Single account
1 accountName = 'Joe'
accountBalance = 100
accountPassword = 'soup'
while True:
2 print()
print('Press b to get the balance')
print('Press d to make a deposit')
print('Press w to make a withdrawal')
print('Press s to show the account')
print('Press q to quit')
print()
action = input('What do you want to do? ')
action = action.lower() # force lowercase
action = action[0] # just use first letter
print()
if action == 'b':
print('Get Balance:')
userPassword = input('Please enter the password: ')
if userPassword != accountPassword:
print('Incorrect password')
else:
print('Your balance is:', accountBalance)
elif action == 'd':
print('Deposit:')
userDepositAmount = input('Please enter amount to
deposit: ')
userDepositAmount = int(userDepositAmount)
userPassword = input('Please enter the password: ')
if userDepositAmount < 0:
print('You cannot deposit a negative amount!')
elif userPassword != accountPassword:
print('Incorrect password')
else: # OK
accountBalance = accountBalance +
userDepositAmount](https://image.slidesharecdn.com/28089-250322025241-2640f1b9/85/Object-Oriented-Python-1st-Edition-Irv-Kalb-41-320.jpg)
![global accountName, accountBalance, accountPassword
if amountToDeposit < 0:
print('You cannot deposit a negative amount!')
return None
if password != accountPassword:
print('Incorrect password')
return None
accountBalance = accountBalance + amountToDeposit
return accountBalance
4 def withdraw(amountToWithdraw, password):
5 global accountName, accountBalance, accountPassword
if amountToWithdraw < 0:
print('You cannot withdraw a negative amount')
return None
if password != accountPassword:
print('Incorrect password for this account')
return None
if amountToWithdraw > accountBalance:
print('You cannot withdraw more than you have in your
account')
return None
6 accountBalance = accountBalance - amountToWithdraw
return accountBalance
newAccount("Joe", 100, 'soup') # create an account
while True:
print()
print('Press b to get the balance')
print('Press d to make a deposit')
print('Press w to make a withdrawal')
print('Press s to show the account')
print('Press q to quit')
print()
action = input('What do you want to do? ')
action = action.lower() # force lowercase
action = action[0] # just use first letter
print()
if action == 'b':](https://image.slidesharecdn.com/28089-250322025241-2640f1b9/85/Object-Oriented-Python-1st-Edition-Irv-Kalb-44-320.jpg)
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- 6. CONTENTS IN DETAIL TITLE PAGE COPYRIGHT DEDICATION ABOUT THE AUTHOR ACKNOWLEDGMENTS INTRODUCTION Who Is This Book For? Python Version(s) and Installation How Will I Explain OOP? What’s in the Book Development Environments Widgets and Example Games PART I: INTRODUCING OBJECT-ORIENTED PROGRAMMING CHAPTER 1: PROCEDURAL PYTHON EXAMPLES Higher or Lower Card Game Representing the Data Implementation Reusable Code Bank Account Simulations
- 7. Analysis of Required Operations and Data Implementation 1—Single Account Without Functions Implementation 2—Single Account with Functions Implementation 3—Two Accounts Implementation 4—Multiple Accounts Using Lists Implementation 5—List of Account Dictionaries Common Problems with Procedural Implementation Object-Oriented Solution—First Look at a Class Summary CHAPTER 2: MODELING PHYSICAL OBJECTS WITH OBJECT- ORIENTED PROGRAMMING Building Software Models of Physical Objects State and Behavior: Light Switch Example Classes, Objects, and Instantiation Writing a Class in Python Scope and Instance Variables Differences Between Functions and Methods Creating an Object from a Class Calling Methods of an Object Creating Multiple Instances from the Same Class Python Data Types Are Implemented as Classes Definition of an Object Building a Slightly More Complicated Class Representing a More Complicated Physical Object as a Class Passing Arguments to a Method Multiple Instances Initialization Parameters Classes in Use
- 8. OOP as a Solution Summary CHAPTER 3: MENTAL MODELS OF OBJECTS AND THE MEANING OF “SELF” Revisiting the DimmerSwitch Class High-Level Mental Model #1 A Deeper Mental Model #2 What Is the Meaning of “self”? Summary CHAPTER 4: MANAGING MULTIPLE OBJECTS Bank Account Class Importing Class Code Creating Some Test Code Creating Multiple Accounts Multiple Account Objects in a List Multiple Objects with Unique Identifiers Building an Interactive Menu Creating an Object Manager Object Building the Object Manager Object Main Code That Creates an Object Manager Object Better Error Handling with Exceptions try and except The raise Statement and Custom Exceptions Using Exceptions in Our Bank Program Account Class with Exceptions Optimized Bank Class Main Code That Handles Exceptions
- 9. Calling the Same Method on a List of Objects Interface vs. Implementation Summary PART II: GRAPHICAL USER INTERFACES WITH PYGAME CHAPTER 5: INTRODUCTION TO PYGAME Installing Pygame Window Details The Window Coordinate System Pixel Colors Event-Driven Programs Using Pygame Bringing Up a Blank Window Drawing an Image Detecting a Mouse Click Handling the Keyboard Creating a Location-Based Animation Using Pygame rects Playing Sounds Playing Sound Effects Playing Background Music Drawing Shapes Reference for Primitive Shapes Summary CHAPTER 6: OBJECT-ORIENTED PYGAME Building the Screensaver Ball with OOP Pygame
- 10. Creating a Ball Class Using the Ball Class Creating Many Ball Objects Creating Many, Many Ball Objects Building a Reusable Object-Oriented Button Building a Button Class Main Code Using a SimpleButton Creating a Program with Multiple Buttons Building a Reusable Object-Oriented Text Display Steps to Display Text Creating a SimpleText Class Demo Ball with SimpleText and SimpleButton Interface vs. Implementation Callbacks Creating a Callback Using a Callback with SimpleButton Summary CHAPTER 7: PYGAME GUI WIDGETS Passing Arguments into a Function or Method Positional and Keyword Parameters Additional Notes on Keyword Parameters Using None as a Default Value Choosing Keywords and Default Values Default Values in GUI Widgets The pygwidgets Package Setting Up Overall Design Approach
- 11. Adding an Image Adding Buttons, Checkboxes, and Radio Buttons Text Output and Input Other pygwidgets Classes pygwidgets Example Program The Importance of a Consistent API Summary PART III: ENCAPSULATION, POLYMORPHISM, AND INHERITANCE CHAPTER 8: ENCAPSULATION Encapsulation with Functions Encapsulation with Objects Objects Own Their Data Interpretations of Encapsulation Direct Access and Why You Should Avoid It Strict Interpretation with Getters and Setters Safe Direct Access Making Instance Variables More Private Implicitly Private More Explicitly Private Decorators and @property Encapsulation in pygwidgets Classes A Story from the Real World Abstraction Summary CHAPTER 9: POLYMORPHISM
- 12. Sending Messages to Real-World Objects A Classic Example of Polymorphism in Programming Example Using Pygame Shapes The Square Shape Class The Circle and Triangle Shape Classes The Main Program Creating Shapes Extending a Pattern pygwidgets Exhibits Polymorphism Polymorphism for Operators Magic Methods Comparison Operator Magic Methods A Rectangle Class with Magic Methods Main Program Using Magic Methods Math Operator Magic Methods Vector Example Creating a String Representation of Values in an Object A Fraction Class with Magic Methods Summary CHAPTER 10: INHERITANCE Inheritance in Object-Oriented Programming Implementing Inheritance Employee and Manager Example Base Class: Employee Subclass: Manager Test Code The Client’s View of a Subclass Real-World Examples of Inheritance InputNumber
- 13. DisplayMoney Example Usage Multiple Classes Inheriting from the Same Base Class Abstract Classes and Methods How pygwidgets Uses Inheritance Class Hierarchy The Difficulty of Programming with Inheritance Summary CHAPTER 11: MANAGING MEMORY USED BY OBJECTS Object Lifetime Reference Count Garbage Collection Class Variables Class Variable Constants Class Variables for Counting Putting It All Together: Balloon Sample Program Module of Constants Main Program Code Balloon Manager Balloon Class and Objects Managing Memory: Slots Summary PART IV: USING OOP IN GAME DEVELOPMENT CHAPTER 12: CARD GAMES The Card Class The Deck Class
- 14. The Higher or Lower Game Main Program Game Object Testing with __name__ Other Card Games Blackjack Deck Games with Unusual Card Decks Summary CHAPTER 13: TIMERS Timer Demonstration Program Three Approaches for Implementing Timers Counting Frames Timer Event Building a Timer by Calculating Elapsed Time Installing pyghelpers The Timer Class Displaying Time CountUpTimer CountDownTimer Summary CHAPTER 14: ANIMATION Building Animation Classes SimpleAnimation Class SimpleSpriteSheetAnimation Class Merging Two Classes Animation Classes in pygwidgets Animation Class
- 15. SpriteSheetAnimation Class Common Base Class: PygAnimation Example Animation Program Summary CHAPTER 15: SCENES The State Machine Approach A pygame Example with a State Machine A Scene Manager for Managing Many Scenes A Demo Program Using a Scene Manager The Main Program Building the Scenes A Typical Scene Rock, Paper, Scissors Using Scenes Communication Between Scenes Requesting Information from a Target Scene Sending Information to a Target Scene Sending Information to All Scenes Testing Communications Among Scenes Implementation of the Scene Manager run() Method Main Methods Communication Between Scenes Summary CHAPTER 16: FULL GAME: DODGER Modal Dialogs Yes/No and Alert Dialogs Answer Dialogs
- 16. Building a Full Game: Dodger Game Overview Implementation Extensions to the Game Summary CHAPTER 17: DESIGN PATTERNS AND WRAP-UP Model View Controller File Display Example Statistical Display Example Advantages of the MVC Pattern Wrap-Up INDEX
- 17. OBJECT-ORIENTED PYTHON Master OOP by Building Games and GUIs by Irv Kalb
- 18. Object-Oriented Python. Copyright © 2022 by Irv Kalb. All rights reserved. No part of this work may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage or retrieval system, without the prior written permission of the copyright owner and the publisher. First printing 25 24 23 22 21 1 2 3 4 5 6 7 8 9 ISBN-13: 978-1-7185-0206-2 (print) ISBN-13: 978-1-7185-0207-9 (ebook) Publisher: William Pollock Managing Editor: Jill Franklin Production Manager: Rachel Monaghan Production Editor: Kate Kaminski Developmental Editor: Liz Chadwick Cover Illustrator: James L. Barry Interior Design: Octopod Studios Technical Reviewer: Monte Davidoff Copyeditor: Rachel Head Compositor: Maureen Forys, Happenstance Type-O-Rama Proofreader: Paula L. Fleming Indexer: Valerie Haynes Perry The following images are reproduced with permission: Figure 2-1, photo by David Benbennick, printed under the Creative Commons Attribution-Share Alike 3.0 Unported license, https://creativecommons.org/licenses/by-sa/3.0/deed.en. For information on book distributors or translations, please contact No Starch Press, Inc. directly: No Starch Press, Inc. 245 8th Street, San Francisco, CA 94103 phone: 1.415.863.9900; [email protected] www.nostarch.com Library of Congress Cataloging-in-Publication Data Names: Kalb, Irv, author. Title: Object-oriented Python: master OOP by building games and GUIs / Irv Kalb. Description: San Francisco : No Starch Press, [2021] | Includes index. | Identifiers: LCCN 2021044174 (print) | LCCN 2021044175 (ebook) | ISBN 9781718502062 (print) | ISBN 9781718502079 (ebook) Subjects: LCSH: Object-oriented programming (Computer science) | Python (Computer program language) Classification: LCC QA76.64 .K3563 2021 (print) | LCC QA76.64 (ebook) | DDC 005.1/17--dc23 LC record available at https://lccn.loc.gov/2021044174 LC ebook record available at https://lccn.loc.gov/2021044175 No Starch Press and the No Starch Press logo are registered trademarks of No Starch Press, Inc. Other product and company names mentioned herein may be the trademarks of their respective owners. Rather than use a trademark symbol with every occurrence of a trademarked name, we are using the names only in an editorial fashion and to the benefit of the trademark owner, with no intention of infringement of the trademark.
- 19. The information in this book is distributed on an “As Is” basis, without warranty. While every precaution has been taken in the preparation of this work, neither the author nor No Starch Press, Inc. shall have any liability to any person or entity with respect to any loss or damage caused or alleged to be caused directly or indirectly by the information contained in it.
- 20. To my wonderful wife, Doreen. You are the glue that keeps our family together. Many years ago, I said, “I do,” but what I meant was, “I will.”
- 21. About the Author Irv Kalb is an adjunct professor at UCSC Silicon Valley Extension and the University of Silicon Valley (formerly Cogswell Polytechnical College), where he teaches introductory and object-oriented programming courses in Python. Irv has a bachelor’s and a master’s degree in computer science, has been using object-oriented programming for over 30 years in a number of different computer languages, and has been teaching for over 10 years. He has decades of experience developing software, with a focus on educational software. As Furry Pants Productions, he and his wife created and shipped two edutainment CD-ROMs based on the character Darby the Dalmatian. Irv is also the author of Learn to Program with Python 3: A Step-by-Step Guide to Programming (Apress). Irv was heavily involved in the early development of the sport of Ultimate Frisbee®. He led the effort of writing many versions of the official rule book and co-authored and self-published the first book on the sport, Ultimate: Fundamentals of the Sport. About the Technical Reviewer Monte Davidoff is an independent software development consultant. His areas of expertise include DevOps and Linux. Monte has been programming in Python for over 20 years. He has used Python to develop a variety of software, including business-critical applications and embedded software.
- 22. ACKNOWLEDGMENTS I would like to thank the following people, who helped make this book possible: Al Sweigart, for getting me started in the use of pygame (especially with his “Pygbutton” code) and for allowing me to use the concept of his “Dodger” game. Monte Davidoff, who was instrumental in helping me get the source code and documentation of that code to build correctly through the use of GitHub, Sphinx, and ReadTheDocs. He worked miracles using a myriad of tools to wrestle the appropriate files into submission. Monte Davidoff (yes, the same guy), for being an outstanding technical reviewer. Monte made excellent technical and writing suggestions throughout the book, and many of the code examples are more Pythonic and more OOP-ish because of his comments. Tep Sathya Khieu, who did a stellar job of drawing all the original diagrams for this book. I am not an artist (I don’t even play one on TV). Tep was able to take my primitive pencil sketches and turn them into clear, consistent pieces of art. Harrison Yung, Kevin Ly, and Emily Allis, for their contributions of artwork in some of the game art. The early reviewers, Illya Katsyuk, Jamie Kalb, Gergana Angelova, and Joe Langmuir, who found and corrected many typos and made excellent suggestions for modifications and clarifications. All the editors who worked on this book: Liz Chadwick (developmental editor), Rachel Head (copyeditor), and Kate Kaminski (production editor). They all made huge contributions by questioning and often rewording and reorganizing some of my explanations of concepts. They were also extremely helpful in adding and removing commas [do I need one here?]
- 23. and lengthening my sentences as I am doing here to make sure that the point comes across cleanly (OK, I’ll stop!). I’m afraid that I’ll never understand when to use “which” versus “that,” or when to use a comma and when to use a dash, but I’m glad that they know! Thanks also to Maureen Forys (compositor) for her valuable contributions to the finished product. All the students who have been in my classes over the years at the UCSC Silicon Valley Extension and at the University of Silicon Valley (formerly Cogswell Polytechnical College). Their feedback, suggestions, smiles, frowns, light-bulb moments, frustrations, knowing head nods, and even thumbs-up (in Zoom classes during the COVID era) were extremely helpful in shaping the content of this book and my overall teaching style. Finally, my family, who supported me through the long process of writing, testing, editing, rewriting, editing, debugging, editing, rewriting, editing (and so on) this book and the associated code. I couldn’t have done it without them. I wasn’t sure if we had enough books in our library, so I wrote another one!
- 24. INTRODUCTION This book is about a software development technique called object- oriented programming (OOP) and how it can be used with Python. Before OOP, programmers used an approach known as procedural programming, also called structured programming, which involves building a set of functions (procedures) and passing data around through calls to those functions. The OOP paradigm gives programmers an efficient way to combine code and data into cohesive units that are often highly reusable. In preparation for writing this book, I extensively researched existing literature and videos, looking specifically at the approaches taken to explain this important and wide-ranging topic. I found that instructors and writers typically start by defining certain key terms: class, instance variable, method, encapsulation, inheritance, polymorphism, and so on. While these are all important concepts, and I’ll cover all of them in depth in this book, I’ll begin in a different way: by considering the question, “What problem are we solving?” That is, if OOP is the solution, then what is the problem? To answer this question, I’ll start by presenting a few examples of programs built using procedural programming and identifying complications inherent in this style. Then I’ll show you how an object-
- 25. oriented approach can make the construction of such programs much easier and the programs themselves more maintainable.
- 26. Who Is This Book For? This book is intended for people who already have some familiarity with Python and with using basic functions from the Python Standard Library. I will assume that you understand the fundamental syntax of the language and can write small- to medium-sized programs using variables, assignment statements, if/elif/else statements, while and for loops, functions and function calls, lists, dictionaries, and so on. If you aren’t comfortable with all of these concepts, then I suggest that you get a copy of my earlier book, Learn to Program with Python 3 (Apress), and read that first. This is an intermediate-level text, so there are a number of more advanced topics that I will not address. For example, to keep the book practical, I will not often go into detail on the internal implementation of Python. For simplicity and clarity, and to keep the focus on mastering OOP techniques, the examples are written using a limited subset of the language. There are more advanced and concise ways to code in Python that are beyond the scope of this book. I will cover the underlying details of OOP in a mostly language- independent way, but will point out areas where there are differences between Python and other OOP languages. Having learned the basics of OOP-style coding through this book, if you wish, you should be able to easily apply these techniques to other OOP languages. Python Version(s) and Installation All the example code in this book was written and tested using Python versions 3.6 through 3.9. All the examples should work fine with version 3.6 or newer. Python is available for free at https://www.python.org. If you don’t have Python installed, or you want to upgrade to the latest version, go to that site, find the Downloads tab, and click the Download button. This will download an installable file onto your computer. Double-click the file that was downloaded to install Python.
- 27. WINDOWS INSTALLATION If you’re installing on a Windows system, there is one important option that you need to set correctly. When running through the installation steps, you should see a screen like this: At the bottom of the dialog is a checkbox labeled “Add Python 3.x to PATH.” Please be sure to check this box (it defaults to unchecked). This setting will make the installation of the pygame package (which is introduced later in the book) work correctly. NOTE I am aware of the “PEP 8 – Style Guide for Python Code” and its specific recommendation to use the snake case convention (snake_case) for variable and function names. However, I’d been using the camel case naming convention (camelCase) for many years before the PEP 8 document was written and have become comfortable with it during my career. Therefore, all variable and function names in this book are written using camel case.
- 28. How Will I Explain OOP? The examples in the first few chapters use text-based Python; these sample programs get input from the user and output information to the user purely in the form of text. I’ll introduce OOP by showing you how to develop text- based simulations of physical objects in code. We’ll start by creating representations of light switches, dimmer switches, and TV remote controls as objects. I’ll then show you how we can use OOP to simulate bank accounts and a bank that controls many accounts. Once we’ve covered the basics of OOP, I’ll introduce the pygame module, which allows programmers to write games and applications that use a graphical user interface (GUI). With GUI-based programs, the user intuitively interacts with buttons, checkboxes, text input and output fields, and other user-friendly widgets. I chose to use pygame with Python because this combination allows me to demonstrate OOP concepts in a highly visual way using elements on the screen. Pygame is extremely portable and runs on nearly every platform and operating system. All the sample programs that use the pygame package have been tested with the recently released pygame version 2.0. I’ve created a package called pygwidgets that works with pygame and implements a number of basic widgets, all of which are built using an OOP approach. I’ll introduce this package later in the book, providing sample code you can run and experiment with. This approach will allow you to see real, practical examples of key object-oriented concepts, while incorporating these techniques to produce fun, playable games. I’ll also introduce my pyghelpers package, which provides code to help write more complicated games and applications. All the example code shown in the book is available as a single download from the No Starch website: https://www.nostarch.com/object-oriented- python/. The code is also available on a chapter-by-chapter basis from my GitHub repository: https://github.com/IrvKalb/Object-Oriented-Python-Code/. What’s in the Book
- 29. This book is divided into four parts. Part I introduces object-oriented programming: Chapter 1 provides a review of coding using procedural programming. I’ll show you how to implement a text-based card game and simulate a bank performing operations on one or more accounts. Along the way, I discuss common problems with the procedural approach. Chapter 2 introduces classes and objects and shows how you can represent real-world objects like light switches or a TV remote in Python using classes. You’ll see how an object-oriented approach solves the problems highlighted in the first chapter. Chapter 3 presents two mental models that you can use to think about what’s going on behind the scenes when you create objects in Python. We’ll use Python Tutor to step through code and see how objects are created. Chapter 4 demonstrates a standard way to handle multiple objects of the same type by introducing the concept of an object manager object. We’ll expand the bank account simulation using classes, and I’ll show you how to handle errors using exceptions. Part II focuses on building GUIs with pygame: Chapter 5 introduces the pygame package and the event-driven model of programming. We’ll build a few simple programs to get you started with placing graphics in a window and handling keyboard and mouse input, then develop a more complicated ball-bouncing program. Chapter 6 goes into much more detail on using OOP with pygame programs. We’ll rewrite the ball-bouncing program in an OOP style and develop some simple GUI elements. Chapter 7 introduces the pygwidgets module, which contains full implementations of many standard GUI elements (buttons, checkboxes, and so on), each developed as a class. Part III delves into the main tenets of OOP: Chapter 8 discusses encapsulation, which involves hiding implementation details from external code and placing all related methods in one place: a class.
- 30. Chapter 9 introduces polymorphism—the idea that multiple classes can have methods with the same names—and shows how it enables you to make calls to methods in multiple objects, without having to know the type of each object. We’ll build a Shapes program to demonstrate this concept. Chapter 10 covers inheritance, which allows you to create a set of subclasses that all use common code built into a base class, rather than having to reinvent the wheel with similar classes. We’ll look at a few real- world examples where inheritance comes in handy, such as implementing an input field that only accepts numbers, then rewrite our Shapes example program to use this feature. Chapter 11 wraps up this part of the book by discussing some additional important OOP topics, mostly related to memory management. We’ll look at the lifetime of an object, and as an example we’ll build a small balloon- popping game. Part IV explores several topics related to using OOP in game development: Chapter 12 demonstrates how we can rebuild the card game developed in Chapter 1 as a pygame-based GUI program. I also show you how to build reusable Deck and Card classes that you can use in other card games you create. Chapter 13 covers timing. We’ll develop different timer classes that allow a program to keep running while concurrently checking for a given time limit. Chapter 14 explains animation classes you can use to show sequences of images. We’ll look at two animation techniques: building animations from a collection of separate image files and extracting and using multiple images from a single sprite sheet file. Chapter 15 explains the concept of a state machine, which represents and controls the flow of your programs, and a scene manager, which you can use to build a program with multiple scenes. To demonstrate the use of each of these, we’ll build two versions of a Rock, Paper, Scissors game. Chapter 16 discusses different types of modal dialogs, another important user interaction feature. We then walk through building a full-featured OOP-based video game called Dodger that demonstrates many of the techniques described in the book.
- 31. Chapter 17 introduces the concept of design patterns, focusing on the Model View Controller pattern, then presents a dice-rolling program that uses this pattern to allow the user to visualize data in numerous different ways. It concludes with a short wrap-up for the book. Development Environments In this book, you’ll need to use the command line only minimally for installing software. All installation instructions will be clearly written out, so you won’t need to learn any additional command line syntax. Rather than using the command line for development, I believe strongly in using an interactive development environment (IDE). An IDE handles many of the details of the underlying operating system for you, and it allows you to write, edit, and run your code using a single program. IDEs are typically cross-platform, allowing programmers to easily move from a Mac to a Windows computer or vice versa. The short example programs in the book can be run in the IDLE development environment that is installed when you install Python. IDLE is very simple to use and works well for programs that can be written in a single file. When we get into more complicated programs that use multiple Python files, I encourage you to use a more sophisticated environment instead; I use the JetBrains PyCharm development environment, which handles multiple-file projects more easily. The Community Edition is available for free from https://www.jetbrains.com/, and I highly recommend it. PyCharm also has a fully integrated debugger that can be extremely useful when writing larger programs. For more information on how to use the debugger, please see my YouTube video “Debugging Python 3 with PyCharm” at https://www.youtube.com/watch?v=cxAOSQQwDJ4&t=43s/. Widgets and Example Games The book introduces and makes available two Python packages: pygwidgets and pyghelpers. Using these packages, you should be able to build full GUI programs—but more importantly, you should gain an
- 32. understanding of how each of the widgets is coded as a class and used as an object. Incorporating various widgets, the example games in the book start out relatively simple and get progressively more complicated. Chapter 16 walks you through the development and implementation of a full-featured video game, complete with a high-scores table that is saved to a file. By the end of this book, you should be able to code your own games— card games, or video games in the style of Pong, Hangman, Breakout, Space Invaders, and so on. Object-oriented programming gives you the ability to write programs that can easily display and control multiple items of the same type, which is often required when building user interfaces and is frequently necessary in game play. Object-oriented programming is a general style that can be used in all aspects of programming, well beyond the game examples I use to demonstrate OOP techniques here. I hope you find this approach to learning OOP enjoyable. Let’s get started!
- 33. PART I INTRODUCING OBJECT-ORIENTED PROGRAMMING This part of the book introduces you to object- oriented programming. We’ll discuss problems inherent in procedural code, then see how object- oriented programming addresses those concerns. Thinking in objects (with state and behavior) will give you a new perspective about how to write code. Chapter 1 provides a review of procedural Python. I start by presenting a text-based card game named Higher or Lower, then work through a few progressively more complex implementations of a bank account in Python to help you better understand common problems with coding in a procedural style. Chapter 2 shows how we might represent real-world objects in Python using classes. We’ll write a program to simulate a light switch, modify it to include dimming capabilities, then move on to a more complicated TV remote simulation. Chapter 3 gives you two different ways to think about what is going on behind the scenes when you create objects in Python. Chapter 4 then demonstrates a standard way to handle multiple objects of the same type (for example, consider a simple game like checkers where you have to keep track of many similar game pieces). We’ll expand the bank account programs from Chapter 1, and explore how to handle errors.
- 34. 1 PROCEDURAL PYTHON EXAMPLES Introductory courses and books typically teach software development using the procedural programming style, which involves splitting a program into a number of functions (also known as procedures or subroutines). You pass data into functions, each of which performs one or more computations and, typically, passes back results. This book is about a different paradigm of programming known as object-oriented programming (OOP) that allows programmers to think differently about how to build software. Object- oriented programming gives programmers a way to combine code and data together into cohesive units, thereby avoiding some complications inherent in procedural programming. In this chapter, I’ll review a number of concepts in basic Python by building two small programs that incorporate various Python constructs. The first will be a small card game called Higher or Lower; the second will
- 35. be a simulation of a bank, performing operations on one, two, and multiple accounts. Both will be built using procedural programming—that is, using the standard techniques of data and functions. Later, I’ll rewrite these programs using OOP techniques. The purpose of this chapter is to demonstrate some key problems inherent in procedural programming. With that understanding, the chapters that follow will explain how OOP solves those problems. Higher or Lower Card Game My first example is a simple card game called Higher or Lower. In this game, eight cards are randomly chosen from a deck. The first card is shown face up. The game asks the player to predict whether the next card in the selection will have a higher or lower value than the currently showing card. For example, say the card that’s shown is a 3. The player chooses “higher,” and the next card is shown. If that card has a higher value, the player is correct. In this example, if the player had chosen “lower,” they would have been incorrect. If the player guesses correctly, they get 20 points. If they choose incorrectly, they lose 15 points. If the next card to be turned over has the same value as the previous card, the player is incorrect. Representing the Data The program needs to represent a deck of 52 cards, which I’ll build as a list. Each of the 52 elements in the list will be a dictionary (a set of key/value pairs). To represent any card, each dictionary will contain three key/value pairs: 'rank', 'suit', and 'value'. The rank is the name of the card (Ace, 2, 3, … 10, Jack, Queen, King), but the value is an integer used for comparing cards (1, 2, 3, … 10, 11, 12, 13). For example, the Jack of Clubs would be represented as the following dictionary: {'rank': 'Jack', 'suit': 'Clubs', 'value': 11} Before the player plays a round, the list representing the deck is created and shuffled to randomize the order of the cards. I have no graphical
- 36. representation of the cards, so each time the user chooses “higher” or “lower,” the program gets a card dictionary from the deck and prints the rank and the suit for the user. The program then compares the value of the new card to that of the previous card and gives feedback based on the correctness of the user’s answer. Implementation Listing 1-1 shows the code of the Higher or Lower game. NOTE As a reminder, the code associated with all the major listings in this book is available for download at https://www.nostarch.com/object- oriented-python/ and https://github.com/IrvKalb/Object-Oriented- Python-Code/. You can either download and run the code or type it in yourself. File: HigherOrLowerProcedural.py # HigherOrLower import random # Card constants SUIT_TUPLE = ('Spades', 'Hearts', 'Clubs', 'Diamonds') RANK_TUPLE = ('Ace', '2', '3', '4', '5', '6', '7', '8', '9', '10', 'Jack', 'Queen', 'King') NCARDS = 8 # Pass in a deck and this function returns a random card from the deck def getCard(deckListIn): thisCard = deckListIn.pop() # pop one off the top of the deck and return return thisCard # Pass in a deck and this function returns a shuffled copy of the deck def shuffle(deckListIn):
- 37. deckListOut = deckListIn.copy() # make a copy of the starting deck random.shuffle(deckListOut) return deckListOut # Main code print('Welcome to Higher or Lower.') print('You have to choose whether the next card to be shown will be higher or lower than the current card.') print('Getting it right adds 20 points; get it wrong and you lose 15 points.') print('You have 50 points to start.') print() startingDeckList = [] 1 for suit in SUIT_TUPLE: for thisValue, rank in enumerate(RANK_TUPLE): cardDict = {'rank':rank, 'suit':suit, 'value':thisValue + 1} startingDeckList.append(cardDict) score = 50 while True: # play multiple games print() gameDeckList = shuffle(startingDeckList) 2 currentCardDict = getCard(gameDeckList) currentCardRank = currentCardDict['rank'] currentCardValue = currentCardDict['value'] currentCardSuit = currentCardDict['suit'] print('Starting card is:', currentCardRank + ' of ' + currentCardSuit) print() 3 for cardNumber in range(0, NCARDS): # play one game of this many cards answer = input('Will the next card be higher or lower than the ' + currentCardRank + ' of ' + currentCardSuit + '? (enter h or l): ') answer = answer.casefold() # force lowercase 4 nextCardDict = getCard(gameDeckList) nextCardRank = nextCardDict['rank'] nextCardSuit = nextCardDict['suit'] nextCardValue = nextCardDict['value']
- 38. print('Next card is:', nextCardRank + ' of ' + nextCardSuit) 5 if answer == 'h': if nextCardValue > currentCardValue: print('You got it right, it was higher') score = score + 20 else: print('Sorry, it was not higher') score = score - 15 elif answer == 'l': if nextCardValue < currentCardValue: score = score + 20 print('You got it right, it was lower') else: score = score - 15 print('Sorry, it was not lower') print('Your score is:', score) print() currentCardRank = nextCardRank currentCardValue = nextCardValue # don't need current suit 6 goAgain = input('To play again, press ENTER, or "q" to quit: ') if goAgain == 'q': break print('OK bye') Listing 1-1: A Higher or Lower game using procedural Python The program starts by creating a deck as a list 1. Each card is a dictionary made up of a rank, a suit, and a value. For each round of the game, I retrieve the first card from the deck and save the components in variables 2. For the next seven cards, the user is asked to predict whether the next card will be higher or lower than the most recently showing card 3. The next card is retrieved from the deck, and its components are saved in a second set of variables 4. The game compares the user’s answer to the card drawn and gives the user feedback and points based on the outcome 5. When the
- 39. user has made predictions for all seven cards in the selection, we ask if they want to play again 6. This program demonstrates many elements of programming in general and Python in particular: variables, assignment statements, functions and function calls, if/else statements, print statements, while loops, lists, strings, and dictionaries. This book will assume you're already familiar with everything shown in this example. If there is anything in this program that is unfamiliar or not clear to you, it would probably be worth your time to review the appropriate material before moving on. Reusable Code Since this is a playing card–based game, the code obviously creates and manipulates a simulated deck of cards. If we wanted to write another card- based game, it would be great to be able to reuse the code for the deck and cards. In a procedural program, it can often be difficult to identify all the pieces of code associated with one portion of the program, such as the deck and cards in this example. In Listing 1-1, the code for the deck consists of two tuple constants, two functions, some main code to build a global list that represents the starting deck of 52 cards, and another global list that represents the deck that is used while the game is being played. Further, notice that even in a small program like this, the data and the code that manipulates the data might not be closely grouped together. Therefore, reusing the deck and card code in another program is not that easy or straightforward. In Chapter 12, we will revisit this program and show how an OOP solution makes reusing code like this much easier. Bank Account Simulations In this second example of procedural coding, I’ll present a number of variations of a program that simulates running a bank. In each new version of the program, I’ll add more functionality. Note that these programs are not production-ready; invalid user entries or misuse will lead to errors. The
- 40. intent is to have you focus on how the code interacts with the data associated with one or more bank accounts. To start, consider what operations a client would want to do with a bank account and what data would be needed to represent an account. Analysis of Required Operations and Data A list of operations a person would want to do with a bank account would include: Create (an account) Deposit Withdraw Check balance Next, here is a minimal list of the data we would need to represent a bank account: Customer name Password Balance Notice that all the operations are action words (verbs) and all the data items are things (nouns). A real bank account would certainly be capable of many more operations and would contain additional pieces of data (such as the account holder’s address, phone number, and Social Security number), but to keep the discussion clear, I’ll start with just these four actions and three pieces of data. Further, to keep things simple and focused, I’ll make all amounts an integer number of dollars. I should also point out that in a real bank application, passwords would not be kept in cleartext (unencrypted) as it is in these examples. Implementation 1—Single Account Without Functions In the starting version in Listing 1-2, there is only a single account. File: Bank1_OneAccount.py
- 41. # Non-OOP # Bank Version 1 # Single account 1 accountName = 'Joe' accountBalance = 100 accountPassword = 'soup' while True: 2 print() print('Press b to get the balance') print('Press d to make a deposit') print('Press w to make a withdrawal') print('Press s to show the account') print('Press q to quit') print() action = input('What do you want to do? ') action = action.lower() # force lowercase action = action[0] # just use first letter print() if action == 'b': print('Get Balance:') userPassword = input('Please enter the password: ') if userPassword != accountPassword: print('Incorrect password') else: print('Your balance is:', accountBalance) elif action == 'd': print('Deposit:') userDepositAmount = input('Please enter amount to deposit: ') userDepositAmount = int(userDepositAmount) userPassword = input('Please enter the password: ') if userDepositAmount < 0: print('You cannot deposit a negative amount!') elif userPassword != accountPassword: print('Incorrect password') else: # OK accountBalance = accountBalance + userDepositAmount
- 42. print('Your new balance is:', accountBalance) elif action == 's': # show print('Show:') print(' Name', accountName) print(' Balance:', accountBalance) print(' Password:', accountPassword) print() elif action == 'q': break elif action == 'w': print('Withdraw:') userWithdrawAmount = input('Please enter the amount to withdraw: ') userWithdrawAmount = int(userWithdrawAmount) userPassword = input('Please enter the password: ') if userWithdrawAmount < 0: print('You cannot withdraw a negative amount') elif userPassword != accountPassword: print('Incorrect password for this account') elif userWithdrawAmount > accountBalance: print('You cannot withdraw more than you have in your account') else: #OK accountBalance = accountBalance - userWithdrawAmount print('Your new balance is:', accountBalance) print('Done') Listing 1-2: Bank simulation for a single account The program starts off by initializing three variables to represent the data of one account 1. Then it displays a menu that allows a choice of operations 2. The main code of the program acts directly on the global account variables.
- 43. In this example, all the actions are at the main level; there are no functions in the code. The program works fine, but it may seem a little long. A typical approach to make longer programs clearer is to move related code into functions and make calls to those functions. We’ll explore that in the next implementation of the banking program. Implementation 2—Single Account with Functions In the version of the program in Listing 1-3, the code is broken up into separate functions, one for each action. Again, this simulation is for a single account. File: Bank2_OneAccountWithFunctions.py # Non-OOP # Bank 2 # Single account accountName = '' accountBalance = 0 accountPassword = '' 1 def newAccount(name, balance, password): global accountName, accountBalance, accountPassword accountName = name accountBalance = balance accountPassword = password def show(): global accountName, accountBalance, accountPassword print(' Name', accountName) print(' Balance:', accountBalance) print(' Password:', accountPassword) print() 2 def getBalance(password): global accountName, accountBalance, accountPassword if password != accountPassword: print('Incorrect password') return None return accountBalance 3 def deposit(amountToDeposit, password):
- 44. global accountName, accountBalance, accountPassword if amountToDeposit < 0: print('You cannot deposit a negative amount!') return None if password != accountPassword: print('Incorrect password') return None accountBalance = accountBalance + amountToDeposit return accountBalance 4 def withdraw(amountToWithdraw, password): 5 global accountName, accountBalance, accountPassword if amountToWithdraw < 0: print('You cannot withdraw a negative amount') return None if password != accountPassword: print('Incorrect password for this account') return None if amountToWithdraw > accountBalance: print('You cannot withdraw more than you have in your account') return None 6 accountBalance = accountBalance - amountToWithdraw return accountBalance newAccount("Joe", 100, 'soup') # create an account while True: print() print('Press b to get the balance') print('Press d to make a deposit') print('Press w to make a withdrawal') print('Press s to show the account') print('Press q to quit') print() action = input('What do you want to do? ') action = action.lower() # force lowercase action = action[0] # just use first letter print() if action == 'b':
- 45. Other documents randomly have different content
- 46. astronomers, who, in the plain of Sennaar, measured two degrees of its circumference. The victorious arms of the Saracens carried into Spain the learning, as well as the gallantry, of the East; and along with it, the tables of Almamon, and the Arabian translations of Ptolemy and Aristotle; and thus Europe received a second time, from Babylon, the rudiments of the science of the heavens. The writings of Ptolemy were translated from Arabic into Latin; and the Peripatetic philosophy was studied in Averroes and Avicenna with as much eagerness and as much submission to its doctrines in the West, as it had been in the East. The doctrine of the Solid Spheres had, originally, been invented, in order to give a physical account of the revolutions of the heavenly bodies, according to the system of Concentric Circles, to which that doctrine was very easily accommodated. Those mathematicians who invented the doctrine of Eccentric Circles and Epicycles, contented themselves with showing, how, by supposing the heavenly bodies to revolve in such orbits, the phenomena might be connected together, 355 and some sort of uniformity and coherence be bestowed upon their real motions. The physical causes of those motions they left to the consideration of the philosophers; though, as appears from some passages of Ptolemy, they had some general apprehension, that they were to be explained by a like hypothesis. But, though the system of Hipparchus was adopted by all astronomers and mathematicians, it never was received, as we have already observed, by any one sect of philosophers among the ancients. No attempt, therefore, seems to have been made amongst them, to accommodate to it any such hypothesis.
- 47. The schoolmen, who received, at once, from the Arabians, the philosophy of Aristotle, and the astronomy of Hipparchus, were necessarily obliged to reconcile them to one another, and to connect together the revolutions of the Eccentric Circles and Epicycles of the one, by the solid Spheres of the other. Many different attempts of this kind were made by many different philosophers: but, of them all, that of Purbach, in the fifteenth century, was the happiest and the most esteemed. Though his hypothesis is the simplest of any of them, it would be in vain to describe it without a scheme; neither is it easily intelligible with one; for, if the system of Eccentric Circles and Epicycles was before too perplexed and intricate for the imagination to rest in it with complete tranquillity and satisfaction, it became much more so, when this addition had been made to it. The world, justly indeed, applauded the ingenuity of that philosopher, who could unite, so happily, two such seemingly inconsistent systems. His labours, however, seem rather to have increased than to have diminished the causes of that dissatisfaction, which the learned soon began to feel with the system of Ptolemy. He, as well as all those who had worked upon the same plan before, by rendering this account of things more complex, rendered it more embarrassing than it had been before. Neither was the complexness of this system the sole cause of the dissatisfaction, which the world in general began, soon after the days of Purbach, to express for it. The tables of Ptolemy having, upon account of the inaccuracy of the observations on which they were founded, become altogether wide of the real situation of the heavenly bodies, those of Almamon, in the ninth century, were, upon the same hypothesis, composed to correct their deviations. These again, a few ages afterwards, became, for the same reason, equally useless. In the thirteenth century, Alphonsus, the philosophical King
- 48. of Castile, found it necessary to give orders for the composition of those tables, which bear his name. It is he, who is so well known for the whimsical impiety of using to say, that, had he been consulted at the creation of the universe, he could have given good advice; an apophthegm which is supposed to have proceeded from his dislike to the intricate system of Ptolemy. In the fifteenth century, the deviation of the Alphonsine tables began to be as sensible, as those of Ptolemy and 356 Almamon had been before. It appeared evident, therefore, that, though the system of Ptolemy might, in the main, be true, certain corrections were necessary to be made in it before it could be brought to correspond with exact precision to the phenomena. For the revolution of his Eccentric Circles and Epicycles, supposing them to exist, could not, it was evident, be precisely such as he represented them; since the revolutions of the heavenly bodies deviated, in a short time, so widely from what the most exact calculations, that were founded upon his hypothesis, represented them. It had plainly, therefore, become necessary to correct, by more accurate observations, both the velocities and directions of all the wheels and circles of which his hypothesis is composed. This, accordingly, was begun by Purbach, and carried on by Regiomontanus, the disciple, the continuator, and the perfecter of the system of Purbach; and one, whose untimely death, amidst innumerable projects for the recovery of old, and the invention and advancement of new sciences, is, even at this day, to be regretted. When you have convinced the world, that an established system ought to be corrected, it is not very difficult to persuade them that it should be destroyed. Not long, therefore, after the death of Regiomontanus, Copernicus began to meditate a new system, which should connect together the new appearances, in a more simple as well as a more accurate manner, than that of Ptolemy.
- 49. The confusion, in which the old hypothesis represented the motions of the heavenly bodies, was, he tells us, what first suggested to him the design of forming a new system, that these, the noblest works of nature, might no longer appear devoid of that harmony and proportion which discover themselves in her meanest productions. What most of all dissatisfied him, was the notion of the Equalizing Circle, which, by representing the revolutions of the Celestial Spheres, as equable only, when surveyed from a point that was different from their centres, introduced a real inequality into their motions; contrary to that most natural, and indeed fundamental idea, with which all the authors of astronomical systems, Plato, Eudoxus, Aristotle, even Hipparchus and Ptolemy themselves, had hitherto set out, that the real motions of such beautiful and divine objects must necessarily be perfectly regular, and go on, in a manner, as agreeable to the imagination, as the objects themselves are to the senses. He began to consider, therefore, whether, by supposing the heavenly bodies to be arranged in a different order from that in which Aristotle and Hipparchus has placed them, this so much sought for uniformity might not be bestowed upon their motions. To discover this arrangement, he examined all the obscure traditions delivered down to us, concerning every other hypothesis which the ancients had invented, for the same purpose. He found, in Plutarch, that some old Pythagoreans had represented the Earth as revolving in the centre of the universe, like a wheel round its own axis; and that 357 others, of the same sect, had removed it from the centre, and represented it as revolving in the Ecliptic like a star round the central fire. By this central fire, he supposed they meant the Sun; and though in this he was very widely mistaken, it was, it seems, upon this interpretation, that he began to consider how such an hypothesis might be made to correspond to the appearances. The
- 50. supposed authority of these old philosophers, if it did not originally suggest to him his system, seems, at least, to have confirmed him in an opinion, which, it is not improbable, that he had beforehand other reasons for embracing, notwithstanding what he himself would affirm to the contrary. It then occurred to him, that, if the Earth was supposed to revolve every day round its axis, from west to east, all the heavenly bodies would appear to revolve, in a contrary direction, from east to west. The diurnal revolution of the heavens, upon this hypothesis, might be only apparent; the firmament, which has no other sensible motion, might be perfectly at rest; while the Sun, the Moon, and the Five Planets, might have no other movement beside that eastward revolution, which is peculiar to themselves. That, by supposing the Earth to revolve with the Planets, round the Sun, in an orbit, which comprehended within it the orbits of Venus and Mercury, but was comprehended within those of Mars, Jupiter, and Saturn, he could, without the embarrassment of Epicycles, connect together the apparent annual revolutions of the Sun, and the direct, retrograde, and stationary appearances of the Planets: that while the Earth really revolved round the Sun on one side of the heavens, the Sun would appear to revolve round the Earth on the other; that while she really advanced in her annual course, he would appear to advance eastward in that movement which is peculiar to himself. That, by supposing the axis of the Earth to be always parallel to itself, not to be quite perpendicular, but somewhat inclined to the plane of her orbit, and consequently to present to the Sun, the one pole when on the one side of him, and the other when on the other, he would account for the obliquity of the Ecliptic; the Sun’s seemingly alternate progression from north to south, and from south to north,
- 51. the consequent change of the seasons, and different lengths of the days and nights in the different seasons. If this new hypothesis thus connected together all these appearances as happily as that of Ptolemy, there were others which it connected together much better. The three superior Planets, when nearly in conjunction with the Sun, appear always at the greatest distance from the Earth, are smallest, and least sensible to the eye, and seem to revolve forward in their direct motion with the greatest rapidity. On the contrary, when in opposition to the Sun, that is, when in their meridian about midnight, they appear nearest the Earth, are largest, and most sensible to the eye, and seem to revolve backwards in their retrograde motion. To explain these appearances, the system of Ptolemy supposed 358 each of these Planets to be at the upper part of their several Epicycles, in the one case; and at the lower, in the other. But it afforded no satisfactory principle of connection, which could lead the mind easily to conceive how the Epicycles of those Planets, whose spheres were so distant from the sphere of the Sun, should thus, if one may say so, keep time to his motion. The system of Copernicus afforded this easily, and like a more simple machine, without the assistance of Epicycles, connected together, by fewer movements, the complex appearances of the heavens. When the superior Planets appear nearly in conjunction with the Sun, they are then in the side of their orbits, which is almost opposite to, and most distant from the Earth, and therefore appear smallest, and least sensible to the eye. But, as they then revolve in a direction which is almost contrary to that of the Earth, they appear to advance forward with double velocity; as a ship, that sails in a contrary direction to another, appears from that other, to sail both with its own velocity, and the velocity of that from which it is seen. On the contrary, when those Planets are in opposition to the
- 52. Sun, they are on the same side of the Sun with the Earth, are nearest it, most sensible to the eye, and revolve in the same direction with it; but, as their revolutions round the Sun are slower than that of the Earth, they are necessarily left behind by it, and therefore seem to revolve backwards; as a ship which sails slower than another, though it sails in the same direction, appears from that other to sail backwards. After the same manner, by the same annual revolution of the Earth, he connected together the direct and retrograde motions of the two inferior Planets, as well as the stationary appearances of all the Five. There are some other particular phenomena of the two inferior Planets, which correspond still better to this system, and still worse to that of Ptolemy. Venus and Mercury seem to attend constantly upon the motion of the Sun, appearing, sometimes on the one side, and sometimes on the other, of that great luminary; Mercury being almost always buried in his rays, and Venus never receding above forty-eight degrees from him, contrary to what is observed in the other three Planets, which are often seen in the opposite side of the heavens, at the greatest possible distance from the Sun. The system of Ptolemy accounted for this, by supposing that the centres of the Epicycles of these two Planets were always in the same line with those of the Sun and the Earth; that they appeared therefore in conjunction with the Sun, when either in the upper or lower part of their Epicycles, and at the greatest distance from him, when in the sides of them. It assigned, however, no reason why the Epicycles of these two Planets should observe so different a rule from that which takes place in those of the other three, nor for the enormous Epicycle of Venus, whose sides must have been forty-eight degrees distant from the Sun, while its centre was in conjunction with him, and whose diameter must have covered 359 more than a quadrant of
- 53. the Great Circle. But how easily all these appearances coincide with the hypothesis, which represents those two inferior Planets revolving round the Sun in orbits comprehended within the orbit of the Earth, is too obvious to require an explanation. Thus far did this new account of things render the appearances of the heavens more completely coherent than had been done by any of the former systems. It did this, too, by a more simple and intelligible, as well as more beautiful machinery. It represented the Sun, the great enlightener of the universe, whose body was alone larger than all the Planets taken together, as established immovable in the centre, shedding light and heat on all the worlds that circulated around him in one uniform direction, but in longer or shorter periods, according to their different distances. It took away the diurnal revolution of the firmament, whose rapidity, upon the old hypothesis, was beyond what even thought could conceive. It not only delivered the imagination from the embarrassment of Epicycles, but from the difficulty of conceiving these two opposite motions going on at the same time, which the system of Ptolemy and Aristotle bestowed upon all the Planets; I mean, their diurnal westward, and periodical eastward revolutions. The Earth’s revolution round its own axis took away the necessity for supposing the first, and the second was easily conceived when by itself. The Five Planets, which seem, upon all other systems, to be objects of a species by themselves, unlike to every thing to which the imagination has been accustomed, when supposed to revolve along with the Earth round the Sun, were naturally apprehended to be objects of the same kind with the Earth, habitable, opaque, and enlightened only by the rays of the Sun. And thus this hypothesis, by classing them in the same species of things, with an object that is of all others the most familiar to us, took off that wonder and that
- 54. uncertainty which the strangeness and singularity of their appearance had excited; and thus far, too, better answered the great end of Philosophy. Neither did the beauty and simplicity of this system alone recommend it to the imagination; the novelty and unexpectedness of that view of nature, which it opened to the fancy, excited more wonder and surprise than the strangest of those appearances, which it had been invented to render natural and familiar, and these sentiments still more endeared it. For, though it is the end of Philosophy, to allay that wonder, which either the unusual or seemingly disjointed appearances of nature excite, yet she never triumphs so much, as when, in order to connect together a few, in themselves, perhaps, inconsiderable objects, she has, if I may say so, created another constitution of things, more natural, indeed, and such as the imagination can more easily attend to, but more new, more contrary to common opinion and expectation, than any of those appearances themselves. As, in the instance before us, in order to connect together some seeming irregularities in the motions of 360 the Planets, the most inconsiderable objects in the heavens, and of which the greater part of mankind have no occasion to take any notice during the whole course of their lives, she has, to talk in the hyperbolical language of Tycho Brahe, moved the Earth from its foundations, stopped the revolution of the Firmament, made the Sun stand still, and subverted the whole order of the Universe. Such were the advantages of this new hypothesis, as they appeared to its author, when he first invented it. But, though that love of paradox, so natural to the learned, and that pleasure, which they are so apt to take in exciting, by the novelties of their supposed discoveries, the amazement of mankind, may, notwithstanding what
- 55. one of his disciples tells us to the contrary, have had its weight in prompting Copernicus to adopt this system; yet, when he had completed his Treatise of Revolutions, and began coolly to consider what a strange doctrine he was about to offer to the world, he so much dreaded the prejudice of mankind against it, that, by a species of continence, of all others the most difficult to a philosopher, he detained it in his closet for thirty years together. At last, in the extremity of old age, he allowed it to be extorted from him, but he died as soon as it was printed, and before it was published to the world. When it appeared in the world, it was almost universally disapproved of, by the learned as well as by the ignorant. The natural prejudices of sense, confirmed by education, prevailed too much with both, to allow them to give it a fair examination. A few disciples only, whom he himself had instructed in his doctrine, received it with esteem and admiration. One of them, Reinholdus, formed, upon this hypothesis, larger and more accurate astronomical tables, than what accompanied the Treatise of Revolutions, in which Copernicus had been guilty of some errors in calculation. It soon appeared, that these Prutenic Tables, as they were called, corresponded more exactly with the heavens, than the Tables of Alphonsus. This ought naturally to have formed a prejudice in favour of the diligence and accuracy of Copernicus in observing the heavens. But it ought to have formed none in favour of his hypothesis; since the same observations, and the result of the same calculations, might have been accommodated to the system of Ptolemy, without making any greater alteration in that system than what Ptolemy had foreseen, and had even foretold should be made. It formed, however, a prejudice in favour of both, and the learned began to examine, with some attention, an hypothesis which
- 56. afforded the easiest methods of calculation, and upon which the most exact predictions had been made. The superior degree of coherence, which it bestowed upon the celestial appearances, the simplicity and uniformity which it introduced into the real directions and velocities of the Planets, soon disposed many astronomers, first to favour, and at last to embrace a system, which thus connected together so happily, 361 the most disjointed of those objects that chiefly occupied their thoughts. Nor can any thing more evidently demonstrate, how easily the learned give up the evidence of their senses to preserve the coherence of the ideas of their imagination, than the readiness with which this, the most violent paradox in all philosophy, was adopted by many ingenious astronomers, notwithstanding its inconsistency with every system of physics then known in the world, and notwithstanding the great number of other more real objections, to which, as Copernicus left it, this account of things was most justly exposed. It was adopted, however, nor can this be wondered at, by astronomers only. The learned in all other sciences, continued to regard it with the same contempt as the vulgar. Even astronomers were divided about its merit; and many of them rejected a doctrine, which not only contradicted the established system of Natural Philosophy, but which, considered astronomically only, seemed, to them, to labour under several difficulties. Some of the objections against the motion of the Earth, that were drawn from the prejudices of sense, the patrons of this system, indeed, easily enough got over. They represented, that the Earth might really be in motion, though, to its inhabitants, it seemed to be at rest; and that the Sun and Fixed Stars might really be at rest, though from the Earth they seemed to be in motion; in the same
- 57. manner as a ship, which sails through a smooth sea, seems to those who are in it, to be at rest, though really in motion; while the objects which she passes along, seem to be in motion, though really at rest. But there were some other objections, which, though grounded upon the same natural prejudices, they found it more difficult to get over. The earth had always presented itself to the senses, not only as at rest, but as inert, ponderous, and even averse to motion. The imagination had always been accustomed to conceive it as such, and suffered the greatest violence, when obliged to pursue, and attend it, in that rapid motion which the system of Copernicus bestowed upon it. To enforce their objection, the adversaries of this hypothesis were at pains to calculate the extreme rapidity of this motion. They represented, that the circumference of the Earth had been computed to be above twenty-thousand miles: if the Earth, therefore, was supposed to revolve every day round its axis, every point of it near the equator would pass over above twenty-three thousand miles in a day; and consequently, near a thousand miles in an hour, and about sixteen miles in a minute; a motion more rapid than that of a cannon ball, or even than the swifter progress of sound. The rapidity of its periodical revolution was yet more violent than that of its diurnal rotation. How, therefore, could the imagination ever conceive so ponderous a body to be naturally endowed with so dreadful a movement? The Peripatetic Philosophy, the only philosophy then known in the world, still further confirmed 362 this prejudice. That philosophy, by a very natural, though, perhaps, groundless distinction, divided all motion into Natural and Violent. Natural motion was that which flowed from an innate tendency in the body, as when a stone fell downwards: Violent motion, that which arose from external force, and which was, in some measure, contrary to
- 58. the natural tendency of the body, as when a stone was thrown upwards, or horizontally. No violent motion could be lasting; for, being constantly weakened by the natural tendency of the body, it would soon be destroyed. The natural motion of the Earth, as was evident in all its parts, was downwards, in a straight line to the centre; as that of fire and air was upwards, in a straight line from the centre. It was the heavens only that revolved naturally in a circle. Neither, therefore, the supposed revolution of the Earth round its own centre, nor that round the Sun, could be natural motions; they must therefore be violent, and consequently could be of no long continuance. It was in vain that Copernicus replied, that gravity was, probably, nothing else besides a tendency in the different parts of the same Planet, to unite themselves to one another; that this tendency took place, probably, in the parts of the other Planets, as well as in those of the Earth; that it could very well be united with a circular motion; that it might be equally natural to the whole body of the Planet, and to every part of it; that his adversaries themselves allowed, that a circular motion was natural to the heavens, whose diurnal revolution was infinitely more rapid than even that motion which he had bestowed upon the Earth; that though a like motion was natural to the Earth, it would still appear to be at rest to its inhabitants, and all the parts of it to tend in a straight line to the centre, in the same manner as at present. But this answer, how satisfactory soever it may appear to be now, neither did nor could appear to be satisfactory then. By admitting the distinction betwixt natural and violent motions, it was founded upon the same ignorance of mechanical principles with the objection. The systems of Aristotle and Hipparchus supposed, indeed, the diurnal motion of the heavenly bodies to be infinitely more rapid than even that dreadful movement which Copernicus bestowed upon the Earth. But
- 59. they supposed, at the same time, that those bodies were objects of a quite different species, from any we are acquainted with, near the surface of the Earth, and to which, therefore, it was less difficult to conceive that any sort of motion might be natural. Those objects, besides, had never presented themselves to the senses, as moving otherwise, or with less rapidity, than these systems represented them. The imagination, therefore, could feel no difficulty in following a representation which the senses had rendered quite familiar to it. But when the Planets came to be regarded as so many Earths, the case was quite altered. The imagination had been accustomed to conceive such objects as tending rather to rest than motion; and this idea of their natural 363 inertness, encumbered, if one may say so, and clogged its flight whenever it endeavoured to pursue them in their periodical courses, and to conceive them as continually rushing through the celestial spaces, with such violent and unremitting rapidity. Nor were the first followers of Copernicus more fortunate in their answers to some other objections, which were founded indeed in the same ignorance of the laws of motion, but which, at the same time, were necessarily connected with that way of conceiving things, which then prevailed universally in the learned world. If the earth, it was said, revolved so rapidly from west to east, a perpetual wind would set in from east to west, more violent than what blows in the greatest hurricanes; a stone, thrown westwards would fly to a much greater distance than one thrown with the same force eastwards; as what moved in a direction, contrary to the motion of the Earth, would necessarily pass over a greater portion of its surface, than what, with the same velocity, moved along with it. A ball, it was said, dropped from the mast of a ship under sail, does
- 60. not fall precisely at the foot of the mast, but behind it; and in the same manner, a stone dropped from a high tower would not, upon the supposition of the Earth’s motion, fall precisely at the bottom of the tower, but west of it, the Earth being, in the mean time, carried away eastward from below it. It is amusing to observe, by what, subtile and metaphysical evasions the followers of Copernicus endeavoured to elude this objection, which before the doctrine of the Composition of Motion had been explained by Galileo, was altogether unanswerable. They allowed, that a ball dropped from the mast of a ship under sail would not fall at the foot of the mast, but behind it; because the ball, they said, was no part of the ship, and because the motion of the ship was natural neither to itself nor to the ball. But the stone was a part of the earth, and the diurnal and annual revolutions of the Earth were natural to the whole, and to every part of it, and therefore to the stone. The stone, therefore, having naturally the same motion with the Earth, fell precisely at the bottom of the tower. But this answer could not satisfy the imagination, which still found it difficult to conceive how these motions could be natural to the earth; or how a body, which had always presented itself to the senses as inert, ponderous, and averse to motion, should naturally be continually wheeling about both its own axis and the Sun, with such violent rapidity. It was, besides, argued by Tycho Brahe, upon the principles of the same philosophy which had afforded both the objection and the answer, that even upon the supposition, that any such motion was natural to the whole body of the Earth, yet the stone, which was separated from it, could no longer be actuated by that motion. The limb, which is cut off from an animal, loses those animal motions which were natural to the whole. The branch, which is cut off from the trunk, loses that vegetative 364 motion which is natural to the whole tree. Even the
- 61. metals, minerals, and stones, which were dug out from the bosom of the Earth, lose those motions which occasioned their production and increase, and which were natural to them in their original state. Though the diurnal and annual motion of the Earth, therefore, had been natural to them while they were contained in its bosom, it could no longer be so when they were separated from it. Tycho Brahe, the great restorer of the science of the heavens, who had spent his life, and wasted his fortune upon the advancement of Astronomy, whose observations were both more numerous and more accurate than those of all the astronomers who had gone before him, was himself so much affected by the force of this objection, that, though he had never mentioned the system of Copernicus without some note of high admiration he had conceived for its author, he could never himself be induced to embrace it; yet all his astronomical observations tended to confirm it. They demonstrated, that Venus and Mercury were sometimes above, and sometimes below the Sun; and that, consequently, the Sun, and not the Earth, was the centre of their periodical revolutions. They showed, that Mars, when in his meridian at midnight, was nearer to the Earth than the Earth is to the Sun; though, when in conjunction with the Sun, he was much more remote from the Earth than that luminary; a discovery which was absolutely inconsistent with the system of Ptolemy, which proved, that the Sun, and not the Earth, was the centre of the periodical revolutions of Mars, as well as of Venus and Mercury; and which demonstrated that the Earth was placed betwixt the orbits of Mars and Venus. They made the same thing probable with regard to Jupiter and Saturn; that they, too, revolved round the Sun; and that, therefore, the Sun, if not the centre of the universe, was at least, that of the planetary system. They proved that Comets were superior to the Moon, and moved through the heavens in all
- 62. possible directions; an observation incompatible with the Solid Spheres of Aristotle and Purbach, and which, therefore, overturned the physical part, at least, of the established systems of Astronomy. All these observations, joined to his aversion to the system, and perhaps, notwithstanding the generosity of his character, some little jealousy for the fame of Copernicus, suggested to Tycho the idea of a new hypothesis, in which the Earth continued to be, as in the old account, the immovable centre of the universe, round which the firmament revolved every day from east to west, and, by some secret virtue, carried the Sun, the Moon, and the Five Planets along with it, notwithstanding their immense distance, and notwithstanding that there was nothing betwixt it and them but the most fluid ether. But, although all these seven bodies thus obeyed the diurnal revolution of the Firmament, they had each of them, as in the old system, too, a 365 contrary periodical eastward revolution of their own, which made them appear to be every day, more or less, left behind by the Firmament. The Sun was the centre of the periodical revolutions of the Five Planets; the Earth, that of the Sun and Moon. The Five Planets followed the Sun in his periodical revolution round the Earth, as they did the Firmament in its diurnal rotation. The three superior Planets comprehended the Earth within the orbit in which they revolved round the Sun, and had each of them an Epicycle to connect together, in the same manner as in the system of Ptolemy, their direct, retrograde, and stationary appearances. As, notwithstanding their immense distance, they followed the Sun in his periodical revolution round the Earth, keeping always at an equal distance from him, they were necessarily brought much nearer to the Earth when in opposition to the Sun, than than when in conjunction with him. Mars, the nearest of them, when in his meridian at midnight, came within the orbit which the Sun
- 63. described round the Earth, and consequently was then nearer to the Earth than the Earth was to the Sun. The appearances of the two inferior Planets were explained, in the same manner, as in the system of Copernicus, and consequently required no Epicycle to connect them. The circles in which the Five Planets performed their periodical revolutions round the Sun, as well as those in which the Sun and Moon performed theirs round the Earth, were, as both in the old and new hypothesis, Eccentric Circles, to connect together their differently accelerated and retarded motions. Such was the system of Tycho Brahe, compounded, as is evident, out of these of Ptolemy and Copernicus; happier than that of Ptolemy, in the account which it gives of the motions of the two inferior Planets; more complex, by supposing the different revolutions of all the Five to be performed round two different centres; the diurnal round the Earth, the periodical round the Sun, but, in every respect, more complex and more incoherent than that of Copernicus. Such, however, was the difficulty that mankind felt in conceiving the motion of the Earth, that it long balanced the reputation of that otherwise more beautiful system. It may be said, that those who considered the heavens only, favoured the system of Copernicus, which connected so happily all the appearances which presented themselves there; but that those who looked upon the Earth, adopted the account of Tycho Brahe, which, leaving it at rest in the centre of the universe, did less violence to the usual habits of the imagination. The learned were, indeed, sensible of the intricacy, and of the many incoherences of that system; that it gave no account why the Sun, Moon, and Five Planets, should follow the revolution of the Firmament; or why the Five Planets, notwithstanding the immense distance of the three superior ones, should obey the periodical motion of the Sun; or why the Earth,
- 64. though placed between the orbits of Mars and Venus, should remain immovable in the centre 366 of the Firmament, and constantly resist the influence of whatever it was, which carried bodies that were so much larger than itself, and that were placed on all sides of it, periodically round the Sun. Tycho Brahe died before he had fully explained his system. His great and merited renown disposed many of the learned to believe, that, had his life been longer, he would have connected together many of these incoherences, and knew methods of adapting his system to some other appearances, with which none of his followers could connect it. The objection to the system of Copernicus, which was drawn from the nature of motion, and that was most insisted on by Tycho Brahe, was at last fully answered by Galileo; not, however, till about thirty years after the death of Tycho, and about a hundred after that of Copernicus. It was then that Galileo, by explaining the nature of the composition of motion, by showing, both from reason and experience, that a ball dropped from the mast of a ship under sail would fall precisely at the foot of the mast, and by rendering this doctrine, from a great number of other instances, quite familiar to the imagination, took off, perhaps, the principal objection which had been made to this hypothesis of the astronomers. Several other astronomical difficulties, which encumbered this account of things, were removed by the same philosopher. Copernicus, after altering the centre of the world, and making the Earth, and all the Planets revolve round the Sun, was obliged to leave the Moon to revolve round the Earth as before. But no example of any such secondary Planet having then been discovered in the heavens, there seemed still to be this irregularity remaining in the system. Galileo, who first applied telescopes to Astronomy,
- 65. discovered, by their assistance, the Satellites of Jupiter, which, revolving round that Planet, at the same time that they were carried along with it in its revolution, round either the Earth, or the Sun, made it seem less contrary to the analogy of nature, that the Moon should both revolve round the Earth, and accompany her in her revolution round the Sun. It had been objected to Copernicus, that, if Venus and Mercury revolved round the Sun in an orbit comprehended within the orbit of the Earth, they would show all the same phases with the Moon; present, sometimes their darkened, and sometimes their enlightened sides to the Earth, and sometimes part of the one, and part of the other. He answered, that they undoubtedly did all this; but that their smallness and distance hindered us from perceiving it. This very bold assertion of Copernicus was confirmed by Galileo. His telescopes rendered the phases of Venus quite sensible, and thus demonstrated, more evidently than had been done, even by the observations of Tycho Brahe, the revolutions of these two Planets round the Sun, as well as so far destroyed the system of Ptolemy. The mountains and seas, which, by the help of the same instrument, 367 he discovered, or imagined he had discovered in the Moon, rendering that Planet, in every respect, similar to the Earth, made it seem less contrary to the analogy of nature, that, as the Moon revolved round the Earth, the Earth should revolve round the Sun. The spots which, in the same manner, he discovered in the Sun, demonstrating, by their motion, the revolution of the Sun round his axis, made it seem less improbable that the Earth, a body so much smaller than the Sun, should likewise revolve round her axis in the same manner.
- 66. Succeeding telescopical observations, discovered, in each of the Five Planets, spots not unlike those which Galileo had observed in the Moon, and thereby seemed to demonstrate what Copernicus had only conjectured, that the Planets were naturally opaque, enlightened only by the rays of the Sun, habitable, diversified by seas and mountains, and, in every respect, bodies of the same kind with the earth; and thus added one other probability to this system. By discovering, too, that each of the Planets revolved round its own axis, at the same time that it was carried round either the Earth or the Sun, they made it seem quite agreeable to the analogy of nature, that the Earth, which, in every other respect, resembled the Planets, should, like them too, revolve round its own axis, and at the same time perform its periodical motion round the Sun. While, in Italy, the unfortunate Galileo was adding so many probabilities to the system of Copernicus, there was another philosopher employing himself in Germany, to ascertain, correct, and improve it; Kepler, with great genius, but without the taste, or the order and method of Galileo, possessed, like all his other countrymen, the most laborious industry, joined to that passion for discovering proportions and resemblances betwixt the different parts of nature, which, though common to all philosophers, seems, in him, to have been excessive. He had been instructed, by Mæstlinus, in the system of Copernicus; and his first curiosity was, as he tells us, to find out, why the Planets, the Earth being counted for one, were Six in number; why they were placed at such irregular distances from the Sun; and whether there was any uniform proportion betwixt their several distances, and the times employed in their periodical revolutions. Till some reason, or proportion of this kind, could be discovered, the system did not appear to him to be completely coherent. He endeavoured, first, to find it in the
- 67. proportions of numbers, and plain figures; afterwards, in those of the regular solids; and, last of all, in those of the musical divisions of the Octave. Whatever was the science which Kepler was studying, he seems constantly to have pleased himself with finding some analogy betwixt it and the system of the universe; and thus, arithmetic and music, plane and solid geometry, came all of them by turns to illustrate the doctrine of the Sphere, in the explaining of which he was, by his 368 profession, principally employed. Tycho Brahe, to whom he had presented one of his books, though he could not but disapprove of his system, was pleased, however, with his genius, and with his indefatigable diligence in making the most laborious calculations. That generous and magnificent Dane invited the obscure and indigent Kepler to come and live with him, and communicated to him, as soon as he arrived, his observations upon Mars, in the arranging and methodizing of which his disciples were at that time employed. Kepler, upon comparing them with one another, found, that the orbit of Mars was not a perfect circle; that one of its diameters was somewhat longer than the other; and that it approached to an oval, or an ellipse, which had the Sun placed in one of its foci. He found, too, that the motion of the Planet was not equable; that it was swiftest when nearest the Sun, and slowest when furthest from him; and that its velocity gradually increased, or diminished, according as it approached or receded from him. The observations of the same astronomer discovered to him, though not so evidently, that the same things were true of all the other Planets; that their orbits were elliptical, and that their motions were swiftest when nearest the Sun, and slowest when furthest from him. They showed the same things, too, of the Sun, if supposed to revolve round the Earth; and consequently of the Earth, if it also was supposed to revolve round the Sun.
- 68. That the motions of all the heavenly bodies were perfectly circular, had been the fundamental idea upon which every astronomical hypothesis, except the irregular one of the Stoics, had been built. A circle, as the degree of its curvature is every where the same, is of all curve lines the simplest and the most easily conceived. Since it was evident, therefore, that the heavenly bodies did not move in straight lines, the indolent imagination found, that it could most easily attend to their motions if they were supposed to revolve in perfect circles. It had, upon this account, determined that a circular motion was the most perfect of all motions, and that none but the most perfect motion could be worthy of such beautiful and divine objects; and it had upon this account, so often, in vain, endeavoured to adjust to the appearances, so many different systems, which all supposed them to revolve in this perfect manner. The equality of their motions was another fundamental idea, which, in the same manner, and for the same reason, was supposed by all the founders of astronomical systems. For an equal motion can be more easily attended to, than one that is continually either accelerated or retarded. All inconsistency, therefore, was declared to be unworthy those bodies which revolved in the celestial regions, and to be fit only for inferior and sublunary things. The calculations of Kepler overturned, with regard to the Planets, both these natural prejudices of the imagination; destroyed their circular orbits; and introduced into their 369 real motions, such an equality as no equalizing circle would remedy. It was, however, to render their motion perfectly equable, without even the assistance of a equalizing circle, that Copernicus, as he himself assures us, had originally invented his system. Since the calculations of Kepler, therefore, overturned what Copernicus had principally in view in establishing
- 69. his system, we cannot wonder that they should at first seem rather to embarrass than improve it. It is true, by these elliptical orbits and unequal motions, Kepler disengaged the system from the embarrassment of those small Epicycles, which Copernicus, in order to connect the seemingly accelerated and retarded movements of the Planets, with their supposed real equality, had been obliged to leave in it. For it is remarkable, that though Copernicus had delivered the orbits of the Planets from the enormous Epicycles of Hipparchus, that though in this consisted the great superiority of his system above that of the ancient astronomers, he was yet obliged, himself, to abandon, in some measure, this advantage, and to make use of some small Epicycles, to join together those seeming irregularities. His Epicycles indeed, like the irregularities for whose sake they were introduced, were but small ones, and the imaginations of his first followers seem, accordingly, either to have slurred them over altogether, or scarcely to have observed them. Neither Galileo, nor Gassendi, the two most eloquent of his defenders, take any notice of them. Nor does it seem to have been generally attended to, that there was any such thing as Epicycles in the system of Copernicus, till Kepler, in order to vindicate his own elliptical orbits, insisted, that even, according to Copernicus, the body of the Planet was to be found but at two different places in the circumference of that circle which the centre of its Epicycle described. It is true, too, that an ellipse is, of all curve lines after a circle, the simplest and most easily conceived; and it is true, besides all this, that, while Kepler took from the motion of the Planets the easiest of all proportions, that of equality, he did not leave them absolutely without one, but ascertained the rule by which their velocities
- 70. continually varied; for a genius so fond of analogies, when he had taken away one, would be sure to substitute another in its room. Notwithstanding all this, notwithstanding that his system was better supported by observations than any system had ever been before, yet, such was the attachment to the equal motions and circular orbits of the Planets, that it seems, for some time, to have been in general but little attended to by the learned, to have been altogether neglected by philosophers, and not much regarded even by astronomers. Gassendi, who began to figure in the world about the latter days of Kepler, and who was himself no mean astronomer, seems indeed to have conceived a good deal of esteem for his diligence and accuracy in accommodating the observations of Tycho Brahe to the system of 370 Copernicus. But Gassendi appears to have had no comprehension of the importance of those alterations which Kepler had made in that system, as is evident from his scarcely ever mentioning them in the whole course of his voluminous writings upon Astronomy. Des Cartes, the contemporary and rival of Gassendi, seems to have paid no attention to them at all, but to have built his Theory of the Heavens, without any regard to them. Even those astronomers, whom a serious attention had convinced of the justness of his corrections, were still so enamoured with the circular orbits and equal motion, that they endeavoured to compound his system with those ancient but natural prejudices. Thus, Ward endeavoured to show that, though the Planets moved in elliptical orbits, which had the Sun in one of their foci, and though their velocities in the elliptical line were continually varying, yet, if a ray was supposed to be extended from the centre of any one of them to the other focus, and to be carried along by the periodical motion of the Planet, it would make equal angles in equal times, and
- 71. consequently cut off equal portions of the circle of which that other focus was the centre. To one, therefore, placed in that focus, the motion of the Planet would appear to be perfectly circular and perfectly equable, in the same manner as in the Equalizing Circles of Ptolemy and Hipparchus. Thus Bouillaud, who censured this hypothesis of Ward, invented another of the same kind, infinitely more whimsical and capricious. The Planets, according to that astronomer, always revolve in circles; for that being the most perfect figure, it is impossible they should revolve in any other. No one of them, however, continues to move in any one circle, but is perpetually passing from one to another, through an infinite number of circles, in the course of each revolution; for an ellipse, said he, is an oblique section of a cone, and in a cone, betwixt the two vortices of the ellipse there is an infinite number of circles, out of the infinitely small portions of which the elliptical line is compounded. The Planet, therefore which moves in this line, is, in every point of it, moving in an infinitely small portion of a certain circle. The motion of each Planet, too, according to him, was necessarily, for the same reason, perfectly equable. An equable motion being the most perfect of all motions. It was not, however, in the elliptical line, that it was equable, but in any one of the circles that were parallel to the base of that cone, by whose section this elliptical line had been formed: for, if a ray was extended from the Planet to any one of those circles, and carried along by its periodical motion, it would cut off equal portions of that circle in equal times; another most fantastical equalising circle, supported by no other foundation besides the frivolous connection between a cone and an ellipse, and recommended by nothing but the natural passion for circular orbits and equable motions. It may be regarded as the last effort of this passion, and may serve to show the force of that principle which
- 72. could 371 thus oblige this accurate observer, and great improver of the Theory of the Heavens, to adopt so strange an hypothesis. Such was the difficulty and hesitation with which the followers of Copernicus adopted the corrections of Kepler. The rule, indeed, which Kepler ascertained for determining the gradual acceleration or retardation in the movement of the Planets, was intricate, and difficult to be comprehended; it could therefore but little facilitate the progress of the imagination in tracing those revolutions which were supposed to be conducted by it. According to that astronomer, if a straight line was drawn from the centre of each Planet to the Sun, and carried along by the periodical motion of the Planet, it would describe equal areas in equal times, though the Planet did not pass over equal spaces; and the same rule he found, took place nearly with regard to the Moon. The imagination, when acquainted with the law by which any motion is accelerated or retarded, can follow and attend to it more easily, than when at a loss, and, as it were, wandering in uncertainty with regard to the proportion which regulates its varieties; the discovery of this analogy therefore, no doubt, rendered the system of Kepler more agreeable to the natural taste of mankind: it, was, however, an analogy too difficult to be followed, or comprehended, to render it completely so. Kepler, besides this, introduced another new analogy into the system, and first discovered, that there was one uniform relation observed betwixt the distances of the Planets from the Sun, and the times employed in their periodical motions. He found, that their periodical times were greater than in proportion to their distances, and less than in proportion to the squares of those distances; but, that they were nearly as the mean proportionals betwixt their distances and the squares of their distances; or, in other words, that
- 73. the squares of their periodical times were nearly as the cubes of their distances; an analogy, which, though, like all others, it no doubt rendered the system somewhat more distinct and comprehensible, was, however, as well as the former, of too intricate a nature to facilitate very much the effort of the imagination in conceiving it. The truth of both these analogies, intricate as they were, was at last fully established by the observations of Cassini. That astronomer first discovered, that the secondary Planets of Jupiter and Saturn revolved round their primary ones, according to the same laws which Kepler had observed in the revolutions of the primary ones round the Sun, and that of the Moon round the earth; that each of them described equal areas in equal times, and that the squares of their periodic times were as the cubes of their distances. When these two last abstruse analogies, which, when Kepler at first observed them, were but little regarded, had been thus found to take place in the revolutions of the Four Satellites of Jupiter, and in those of the Five of Saturn, they were 372 now thought not only to confirm the doctrine of Kepler, but to add a new probability to the Copernican hypothesis. The observations of Cassini seem to establish it as a law of the system, that, when one body revolved round another, it described equal areas in equal times; and that, when several revolved round the same body, the squares of their periodic times were as the cubes of their distances. If the Earth and the Five Planets were supposed to revolve round the Sun, these laws, it was said, would take place universally. But if, according to the system of Ptolemy, the Sun, Moon, and Five Planets were supposed to revolve round the Earth, the periodical motions of the Sun and Moon, would, indeed, observe the first of these laws, would each of them describe equal areas in equal times; but they would not observe the second,
- 74. the squares of their periodic times would not be as the cubes of their distances: and the revolutions of the Five Planets would observe neither the one law nor the other. Or if, according to the system of Tycho Brahe, the Five Planets were supposed to revolve round the Sun, while the Sun and Moon revolved round the Earth, the revolutions of the Five Planets round the Sun, would, indeed, observe both these laws; but those of the Sun and Moon round the Earth would observe only the first of them. The analogy of nature, therefore, could be preserved completely, according to no other system but that of Copernicus, which, upon that account, must be the true one. This argument is regarded by Voltaire, and the Cardinal of Polignac, as an irrefragable demonstration; even M‘Laurin, who was more capable of judging, nay, Newton himself, seems to mention it as one of the principal evidences for the truth of that hypothesis. Yet, an analogy of this kind, it would seem, far from a demonstration, could afford, at most, but the shadow of a probability. It is true, that though Cassini supposed the Planets to revolve in an oblong curve, it was in a curve somewhat different from that of Kepler. In the ellipse, the sum of the two lines which are drawn from any one point in the circumference to the two foci, is always equal to that of those which are drawn from any other point in the circumference to the same foci. In the curve of Cassini, it is not the sum of the lines, but the rectangles which are contained under the lines, that are always equal. As this, however, was a proportion more difficult to be comprehended by astronomers than the other, the curve of Cassini has never had the vogue. Nothing now embarrassed the system of Copernicus, but the difficulty which the imagination felt in conceiving bodies so
- 75. immensely ponderous as the Earth and the other Planets revolving round the Sun with such incredible rapidity. It was in vain that Copernicus pretended, that, notwithstanding the prejudices of sense, this circular motion might be as natural to the Planets, as it is to a stone to fall to the ground. The imagination had been accustomed to conceive such 373 objects as tending rather to rest than motion. This habitual idea of their natural inertness was incompatible with that of their natural motion. It was in vain that Kepler, in order to assist the fancy in connecting together this natural inertness with their astonishing velocities, talked of some vital and immaterial virtue, which was shed by the Sun into the surrounding spaces, which was whirled about with his revolution round his own axis, and which, taking hold of the Planets, forced them, in spite of their ponderousness and strong propensity to rest, thus to whirl about the centre of the system. The imagination had no hold of this immaterial virtue, and could form no determinate idea of what it consisted in. The imagination, indeed, felt a gap, or interval, betwixt the constant motion and the supposed inertness of the Planets, and had in this, as in all other cases, some general idea or apprehension that there must be a connecting chain of intermediate objects to link together these discordant qualities. Wherein this connecting chain consisted, it was, indeed, at a loss to conceive; nor did the doctrine of Kepler lend it any assistance in this respect. That doctrine, like almost all those of the philosophy in fashion during his time, bestowed a name upon this invisible chain, called it an immaterial virtue, but afforded no determinate idea of what was its nature. Des Cartes was the first who attempted to ascertain, precisely, wherein this invisible chain consisted, and to afford the imagination a train of intermediate events, which, succeeding each other in an order that was of all others the most familiar to it, should unite those