Transcription of Ten Chapters of the Algebraical Art - QMUL Maths
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Ten Chapters of the Algebraical Art - QMUL Maths
Ten Chapters of the Algebraical Art Peter J. Cameron ii Preface Abu Ja'far Muhammad ibn Musa al-Khwarizmi (whose name gives us the word algorithm') wrote an algebra textbook which included much of what is still regarded as elementary algebra today. The title of his book was Hisab al-jabr w'al-muqabala. The word al-jabr means restoring', referring to the pro- cess of moving a negative quantity to the other side of an equation; the word al-muqabala means compar- ing', and refers to subtracting equal quantities from both sides of an equation. Both processes are famil- iar to anyone who has to solve an equation! The word al-jabr has, of course, been incorporated into our lan- guage as algebra'. In a similar vein, Doctor Johnson gave this definition of algebra in his Dic- tionary of 1755: This is a peculiar kind of arithmetick, which takes the quantity sought, whether it be a number or a line, or any other quantity, as if it were granted, and by means of one or more quantities given, proceeds by consequence, till the quantity at first only supposed to be known, or at least some power thereof, is found to be equal to some quantity or quantities which are known, and consequently itself is known.
2 CHAPTER 1. WHAT IS MATHEMATICS ABOUT? If and only if We will come back to this later. For now, it means that, for any value of n, either the two statements “n is odd” and “ n2 is odd” are both true, or they are both false.
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