HISTORY OF ALGEBRA. . 183 



tion that may be proposed, and to excite men of genius to attempt their 

 solution. Of these I have selected seven, ist. To divide 10 into s parts, 

 such, that when each part is added to its square root and the sums aremuU 

 tiplied together, the product is equal to a supposed number, 2d. What 

 square number is that which being increased or diminished by 10, the 

 sum and remainder are both square numbers ? 3d. A person said he owed 



A 



Zaid 10 all but the square root of what he owed Ame'r, and that he owed 

 Amer 5 all but the square root of what he owed Zaid ; . 4th, To divide a 

 cube number into two cube numbers. 5th- To divide 10 into two parts, 

 such, that if each is divided by the other, and the two quotients are added 

 together, the sum is equal to one of the parts. 6th. There are three square 

 numbers in continued geometrical proportion, such, that the sum of the three 

 is a square number. 7th. There is a square, such, that when it is increas- 

 ed and diminished by its root and 2, the sum and the difference are squares. 

 Know, reader, that in this treatise I have collected in a small space the 

 most beautiful and best rules of this science, more than were ever collect- 

 ed before in one book. Do not underrate the value of this bride ; hide 

 her from the view of those who are unworthy of her, and let her goto 

 the house of him only who aspires towed her." 



It is seen above that these questions are distinctly said to be beyond 1 

 the skill of algebraists. They either involve equations of the higher or- 

 der, or the indeterminate analysis, or are impossible. 



It does not appear that the Arabians used algebraic notation or abbre- 

 viating symbols ; that they had any knowledge of the Diophantine Alge- 

 bra, or of any but the easiest and elementary parts of the science. We 

 have seen that Baha'-ul-din ascribes the invention of the numeral fig- 

 ures in the decimal scale to the Indians, As the proof commonly given 



