.175 ON TKS EARLY 



" Chapter second. On the six rules of Algebra. To find unknown? 

 quantities by Algebra depends on acuteness and sagacity ; an attentive 

 consideration of the terms of the question, and a successful application of 

 the invention to such things as may serve to bring out what is required. 

 Call the unknown quantity Shai, and proceed with it according to the 

 termsof the question, as has been said, till the operation ends with an 

 equation. Let that side where there are negative quantities be made per- 

 feet, and let the negative quantity be added to the other side ; this is cal- 

 led restoration (Jebr.) Let those things which are of the same kind, and 

 equal on both sides, be thrown away : this is opposition (Mukdbalah.) 

 Equality is either of one species to* another, which is of three kinds, called 

 (Mufriddt) simple ; or of one species to two species, which of three kinds B 

 called (Muktarindt) compound. 



i • ' ' ' ' ' 



" Case the first. Mufriddt. Number is equal to things. Divide the 

 number by the co-efficient of the things, and the unknown quantity will 

 be found. For example; a person admitted that he owed Zaid 1000 

 and one half of what he owed Amer; and that he owed Amer 1000 

 all but one half of what he owed to Zaid. Call Zaid's debt Shai. Then 

 Amer's debt is 1000, all but half of Shai. Then Zaid's is 1500 all but a 

 fourth of Shai. This is equal to Shai. After Jebr, 1500 is equal to one 

 Shai and a quarter of Shai. So for Zaid is 1200 and for Amer 400/' 



" Case the second. Multiples of Shai equal to multiples of Mat. 

 Divide the co-efficient of the things by that of the Mdl; the quotient is 

 the unknown quantity. Example. Some sons plundered their father's 

 inheritance, which consisted of Dinars. One took 1, another 2, the third 

 3, and so on increasing by one. The ruling power took back what they 

 had plundered, and divided it among them in equal shares. Then each 



