TRACT 33.

HISTORY OP ALGEBRA.

165

squares; such as (using our own notation), finding 67 a 2 4-1,and 61 a 2 + 1, and 13 a 2 —1, &c, squares; also a generalway or method to make expressions of this kind ax 2 . + bsquares.

Then questions are treated producing simple equations;with the application to some questions about triangles. Thenmore questions about 1- squares; as, to find x±y and xyboth squares; also a 3 + J/ 3 and a 2 + J/ 2 both squares.

Next, some questions producing quadratics. Somethingis also said of a cubic; but it seems to hint that it cannotbe solved generally: a straight ruler is mentioned, whichit is suspected may allude to some mechanical method ofsolution, for there is an omission in the translation. Thenmore about squares ; such as, to find

x —y \ both 7 a 2 + 8 y 1 7 both a 2 +j/ 3 7

a 2 + y 1 5 squares; 7a 2 — 8 <y 1J t- 1 -* squares; a 5 s T iares >

x-y+21a +y + 2 i

squares;

in whole numbers

■ z ' z -y*+ 1

ll

x —y a squaresquares; z , z u1 ’ a 2 + 3 r a cube

*3-

X 2 + j / 2 +

a whole number, &c, &c.

Lastly, more indeterminate questions. In short, a greatpart is about indeterminate, and what we call questions ofthe Diophantine kind, yet without any one being the verysame as in that author; which alone seems to show a differ-ent origin ; besides, they are mostly treated in a very differ-ent way. Several of-them are not easy; and Mr. Burrowhas sometimes given answers in the margin, done in theEuropean manner.

There are three or four questions about right-angled tri-angles, done algebr-aically; and here one might have ex-pected to have found Eucl. 47, I, quoted ; but, instead ofthat, a reference is made to the “ figure of wedding chair.”But from these, and many other parts of their writings, weperceive that they were possessed of, not this propertyonly, but most others the same as in our geometry; andhere it was probably that Pythagoras acquired his mathema-