Diophantus of Alexandria: A Study in the History of Greek Algebra

accordingly added Algebra Arithmetica Assume assumption Bachet becomes beginning Books coefficient common condition contained corresponding course cube difference Diophantus divide double double-equation equal equation Euler expression fact factors Fermat find a right-angled find three numbers find two numbers four fourth fraction given number given ratio gives a square greater Greek half Hence hypotenuse integral least Lemma less letter means method middle minus multiplied namely necessary negative observes obtain original pair particular perpendicular positive possible powers prime number problem proof proposition proved ratio remains respectively result right-angled triangle root rule satisfied shows sides solution solved square number substitute subtract Suppose taken Tannery theorem third three squares unknown whence