# Diophantus Sentence Examples

The Arithmetica, the greatest treatise on which the fame of

**Diophantus**rests, purports to be in thirteen Books, but none of the Greek MSS.The missing books were apparently lost early, for there is no reason to suppose that the Arabs who translated or commented on

**Diophantus**ever had access to more of the work than we now have.Among the great variety of problems solved are problems leading to determinate equations of the first degree in one, two, three or four variables, to determinate quadratic equations, and to indeterminate equations of the first degree in one or more variables, which are, however, transformed into determinate equations by arbitrarily assuming a value for one of the required numbers,

**Diophantus**being always satisfied with a rational, even if fractional, result and not requiring a solution in integers.A word is necessary on

**Diophantus**' notation.Thus

**Diophantus**knew that no number of the form 8n-1-7 can be the sum of three squares.For many centuries algebra was confined almost entirely to the solution of equations; one of the most important steps being the enunciation by

**Diophantus**of Alexandria of the laws governing the use of the minus sign.The first extant work which approaches to a treatise on algebra is by

**Diophantus**, an Alexandrian mathematician, who flourished about A.D.In the preface to this work, which is dedicated to one Dionysius,

**Diophantus**explains his notation, naming the square, cube and fourth powers, dynamis, cubus, dynamodinimus, and so on, according to the sum in the indices.It is difficult to believe that this work of

**Diophantus**arose spontaneously in a period of general stagnation.We find that geometry was neglected except in so far as it was of service to astronomy; trigonometry was advanced, and algebra improved far beyond the attainments of

**Diophantus**.AdvertisementHowever this may be, it is certain that the Hindu algebraists were far in advance of

**Diophantus**.A notable improvement on the ideas of

**Diophantus**is to be found in the fact that the Hindus recognized the existence of two roots of a quadratic equation, but the negative roots were considered to be inadequate, since no interpretation could be found for them.Great advances were made in the study of indeterminate equations, a branch of analysis in which

**Diophantus**excelled.But whereas

**Diophantus**aimed at obtaining a single solution, the Hindus strove for a general method by which any indeterminate problem could be resolved.Ptolemy's Almagest, the works of Apollonius, Archimedes,

**Diophantus**and portions of the Brahmasiddhanta, were also translated.AdvertisementHe follows the methods of

**Diophantus**; his work on indeterminate equations has no resemblance to the Indian methods, and contains nothing that cannot be gathered from**Diophantus**.That principle had been made use of by the Greek authors of the classic age; but of later mathematicians only Hero,

**Diophantus**, &c., ventured to regard lines and surfaces as mere numbers that could be joined to give a new number, their sum.It may be that the study of such sums, which he found in the works of

**Diophantus**, prompted him to lay it down as a principle that quantities occurring in an equation ought to be homogeneous, all of them lines, or surfaces, or solids, or supersolidsan equation between mere numbers being inadmissible.In this respect the fate of Pappus strikingly resembles that of

**Diophantus**.Hypatia, according to Suidas, was the author of commentaries on the Arithmetica of

**Diophantus**of Alexandria, on the Conics of Apollonius of Perga and on the astronomical canon (of Ptolemy).AdvertisementWe know only that the last of them, a Paerisades, unable to make headway against the power of the natives, called in the help of

**Diophantus**, general of Mithradates VI.It is addressed to

**Diophantus**and conveys a moral, that one should work and not dream, illustrated by the story of an old fisherman who dreams that he has caught a fish of gold and narrates his vision to his mate.As Leonidas of Tarentum wrote epigrams on fishermen, and one of them is a dedication of his tackle to Poseidon by

**Diophantus**, the fisher, 8 is likely that the author of this poem was an imitator of Leonidas.A different method was used by

**Diophantus**, accents being omitted, and the denominator being written above and to the right of the numerator.They originally took the form of marginal notes in a copy of Bachet's

**Diophantus**, and were published in 1670 by his son Samuel, who incorporated them in a new edition of this Greek writer.AdvertisementThe first contains the "Arithmetic of

**Diophantus**," with notes and additions.We do know three lemmas contained in The Porisms since

**Diophantus**refers to them in the Arithmetica.