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The germ of algebra may be discerned in the works of Diophantus of Alexandria, who is supposed to have lived in the second century of our era. In that Egyptian school Euclid had formerly collected the great truths of geometry, and arranged them in logical sequence. Archimedes, in Syracuse, had attempted the solution of the higher problems by the method of exhaustions.
DIOPHANTUS. Forms with Delisle, its companion on the N., a noteworthy object. It is about 13 miles in diameter, with a wall, which has a distinct break in its continuity on the N., rising about 2500 feet above the Mare. A rill-valley runs from the E. side of the ring towards the W. face of a triangular-shaped mountain on the E. of a line joining the formation with Delisle.
But Eunica alone would not kiss the herdsman; Eunica, she that is greater than Cybele, and Cypris, and Selene! Well, Cypris, never mayst thou, in city or on hillside, kiss thy darling, and lonely all the long night mayst thou sleep! After some verses addressed to Diophantus, a friend about whom nothing is known, the poet describes the toilsome life of two old fishermen.
'Tis Poverty alone, Diophantus, that awakens the arts; Poverty, the very teacher of labour. Nay, not even sleep is permitted, by weary cares, to men that live by toil, and if, for a little while, one close his eyes in the night, cares throng about him, and suddenly disquiet his slumber.
The chief struggle was for supplies, which were on both sides scarce: for this purpose Mithradates formed the flower of his cavalry and a division of select infantry under Diophantus and Taxiles into a flying corps, which was intended to scour the country between the Lycus and the Halys and to seize the Roman convoys of provisions coming from Cappadocia.
The Pythagoreans gave general solutions in rational numbers of the equations x²+y²=z² and 2x²-y²=±1, which are indeterminate equations of the second degree. Diophantus shows that he solved quadratic equations by rule, like Heron. The collection is extraordinarily varied, and the devices resorted to are highly ingenious. He also wrote a book On Polygonal Numbers of which only a fragment survives.
After Themistokles went into exile the common people grew insolent and produced a numerous brood of informers, who constantly assailed the noblest and most powerful citizens through envy of their prosperity and influence. One of these men, Diophantus of Amphitrope by name, obtained a verdict against Aristeides on a charge of receiving bribes.
It appears too by his laws, that he intends to establish only a small state, as all the artificers are to belong to the public, and add nothing to the complement of citizens; but if all those who are to be employed in public works are to be the slaves of the public, it should be done in the same manner as it is at Epidamnum, and as Diophantus formerly regulated it at Athens.
Orestes had strangled Diophantus in order that there might be no rival to Orestes' claims. The lad lay on his back, and his left arm hung elbow-deep in the water, which swayed it gently. Callistion sat beside the corpse and stroked its limp right hand. She had hated the boy throughout his brief and merry life. She thought now of his likeness to Demetrios.
She reached with her free arm across the body of Diophantus and presently dropped a stone into the pool. She said: "See how the water ripples. There is now not any reflection of my poor face or of your beauty. All is as wavering as a man's heart.... And now your beauty is regathering like coloured mists. Yet I have other stones." "Oh, and the will to use them!" said Dame Melicent.
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