If we arrive at an equation containing on each side the same term but with different coefficients, we must take equals from equals until we get one term equal to another term.
3rd century Alexandrian Greek mathematician
An Alexandrian mathematician whose margin note became the most famous tease in math history — not his own note, but Fermat's, scribbled in a 1621 edition of his work claiming a proof "too large for this margin." The equations he left behind now anchor entire branches of number theory.
Diophantus of Alexandria flourished around 250 CE and authored the Arithmetica in thirteen books, ten still extant, working through arithmetical problems solved by algebraic equations. Lagrange later called him "the inventor of algebra"; his methods became standard in Neoplatonic schools of late antiquity, then shaped medieval Arabic algebra after a 9th-century translation carried his concepts and procedures east. The 1621 Bachet edition found unexpected immortality when Pierre de Fermat annotated his copy with the Last Theorem in the margin. His legacy now extends beyond that famous marginal…
Sourced, dated quotes from Diophantus
If we arrive at an equation containing on each side the same term but with different coefficients, we must take equals from equals until we get one term equal to another term.
Between the time of Regiomontanus and that of Rafael Bombelli Diophantos was once more forgotten, or rather unknown.
The solution of the higher indeterminates depends almost entirely on very favourable numerical conditions and his methods are defective.
Sometimes... Diophantus solves a problem wholly or in part by synthesis.
Though the defects in Diophantus' proofs are in general due to the limitation of his symbolism, it is not so always.
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