Pappus of Alexandria

[3] In many respects, his fate strikingly resembles that of Diophantus', originally of limited importance but becoming very influential in the late Renaissance and Early Modern periods.

[4] A different date is given by a marginal note to a late 10th-century manuscript[3] (a copy of a chronological table by the same Theon), which states, next to an entry on Emperor Diocletian (reigned 284–305), that "at that time wrote Pappus".

The Suda enumerates other works of Pappus: Χωρογραφία οἰκουμενική (Chorographia oikoumenike or Description of the Inhabited World), commentary on the four books of Ptolemy's Almagest, Ποταμοὺς τοὺς ἐν Λιβύῃ (The Rivers in Libya), and Ὀνειροκριτικά (The Interpretation of Dreams).

Pappus also wrote commentaries on Euclid's Elements (of which fragments are preserved in Proclus and the Scholia, while that on the tenth Book has been found in an Arabic manuscript), and on Ptolemy's Ἁρμονικά (Harmonika).

The German classicist and mathematical historian Friedrich Hultsch (1833–1908) published a definitive three-volume presentation of Commandino's translation with both the Greek and Latin versions (Berlin, 1875–1878).

[6] Pappus's Collection contains an account, systematically arranged, of the most important results obtained by his predecessors and notes explanatory of, or extending, previous discoveries.

Heath also found his characteristic exactness made his Collection "a most admirable substitute for the texts of the many valuable treatises of earlier mathematicians of which time has deprived us".

The final propositions deal with multiplying together the numerical values of Greek letters in two lines of poetry, producing two very large numbers approximately equal to 2×1054 and 2×1038.

This and several other propositions on contact, e.g. cases of circles touching one another and inscribed in the figure made of three semicircles and known as arbelos ("shoemakers knife") form the first division of the book; Pappus turns then to a consideration of certain properties of Archimedes's spiral, the conchoid of Nicomedes (already mentioned in Book I as supplying a method of doubling the cube), and the curve discovered most probably by Hippias of Elis about 420 BC, and known by the name, τετραγωνισμός, or quadratrix.

Jones succeeds in showing how Pappus manipulated the complete quadrangle, used the relation of projective harmonic conjugates, and displayed an awareness of cross-ratios of points and lines.

[10] Pappus's Collection was virtually unknown to the Arabs and medieval Europeans, but exerted great influence on 17th-century mathematics after being translated to Latin by Federico Commandino.

[19] Fermat also developed his version of analytic geometry and his method of Maxima and Minima from Pappus's summaries of Apollonius's lost works Plane Loci and On Determinate Section.

[20] Other mathematicians influenced by Pappus were Pacioli, da Vinci, Kepler, van Roomen, Pascal, Newton, Bernoulli, Euler, Gauss, Gergonne, Steiner and Poncelet.