Pappus of Alexandria

The first surviving description of the Archimedean solids is that of the Greek geometer Pappus of Alexandria who lived in the fourth century (around 320).288,289 Pappus of Alexandria attributed the invention of semiregular convex polyhedra to Archimedes (287-212 B.C.) hence, the name Archimedean solids. The painter-mathematicians of the Renaissance were interested in the Golden Cut and in its appearance in the Platonic solids and Archimedean solids.254 In 1492, the Archimedean solids were rediscovered by the painter and... 

The mathematical writer Pappus of Alexandria (fourth century c.e.) reveals that the tradition inaugurated by the Mechanical Problems was still in force half a millennium later. Pappus assures us that mechanics teaches... 

Pappus of Alexandria, La collection mathematique, tr. Paul Ver Eecke (Paris Descl6e, de Brouwer, 1933), 2 810-811. It is true that Pappus also says that mechanics teaches the motion of bodies according to nature [kata physin) as well as against nature para physin), but a few lines later he reiterates that machines themselves, as opposed to the rational mechanics of the mathematicians, work para physin. See pp. 809 and 811 of Ver Eecke s translation. 

Pappus of Alexandria. La collection mathematique, trans. Paul Ver Eecke, 2 vols. (Paris Descl e, de Brouwer Co., 1933). 

A theorem, now considered seminal for projective geometry, was discovered by Pappus of Alexandria in about the year 320 ... 

A torus or anchor ring, drawn in Fig. 1.3, is the approximate shape of a donut or bagel. The radii R and r refer, respectively, to the circle through the center of the torus and the circle made by a cross-sectional cut. Generally, to determine the area and volume of a surface of revolution, it is necessary to evaluate double or triple integrals. However, long before calculus was invented. Pappus of Alexandria (ca. Third Century A.D.) proposed two theorems that can give the same results much more directly. 

See, for instance, the writings of Pappus of Alexandria, a mathematician who lived in the third century and discussed in detail the works of Archimedes. 

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