Guldin 15771643 most of the remaining of the treatise is collections of lemmas that will assist the readers understanding of the original works. Pappus also discusses the three and four lines theorem of apollonius. Pappus s first theorem states that the area of a surface generated by rotating a figure about an external axis a distance from its centroid equals the product of the arc length of the generating figure and the distance traversed by. The theorems are attributed to pappus of alexandria and paul guldin wikimedia commons has media related to pappusguldinus theorem. In mathematics, pappuss centroid theorem is either of two related theorems dealing with the surface areas and volumes of surfaces and solids of revolution. Nowadays the theorem is known as pappusguldin theorem or pappus theorem. Nine proofs and three variations x y z a b c a b z y c x b a z x c y fig. Pappuss area theorem describes the relationship between the areas of three parallelograms attached to three sides of an arbitrary triangle. This file is licensed under the creative commons attributionshare alike 4. Pdf on mar 1, 2006, ximo gualarnau and others published pappusguldin theorems for weighted motions find, read and cite all the.
All structured data from the file and property namespaces is available under the creative commons cc0 license. The theorem, which can also be thought of as a generalization of the pythagorean theorem, is named after the greek mathematician pappus of alexandria 4th century ad, who discovered it. Pdf pappusguldin theorems for weighted motions researchgate. Mato grosso ufmt campus of sinop, in the free software and maxima winplot have. Theorems of pappus on surfaces of revolution wolfram. In mathematics, pappuss centroid theorem also known as the guldinus theorem, pappusguldinus theorem or pappuss theorem is either of two related theorems dealing with the surface areas and volumes of surfaces and solids of revolution. Permission is granted to copy, distribute andor modify this document under the terms of the gnu free documentation license, version 1. The theorems are attributed to pappus of alexandria and paul guldin. Pappuss first theorem states that the area of a surface generated by rotating a figure about an external axis a distance from its centroid equals the product of the arc length of the generating figure and the distance traversed by. The pappusguldin theorems suppose that a plane curve is rotated about an axis external to the curve. Long before the invention of calculus, pappus of alexandria ca. Files are available under licenses specified on their description page. Century ad proposed two theorems for determining the area and volume of surfaces of revolution.
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