Elements of Geometry Containing the First Six Books of Euclid With a Supplem
Elements of Geometry Containing the First Six Books of Euclid With a Supplem
John Playfair
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1 Sup. ) or GO ; now, CG is equal to GR, because CD is equal to DE, and therefore also, the circles described with the distance GR and GL are together equal to the circle described with the distance GO, that is, the circles described by the revolution of GR and GL about the point G, are together equal to the circle described by the revolution of GO about the same point G ; therefore also, the cylinders that stand upon the two first of these circles, having the common altitudes GH, are equal to ...the 216 SUPPLEMENT TO THE ELEMENTS, &c. cylinder which stands on the remaining circle, and which has the same altitude GH. The cylinders described by the revolution of the rectangles Gg, and Gr are therefore equal to the cylinder described by the rectangle GP. And as the same may be shewn of all the rest, therefore the cylin- ders described by the rectangles Hh, Gg, Ff, and by the rectangles Hs, Gr, Fq, DN, are together equal to the cylinder described by BD, that is, to the cylinder having the same base and altitude with the hemisphere.
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