Elements of geometry and trigonometry . PROPOSITION XI. LEMMA. If a triangle and a rectangley havivg the same hase and the samealtitude^turn together about the common base^ the solid describedtry the triangle will be a third of the cylinder described by therectangle. Let ACB be the triangle, and BE the rectangle. On the axis, let fall the perpen-licular AI): tlie cone described bythe triangle ABD is the third part ofthe cylinder <lescribed bv the rectan-gle ÀFBD (In^p. V. CoV.) ; also thecone described by th<r triangle ADCis the third part of the cylinder de-scribed by the rectaiigle* AD
Elements of geometry and trigonometry . PROPOSITION XI. LEMMA. If a triangle and a rectangley havivg the same hase and the samealtitude^turn together about the common base^ the solid describedtry the triangle will be a third of the cylinder described by therectangle. Let ACB be the triangle, and BE the rectangle. On the axis, let fall the perpen-licular AI): tlie cone described bythe triangle ABD is the third part ofthe cylinder <lescribed bv the rectan-gle ÀFBD (In^p. V. CoV.) ; also thecone described by th<r triangle ADCis the third part of the cylinder de-scribed by the rectaiigle* ADCE ; henco the sum of the twocones, or the solid described by ABC\ is the third pail of thetwo cylinders taken t«*gethcr, or of the cylinder described bythe rectangle 1500K Vllf. 179 If llie i)crj>cndicular AD falls withoutthe triangle ; the sohd described by ABCwill, ill iliat case, be the dinerence of thetwo cones described by ABJ) and ACl) ; but at the same time, the cvlinder de- scribed by BCEF will be the- ditfereiire ^ ^ ^ of the two cylinders described by ATBJ) and AlXl). Ilenccthe solid, described l)y the revolution of the trian»:çle, will stillbe a third part of the cylincKr describ(>d by the revolution ofthe rectangle haviu: the same base and the same altitude.
Size: 1986px × 1258px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bo, bookcentury1800, booksubjectgeometry, booksubjecttrigonometry
