Elements of geometry and trigonometry . to three pyramids whose common altitudt; is thatof the frustum and whose bases arc the lower base of thefrustum, the upper base, and a mean proportional between thetwo bases. PROPOSITION XIX. THEOREM. Similar triangular prisms arc to each other as ihe cubes of theithomologous sides. Let CBD-P, cl>d-p, l)c twosimilar triangular j^risms, ofwhich I>(.,/yr, an* hjfnologuus«ides: then will (Ikî prismCHD-P be to the phsm cbd-p,as BC^ to bc\ For, .since the prisnjs aresimilar, the planes whichc(;n-tain the houjologfjus solid an-gles B and I), are similar,
Elements of geometry and trigonometry . to three pyramids whose common altitudt; is thatof the frustum and whose bases arc the lower base of thefrustum, the upper base, and a mean proportional between thetwo bases. PROPOSITION XIX. THEOREM. Similar triangular prisms arc to each other as ihe cubes of theithomologous sides. Let CBD-P, cl>d-p, l)c twosimilar triangular j^risms, ofwhich I>(.,/yr, an* hjfnologuus«ides: then will (Ikî prismCHD-P be to the phsm cbd-p,as BC^ to bc\ For, .since the prisnjs aresimilar, the planes whichc(;n-tain the houjologfjus solid an-gles B and I), are similar, like [)laced, and ((jiially inclined toeach otlur (I)<f. 17.) : hence tin; solid angNH 15 and h, are eciual(Book VI. Prop. XXI. Sfh.). If these solid angles Ixî appliedto each other, the angle chdwiW coincide with (.HI), the side b<iwith BA, and the prism cbd-p will take the position Wcd-p. From Adraw All pcrp«iidi<ular to the common base of (he prisms: thenvrilJ the pUiUj !i.\II i)c perpendicular to the plane of the com-. Î64 GEOMETRY.
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Keywords: ., bo, bookcentury1800, booksubjectgeometry, booksubjecttrigonometry
