Elements of geometry and trigonometry . re parallel, their intersec-tions AB, ab, by a third planeSAB will also be parallel(Book VI. Prop. X.) ; hence the triangles SAB, ^ab are simi-lar, and we have SA : Sa : : SB : S6 ; for a similar reason,we have SB : S6 : : SC : Sc; and so on. Hence the edgesSA, SB, SC, &c. are cut proportionally in a, b, c, &c. Thealtitude SO is likewise cut in the same proportion, at the pointu\ for BO and bo are [)arallel, therefore we haveSO : So : : SB : S6. Secondly. Since ah is parallel to AB, be to BC, cd to CD, « angle abc is ecjual to ABC, the angle bed t
Elements of geometry and trigonometry . re parallel, their intersec-tions AB, ab, by a third planeSAB will also be parallel(Book VI. Prop. X.) ; hence the triangles SAB, ^ab are simi-lar, and we have SA : Sa : : SB : S6 ; for a similar reason,we have SB : S6 : : SC : Sc; and so on. Hence the edgesSA, SB, SC, &c. are cut proportionally in a, b, c, &c. Thealtitude SO is likewise cut in the same proportion, at the pointu\ for BO and bo are [)arallel, therefore we haveSO : So : : SB : S6. Secondly. Since ah is parallel to AB, be to BC, cd to CD, « angle abc is ecjual to ABC, the angle bed to BCD, and so on(Book VI. Prop. Xin.). Also, by reason of the siniilar trian-gles SAB, Sab, we have AB : ah : : SB : Sb ; and by rea^ionof the similar triangles SBC, S6c, we have SB : S6 : : BC :be ; hence AB : ab : : BC : be ; we might likewise haveBC : be : : CD : c</, and so on. Hence the |x)lygons ABCDE,abcde have their angles res^Kîctively ecjual and their homolo-gous sides proportional ; hence they are hiinilar. N 19. 146 GEOMETRY.
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