Elements of geometry and trigonometry . ABC xIK will become f^rxABxIK X CI. But the trianglesABO, CIK, are similar, andgive the proportion AB : BOor MN : : CI : IK; hence ABxIK=MNxCI; hence thesolid described by the isosceles triangle ABC will have for itsmeasure l^txCPxMN : that is, equal to two thirds of n into?the square of the perpendicular let fall on the base, into the,{distance between the two perpendiculars let fall on the axis. Scholium. The general solution appears to include the sup-position that AB produced will meet the axis ; but the results|would be equally true, though AB were

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Elements of geometry and trigonometry . ABC xIK will become f^rxABxIK X CI. But the trianglesABO, CIK, are similar, andgive the proportion AB : BOor MN : : CI : IK; hence ABxIK=MNxCI; hence thesolid described by the isosceles triangle ABC will have for itsmeasure l^txCPxMN : that is, equal to two thirds of n into?the square of the perpendicular let fall on the base, into the,{distance between the two perpendiculars let fall on the axis. Scholium. The general solution appears to include the sup-position that AB produced will meet the axis ; but the results|would be equally true, though AB were parallel to the axis. Thus, the cyhnder described by AMNB p j^ B /is equal to ~.MN ; the cone descri-jbed by ACM is equal to ^^.CM,and the cone described by BCN to^ttAM^ CN. Add the first two solids andtake away the third ; we shall ha;^e thesolid described by ABC equal to i^.AM^.(MN+iCM—-^CN): and since CN—CM r:=MN, this expres-sion is reducible to ^.AM^.fMN, or l^^MN ; which agreeswith the conclusion found

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Keywords: ., bo, bookcentury1800, booksubjectgeometry, booksubjecttrigonometry