Elements of geometry and trigonometry . N 180 M?]Nr But CP being drawn perpendicular to AB, the triangles ABO,DCP will be similar, and give the proportionAO : CP : ; AB : CD ; hence AO x CD = CP x AB ; but CP X AB is double the area of the triangle ABC ; hence we have A0xCD-2ABC; hence the solid described by the triangle ABC is also measured by l^r X ABC X IK, or vyhich is the same thing, by ABC x Icirc. IK, circ, IK being eq«al to 2^ x IK. Hence the solid described hy the revolution of the triangle ABC,/i<z5 for its measure the area of this trnangle multiplied by two thirds
Elements of geometry and trigonometry . N 180 M?]Nr But CP being drawn perpendicular to AB, the triangles ABO,DCP will be similar, and give the proportionAO : CP : ; AB : CD ; hence AO x CD = CP x AB ; but CP X AB is double the area of the triangle ABC ; hence we have A0xCD-2ABC; hence the solid described by the triangle ABC is also measured by l^r X ABC X IK, or vyhich is the same thing, by ABC x Icirc. IK, circ, IK being eq«al to 2^ x IK. Hence the solid described hy the revolution of the triangle ABC,/i<z5 for its measure the area of this trnangle multiplied by two thirds of the circumference traced by I, the middle jjoint of the base. Cor, If the side AC = CB,the line CI will be perpen-dicular to AB, the area ABCwill be equal to ABx|CI,and the solidity ^n x 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
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Keywords: ., bo, bookcentury1800, booksubjectgeometry, booksubjecttrigonometry
