Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 24
... included angle of the one equal to two sides and the included angle of the other , each to each , the triangles will be equal in all their parts . In the triangles ABC and DEF , let AB be equal to DE , AC to DF , and the angle 24 GEOMETRY .
... included angle of the one equal to two sides and the included angle of the other , each to each , the triangles will be equal in all their parts . In the triangles ABC and DEF , let AB be equal to DE , AC to DF , and the angle 24 GEOMETRY .
Page 25
... included side of the one equal to two angles and the included side of the other , each to each , the triangles will be equal in all their parts .. In the triangles ABC and DEF , let the angle B be equal to the angle E , the angle C to ...
... included side of the one equal to two angles and the included side of the other , each to each , the triangles will be equal in all their parts .. In the triangles ABC and DEF , let the angle B be equal to the angle E , the angle C to ...
Page 28
... included angle of the one equal to two sides and the included angle . of the other , each to each ; consequently , GC is equal to EF ( P. V. ) . Now , the point G may be without the triangle ABC , it may be on the side BC , or it may be ...
... included angle of the one equal to two sides and the included angle . of the other , each to each ; consequently , GC is equal to EF ( P. V. ) . Now , the point G may be without the triangle ABC , it may be on the side BC , or it may be ...
Page 30
... included angle of the one equal to two sides and the inclu- ded angle of the other , each to each ; and , consequently , they are cqual in all their parts ( P. V. ) ; which was to be proved . Scholium . In triangles , equal in all their ...
... included angle of the one equal to two sides and the inclu- ded angle of the other , each to each ; and , consequently , they are cqual in all their parts ( P. V. ) ; which was to be proved . Scholium . In triangles , equal in all their ...
Page 31
... included angle ACB equal to the included angle DBC , by hypothesis : hence , the two triangles are equal They in all their parts ( P. V. ) . BOOK I. 31.
... included angle ACB equal to the included angle DBC , by hypothesis : hence , the two triangles are equal They in all their parts ( P. V. ) . BOOK I. 31.
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ABē ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following