Elements of Geometry and Trigonometry |
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Page 86
... similar . H D CE T Take AG = DE , and draw GH paral- lel to BC . The angle AGH will be equal to the angle ABC ( Book ... similar to ABC ; there- fore DEF is also similar to ABC . PROPOSITION XXI . THEOREM . Two triangles , which have 86 ...
... similar . H D CE T Take AG = DE , and draw GH paral- lel to BC . The angle AGH will be equal to the angle ABC ( Book ... similar to ABC ; there- fore DEF is also similar to ABC . PROPOSITION XXI . THEOREM . Two triangles , which have 86 ...
Page 87
... similar . Let BAC , EDF , be two triangles . First . If the side AB is parallel to DE , and BC to EF , the angle ABC will be equal to DEF ( Book I. Prop . XXIV . ) ; if AC is parallel to DF , the angle ACB will be equal to DFE , and ...
... similar . Let BAC , EDF , be two triangles . First . If the side AB is parallel to DE , and BC to EF , the angle ABC will be equal to DEF ( Book I. Prop . XXIV . ) ; if AC is parallel to DF , the angle ACB will be equal to DFE , and ...
Page 88
... similar to each other , and to the whole triangle . 2d . Either side including the right angle will be a mean propor- tional between the hypothenuse and the adjacent segment . 3d . The perpendicular will be a mean proportional between ...
... similar to each other , and to the whole triangle . 2d . Either side including the right angle will be a mean propor- tional between the hypothenuse and the adjacent segment . 3d . The perpendicular will be a mean proportional between ...
Page 89
... similar ; hence all the triangles are equiangular and similar . Secondly . The triangles BAD , BAC , being similar , their homologous sides are proportional . But BD in the small tri- angle , and BA in the large one , are homologous ...
... similar ; hence all the triangles are equiangular and similar . Secondly . The triangles BAD , BAC , being similar , their homologous sides are proportional . But BD in the small tri- angle , and BA in the large one , are homologous ...
Page 91
... similar triangles are to each other as the squares described on their homologous sides . Let ABC , DEF , be two similar trian- gles , having the angle A equal to D , and the angle B = E . Then , first , by reason of the equal an- G gles ...
... similar triangles are to each other as the squares described on their homologous sides . Let ABC , DEF , be two similar trian- gles , having the angle A equal to D , and the angle B = E . Then , first , by reason of the equal an- G gles ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone convex surface Cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex