Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added, Elements of Plane and Spherical TrigonometryB. & S. Collins; W. E. Dean, printer, 1836 - 311 páginas |
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Página 119
... equiangular triangles are proportionals ; and those which are opposite to the equal angles are homologous sides , that is , are the antecedents or consequents of the ratios Let ABC , DCE , be equiangular triangles , having the angle ABC ...
... equiangular triangles are proportionals ; and those which are opposite to the equal angles are homologous sides , that is , are the antecedents or consequents of the ratios Let ABC , DCE , be equiangular triangles , having the angle ABC ...
Página 120
... equiangular , and have their equal angles opposite to the homologous sides . Let the triangles ABC , DEF have their sides proportionals , so that AB is to BC , as DE to EF ; and BC to CA , as EF to FD ; and consequently ex æquali , BA ...
... equiangular , and have their equal angles opposite to the homologous sides . Let the triangles ABC , DEF have their sides proportionals , so that AB is to BC , as DE to EF ; and BC to CA , as EF to FD ; and consequently ex æquali , BA ...
Página 121
... equiangular to the triangle DEF . PROP . VI . THEOR . If two triangles have one angle of the one equal to one angle of the other , and the sides about the equal angles proportionals , the triangles shall be equian- gular , and shall ...
... equiangular to the triangle DEF . PROP . VI . THEOR . If two triangles have one angle of the one equal to one angle of the other , and the sides about the equal angles proportionals , the triangles shall be equian- gular , and shall ...
Página 122
... equiangular , and have those angles equal about which the sides are propor- tionals . Let the two triangles ABC , DEF have one angle in the one equal to one angle in the other , viz . the angle BAC to the angle EDF , and the sides about ...
... equiangular , and have those angles equal about which the sides are propor- tionals . Let the two triangles ABC , DEF have one angle in the one equal to one angle in the other , viz . the angle BAC to the angle EDF , and the sides about ...
Página 123
... equiangular to the triangle DEF , as in the first case . PROP . VIII . THEOR . In a right angled triangle if a ... equiangular to the triangle ABD , and the sides about their equal angles are proportionals ( 4. 6. ) ; wherefore the ...
... equiangular to the triangle DEF , as in the first case . PROP . VIII . THEOR . In a right angled triangle if a ... equiangular to the triangle ABD , and the sides about their equal angles are proportionals ( 4. 6. ) ; wherefore the ...
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Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore