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 TrigonometryE. Duyckinck, and George Long, 1824 - 333 páginas |
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Página 122
... F : D Therefore & c . Q. E. D. * N . B. This proposition is usually cited by the words " ex æquali in proportione pertur " bata ; " or , 66 ex æquo inversely . " PROP . E. THEOR . If four magnitudes be proportionals 122 ELEMENTS.
... F : D Therefore & c . Q. E. D. * N . B. This proposition is usually cited by the words " ex æquali in proportione pertur " bata ; " or , 66 ex æquo inversely . " PROP . E. THEOR . If four magnitudes be proportionals 122 ELEMENTS.
Página 123
... proportionals , the sum of the first two is to their difference as the sum of the other two to their difference . 1 Let A B C D ; then if A7B , A - BA - BC + D : C - D ; or if AZB A + B B - A :: C + D : D - C . For , if A7B , then ...
... proportionals , the sum of the first two is to their difference as the sum of the other two to their difference . 1 Let A B C D ; then if A7B , A - BA - BC + D : C - D ; or if AZB A + B B - A :: C + D : D - C . For , if A7B , then ...
Página 124
... proportionals . II . Two sides of one figure are said to be reciprocally proportional to two sides of another , when one of the sides of the first is to one of the sides of the second , as the remaining side of the second is to the ...
... proportionals . II . Two sides of one figure are said to be reciprocally proportional to two sides of another , when one of the sides of the first is to one of the sides of the second , as the remaining side of the second is to the ...
Página 127
... proportionals , the triangles shall be equiangular , and have their equal angles oppo- site 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 ...
... proportionals , the triangles shall be equiangular , and have their equal angles oppo- site 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 ...
Página 129
... proportionals , the triangles shall be equiangular , and have their equal angles oppo site 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 ...
... proportionals , the triangles shall be equiangular , and have their equal angles oppo site 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 ...
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ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore