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 114
... proportionals , they are proportionals also when taken inversely . If A : B :: C : D , then also B : A :: D : C. Let mA and mC be any equimultiples of A and C ; nB and nD any equimultiples of B and D. Then , because A : B :: C : D , if ...
... proportionals , they are proportionals also when taken inversely . If A : B :: C : D , then also B : A :: D : C. Let mA and mC be any equimultiples of A and C ; nB and nD any equimultiples of B and D. Then , because A : B :: C : D , if ...
Página 117
... proportionals , as one of the antecedents- is to its consequent , so are all the antecedents , taken together , to all the consequents . If A : B :: C : D , and C : D :: E : F ; then also , A : B :: A + C + E : B + D + F . Take mA , mC ...
... proportionals , as one of the antecedents- is to its consequent , so are all the antecedents , taken together , to all the consequents . If A : B :: C : D , and C : D :: E : F ; then also , A : B :: A + C + E : B + D + F . Take mA , mC ...
Página 118
... proportionals , they will also be proportionals when taken alternately . If A B C D , then alternately , A : C :: B : D. : :: Take mA , mB any equimultiples of A and B , and nC , nD any equi- multiples of C and D. Then ( 15. 5. ) A : B ...
... proportionals , they will also be proportionals when taken alternately . If A B C D , then alternately , A : C :: B : D. : :: Take mA , mB any equimultiples of A and B , and nC , nD any equi- multiples of C and D. Then ( 15. 5. ) A : B ...
Página 119
... proportionals , they will also be pro- portionals when taken jointly , that is , if the first be to the second as the third to the fourth , the first and second together will be to the second as the third and fourth together to the ...
... proportionals , they will also be pro- portionals when taken jointly , that is , if the first be to the second as the third to the fourth , the first and second together will be to the second as the third and fourth together to the ...
Página 120
... proportionals , they are also proportionals by con- version , that is , the first is to its excess above the second , as the third to its excess above the fourth . If ABC : D , by conversion , A : A - B :: C : C - D . For , since A : B ...
... proportionals , they are also proportionals by con- version , that is , the first is to its excess above the second , as the third to its excess above the fourth . If ABC : D , by conversion , A : A - B :: C : C - D . For , since A : B ...
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Términos y frases comunes
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