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, Edlemnts of Plane and Spherical TrigonometryW.E. Dean, 1836 - 311 páginas |
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Página 108
... THEOR . Magnitudes which have the same ratio to the same magnitude are equal to one another ; and those to which the same magnitude has the sarne ratio are equal to one another . If A : C : B : C , A = B . For if not , let A be greater ...
... THEOR . Magnitudes which have the same ratio to the same magnitude are equal to one another ; and those to which the same magnitude has the sarne ratio are equal to one another . If A : C : B : C , A = B . For if not , let A be greater ...
Página 109
... THEOR . If any number of magnitudes be proportionals , as one of the antecedents is to its consequent , so are all the antecedents , taken together , to all the conse- quents . If A B C : D , and C : D :: E : F ; then also , A : B :: A ...
... THEOR . If any number of magnitudes be proportionals , as one of the antecedents is to its consequent , so are all the antecedents , taken together , to all the conse- quents . If A B C : D , and C : D :: E : F ; then also , A : B :: A ...
Página 110
... THEOR . If four magnitudes of the same kind be proportionals , they will also be pro- portionals 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 ...
... THEOR . If four magnitudes of the same kind be proportionals , they will also be pro- portionals 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 ...
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Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal arc AC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided draw Prob 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 wherefore