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 108
... Magnitudes which have the same ratio to the same magnitude are equal to one another ; and those to which the same magnitude has the same ratio are equal to one another . If A : C :: B : C , A = B . For if not , let A be greater than B ...
... Magnitudes which have the same ratio to the same magnitude are equal to one another ; and those to which the same magnitude has the same ratio are equal to one another . If A : C :: B : C , A = B . For if not , let A be greater than B ...
Página 109
... magnitudes be proportionals , as one of the antecedents is to its consequent , so are all the antecedents , taken ... Magnitudes have the same ratio to one another which their equimultiples have . If A and B be two magnitudes , and m any ...
... magnitudes be proportionals , as one of the antecedents is to its consequent , so are all the antecedents , taken ... Magnitudes have the same ratio to one another which their equimultiples have . If A and B be two magnitudes , and m any ...
Página 110
... 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 equimul tiples ...
... 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 equimul tiples ...
Página 111
... magnitudes be proportionals , they are also proportionals by conversion , that is , the first is to its excess above ... magnitudes , and other three , which taken two and two , have the same ratio ; if the first be greater than the ...
... magnitudes be proportionals , they are also proportionals by conversion , that is , the first is to its excess above ... magnitudes , and other three , which taken two and two , have the same ratio ; if the first be greater than the ...
Página 112
... magnitudes , and other three , which have the same ratio taken two and two , but in a cross order ; if the first magnitude be greater than the third , the fourth is greater than the sixth ; if equal , equal ; and if less , less . If ...
... magnitudes , and other three , which have the same ratio taken two and two , but in a cross order ; if the first magnitude be greater than the third , the fourth is greater than the sixth ; if equal , equal ; and if less , less . If ...
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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