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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Resultados 11-15 de 61
Página 119
... proved , that when m≈n , m ( A + B ) is greater than nB , and m ( C + D ) greater than nD . Next , let mn , or n7m , then m ( A + B ) may be greater than nB , or may be equal to it , or may be less ; first , let m ( A + B ) be greater ...
... proved , that when m≈n , m ( A + B ) is greater than nB , and m ( C + D ) greater than nD . Next , let mn , or n7m , then m ( A + B ) may be greater than nB , or may be equal to it , or may be less ; first , let m ( A + B ) be greater ...
Página 120
... proved that A : A + B :: C : C + D . PROP . XX . THEOR . If there be three magnitudes , and other three , which taken two and two , have the same ratio ; if the first be greater than the third , the fourth is greater than the sixth ; if ...
... proved that A : A + B :: C : C + D . PROP . XX . THEOR . If there be three magnitudes , and other three , which taken two and two , have the same ratio ; if the first be greater than the third , the fourth is greater than the sixth ; if ...
Página 121
... proved , C : B :: E : D ; and B : A :: F : E , therefore , by the first case , since C7A F7D , that is , DF . Therefore , & c . Q. E. D. PROP . XXII . THEOR . If there be any number of magnitudes , and as many others , which , taken two ...
... proved , C : B :: E : D ; and B : A :: F : E , therefore , by the first case , since C7A F7D , that is , DF . Therefore , & c . Q. E. D. PROP . XXII . THEOR . If there be any number of magnitudes , and as many others , which , taken two ...
Página 123
... proved , that A + B : B ~ A :: C + D : D − C . Q. E. D. Therefore , & c . PROP . F. THEOR . Ratios which are compounded of equal ratios , are equal to one another . Let the ratios of A to B , and of B to C , which compound the ratio of ...
... proved , that A + B : B ~ A :: C + D : D − C . Q. E. D. Therefore , & c . PROP . F. THEOR . Ratios which are compounded of equal ratios , are equal to one another . Let the ratios of A to B , and of B to C , which compound the ratio of ...
Página 127
... proved equal to the angle BAD ; therefore also ACE is equal to the angle AEC , and conse- quently the side AE is equal to the side ( 6. 1. ) AC . And because AD is drawn parallel to one of the sides of the triangle BCE , viz . to EC ...
... proved equal to the angle BAD ; therefore also ACE is equal to the angle AEC , and conse- quently the side AE is equal to the side ( 6. 1. ) AC . And because AD is drawn parallel to one of the sides of the triangle BCE , viz . to EC ...
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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