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 205
... prism BNM is to the parallelepiped CD as the triangle AME to the parallelogram LG . PROP . IX . THEOR . Solid parallelepipeds are to one another in the ratio that is compounded of the ratios of the areas of their bases , and of their ...
... prism BNM is to the parallelepiped CD as the triangle AME to the parallelogram LG . PROP . IX . THEOR . Solid parallelepipeds are to one another in the ratio that is compounded of the ratios of the areas of their bases , and of their ...
Página 206
... prisms are to one another in the ratio com- pounded of the ratios of their bases , and of their altitudes . For every prism is equal to a parallelepiped of the same altitude with it , and of an equal base ( 2. Cor . 8. 3. Sup . ) . PROP ...
... prisms are to one another in the ratio com- pounded of the ratios of their bases , and of their altitudes . For every prism is equal to a parallelepiped of the same altitude with it , and of an equal base ( 2. Cor . 8. 3. Sup . ) . PROP ...
Página 207
... prisms have their bases and altitudes reciprocally proportional , and conversely . PROP . XI . THEOR . Similar solid parallelepipeds are to one another in the triplicate ratio of their homologous sides . Let AG , KQ be two similar ...
... prisms have their bases and altitudes reciprocally proportional , and conversely . PROP . XI . THEOR . Similar solid parallelepipeds are to one another in the triplicate ratio of their homologous sides . Let AG , KQ be two similar ...
Página 208
... prisms are to one another in the triplicate ratio , or in the ratio of the cubes of their homologous sides . PROP . XII . THEOR . If two triangular pyramids , which have equal bases and altitudes , be cut by planes that are parallel to ...
... prisms are to one another in the triplicate ratio , or in the ratio of the cubes of their homologous sides . PROP . XII . THEOR . If two triangular pyramids , which have equal bases and altitudes , be cut by planes that are parallel to ...
Página 210
... prism ( def . 4. 3. Sup . ) . By the same construction , let the prisms PM , RO , TV be described . Also , let the straight line IP , which is in the plane of the triangle ABC be produced till it meet BC in h ; and let the line MQ , be ...
... prism ( def . 4. 3. Sup . ) . By the same construction , let the prisms PM , RO , TV be described . Also , let the straight line IP , which is in the plane of the triangle ABC be produced till it meet BC in h ; and let the line MQ , be ...
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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 definition 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 MDCCCXX 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