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 200
... prisms have their bases and altitudes reciprocally proportional , and conversely . PROP . XI . THEOR . Similar solid parallelopipeds 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 parallelopipeds are to one another in the triplicate ratio of their homologous sides . Let AG , KQ be two similar ...
Página 201
... prisms are to one another in the triplicate ratio , or in the ratio of the cubes of their homolo- gous sides . PROP . XII . THEOR . If two triangular pyramids , which have equal bases and altitudes , be cut by planes that are parallel ...
... prisms are to one another in the triplicate ratio , or in the ratio of the cubes of their homolo- gous sides . PROP . XII . THEOR . If two triangular pyramids , which have equal bases and altitudes , be cut by planes that are parallel ...
Página 202
... prisms of the same altitude may be circumscribed about any pyramid , such that the sum of the prisms shall exceed the pyramid by a solid less than any given solid . Let ABCD be a pyramid , and Z * a given solid ; a series of prisms hav ...
... prisms of the same altitude may be circumscribed about any pyramid , such that the sum of the prisms shall exceed the pyramid by a solid less than any given solid . Let ABCD be a pyramid , and Z * a given solid ; a series of prisms hav ...
Página 203
... prism standing on the same base with the pyramid , viz . the triangle BCD , and having for its altitude the ... prism ( def . 4. 3. Sup . ) . By the same construction , let the prisms PM , RO , TV be described . Also , let the straight ...
... prism standing on the same base with the pyramid , viz . the triangle BCD , and having for its altitude the ... prism ( def . 4. 3. Sup . ) . By the same construction , let the prisms PM , RO , TV be described . Also , let the straight ...
Página 204
... prisms that stand upon the equal sections are equal ( 1. Cor . 8 3. Sup . ) , that is , the prism which stands on the base BCD , and which is between the planes BCD and NQL , is equal to the prism which stands on the base FGH , and ...
... prisms that stand upon the equal sections are equal ( 1. Cor . 8 3. Sup . ) , that is , the prism which stands on the base BCD , and which is between the planes BCD and NQL , is equal to the prism which stands on the base FGH , and ...
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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