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 Trigonometry |
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Página 205
that is , the 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 ...
that is , the 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 ...
Página 206
... therefore it is the same with that of the product L XMXN to the product l xm Xn . Cor . 3. Hence all prisms are to one another in the ratio compounded of the ratios of their bases , and of their altitudes . prism ...
... therefore it is the same with that of the product L XMXN to the product l xm Xn . Cor . 3. Hence all prisms are to one another in the ratio compounded of the ratios of their bases , and of their altitudes . prism ...
Página 207
It may be demonstrated , that equal 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 ...
It may be demonstrated , that equal 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 ...
Página 208
In the same manner it is proved , that similar 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 ...
In the same manner it is proved , that similar 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 ...
Página 210
THEOR : A series of prisms of the same altitude may be circumscribed about any pyramid , such that the sum of the ... so that their sum shall exceed ABCD , by a solid less than Z. Let Z be equal to a prism standing on the same base with ...
THEOR : A series of prisms of the same altitude may be circumscribed about any pyramid , such that the sum of the ... so that their sum shall exceed ABCD , by a solid less than Z. Let Z be equal to a prism standing on the same base with ...
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Términos y frases comunes
ABC is equal ABCD altitude angle ABC angle BAC arch base bisected Book called centre circle circle ABC circumference coincide common cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular Euclid exterior angle extremity fall fore four fourth given given straight line greater half inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism produced PROP proportionals proposition proved radius ratio reason rectangle contained rectilineal figure right angles segment shewn sides similar sine solid square straight line taken tangent THEOR thing third touches triangle ABC wherefore whole
Información bibliográfica
| Título | 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 Trigonometry |
| Autor | John Playfair |
| Editor | E. Duyckinck, and George Long, 1824 |
| Procedencia del original | Universidad de Indiana |
| Digitalizado | 15 Ene. 2009 |
| Largo | 333 páginas |
| Exportar cita | BiBTeX EndNote RefMan |