Geometry the Elements of Euclid And Legendre Simplified And Arranged to Exclud
Geometry the Elements of Euclid And Legendre Simplified And Arranged to Exclud
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In our eReader you can find the full English version of the book. Read Geometry the Elements of Euclid And Legendre Simplified And Arranged to Exclud Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Geometry the Elements of Euclid And Legendre Simplified And Arranged to Exclud
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Let ABCDEFG and ahcdefg be similar polyhedrons, having the solid angles equal which are marked with the corresponding large and small letters ; they may be divided into the same number of similar triangular jjyramids similarly situated.
The surfaces of the polygons may be divided (VI. 20) into the same number of sim lar triangles, similarly situated; then planes passing through any two corresponding solid angles, A, a, and through the sides of all these triangles, except those forming the solid... angles. A, a, will divide the polyhedrons into triangular pyramids, similar to one another, and similarly sit- uated.
174 TnE ELEMENTS OF [book VT.
The pyramids thus formocl have each one solid anole at the common vertex A or a ; and these solid angles may be of three classes: Is^ those which have two of their faces coincidins with faces of one of the polyhedi'ons; 2f/, those which have only one face coinciding ; and 3o?, those which lie wholly with- in the solid angle A or a. Now those of the first kind in one of the polyhedrons are similar to the corresponding ones in the other, by the corollary to the twenty-first proposition of this Look ; and those of the second kind by the twenty-first From the polyhedrons take two of these similar ])yramids, and the remaining bodies will be similar, as the boundaries common to them and the pyramids are (VI.
What to read after Geometry the Elements of Euclid And Legendre Simplified And Arranged to Exclud?
You can find similar books in the "Read Also" column, or choose other free books by Lawrence S Lawrence Sluter Benson to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Let ABCDEFG and ahcdefg be similar polyhedrons, having the solid angles equal which are marked with the corresponding large and small letters ; they may be divided into the same number of similar triangular jjyramids similarly situated.
The surfaces of the polygons may be divided (VI. 20) into the same number of sim lar triangles, similarly situated; then planes passing through any two corresponding solid angles, A, a, and through the sides of all these triangles, except those forming the solid... angles. A, a, will divide the polyhedrons into triangular pyramids, similar to one another, and similarly sit- uated.
174 TnE ELEMENTS OF [book VT.
The pyramids thus formocl have each one solid anole at the common vertex A or a ; and these solid angles may be of three classes: Is^ those which have two of their faces coincidins with faces of one of the polyhedi'ons; 2f/, those which have only one face coinciding ; and 3o?, those which lie wholly with- in the solid angle A or a. Now those of the first kind in one of the polyhedrons are similar to the corresponding ones in the other, by the corollary to the twenty-first proposition of this Look ; and those of the second kind by the twenty-first From the polyhedrons take two of these similar ])yramids, and the remaining bodies will be similar, as the boundaries common to them and the pyramids are (VI.
What to read after Geometry the Elements of Euclid And Legendre Simplified And Arranged to Exclud?
You can find similar books in the "Read Also" column, or choose other free books by Lawrence S Lawrence Sluter Benson to read onlineMoreLess
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