Elements of Synthetic Solid Geometry
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In our eReader you can find the full English version of the book. Read Elements of Synthetic Solid Geometry 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 Elements of Synthetic Solid Geometry
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AA', BB 1, etc. , are the diagonals of a ppd. Show that a plane through DBC' cuts off a pyramid which is one-sixth the ppd.
12. The direction edges of a ppd. Are a, b, c, and the angles between them are Z (be) = X, Z (ca) = /u, Z (aft) v. Then the vol. Is abc Y/ { 1 cos 2 X cos 2 /j. Cos 2 v + 2 cos X cos p cos v}. OA, OB, OC are the direction edges; Z COB = X, Z COA = M, ZAOB = v.
Let CP be normal to the plane of A OB, and PQ, PE be J_s upon OA and OB.
vol. Of ppd. = OA- OB sin v CP.
(P. Art. ...215. ) ot OQPR are concyclic, and OP is a diameter of the circumcircle ; (P. Art. 228. ) and But and CT=V(L~ \ sin 2 v) sm v ' vol. = ab -v/( c2 s i n2 * ~ QR 2 )- QR 2 = OO, 2 + OR 2 - '20Q OR cos v ; OQ 2 = c 2 cos 2 fi, and O. R 2 = c 2 cos 2 X.
REGULAR POLYHEDKA. 123 Whence, by substitution, vol. = abc - x /{ 1 cos 2 X cos 2 fj. Cos 2 v + 2 cos X cos p cos v}. 1 13. Show from the character of the result in Ex. 12 that if in fcny ppd. X, /*, v are all acute, all vertices except the one opposite have one acute and two obtuse angles, etc.
What to read after Elements of Synthetic Solid Geometry?
You can find similar books in the "Read Also" column, or choose other free books by N F Nathan Fellowes Dupuis to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
AA', BB 1, etc. , are the diagonals of a ppd. Show that a plane through DBC' cuts off a pyramid which is one-sixth the ppd.
12. The direction edges of a ppd. Are a, b, c, and the angles between them are Z (be) = X, Z (ca) = /u, Z (aft) v. Then the vol. Is abc Y/ { 1 cos 2 X cos 2 /j. Cos 2 v + 2 cos X cos p cos v}. OA, OB, OC are the direction edges; Z COB = X, Z COA = M, ZAOB = v.
Let CP be normal to the plane of A OB, and PQ, PE be J_s upon OA and OB.
vol. Of ppd. = OA- OB sin v CP.
(P. Art. ...215. ) ot OQPR are concyclic, and OP is a diameter of the circumcircle ; (P. Art. 228. ) and But and CT=V(L~ \ sin 2 v) sm v ' vol. = ab -v/( c2 s i n2 * ~ QR 2 )- QR 2 = OO, 2 + OR 2 - '20Q OR cos v ; OQ 2 = c 2 cos 2 fi, and O. R 2 = c 2 cos 2 X.
REGULAR POLYHEDKA. 123 Whence, by substitution, vol. = abc - x /{ 1 cos 2 X cos 2 fj. Cos 2 v + 2 cos X cos p cos v}. 1 13. Show from the character of the result in Ex. 12 that if in fcny ppd. X, /*, v are all acute, all vertices except the one opposite have one acute and two obtuse angles, etc.
What to read after Elements of Synthetic Solid Geometry?
You can find similar books in the "Read Also" column, or choose other free books by N F Nathan Fellowes Dupuis to read onlineMoreLess
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