Solid Geometry
Solid Geometry
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In our eReader you can find the full English version of the book. Read 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 Solid Geometry
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635. In the figure on p. 296, suppose Z ABC a right angle, AB=iZ 'm.,AC = 6 in., VB = 10 in., and the areaof A^'^C" = 12 sq. in.; find the length of VBT, 298 SOLID GEOMETRY. [BK.Vn.
4. THE MBlfSUfiATIOlf OF THE PRISM.
403. Definition. The area of the prismatic surface of a prism is called the lateral area of the prism.
Similarly for the pyramid, and for the cylinder and cone, to be defined hereafter.
Proposition VII.
404. Theorem. The lateral area of a prum equah the product of an edge and the ...perimeter of a right section.
Given the prism P ; a right section R with sides Si, *„ ; /i,/a, the faces of the prism; e, an edge.
To prove that the lateral area of P is e • (si -f «, -f ).
Proof. 1. '.'by definition of right section, R±e,.'.8i±e, § 339 2. \'fi, /a, are ZI7, Prop. V, cor. 2 .*. area/i = e-Si, V, prop. II, cor. 3 3. And '.* the edges are equal, Prop. V, cor. 3 .'. area f2 = e-Sz, and so for the other faces.
4. .'.lateral area = esi + 0-S2 + = e'(«i + «2+ ).
Ax. 2 Sec. 405.] THE MENSURATION OF THE PRISM, 299 405.
What to read after Solid Geometry?
You can find similar books in the "Read Also" column, or choose other free books by William Betz to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
635. In the figure on p. 296, suppose Z ABC a right angle, AB=iZ 'm.,AC = 6 in., VB = 10 in., and the areaof A^'^C" = 12 sq. in.; find the length of VBT, 298 SOLID GEOMETRY. [BK.Vn.
4. THE MBlfSUfiATIOlf OF THE PRISM.
403. Definition. The area of the prismatic surface of a prism is called the lateral area of the prism.
Similarly for the pyramid, and for the cylinder and cone, to be defined hereafter.
Proposition VII.
404. Theorem. The lateral area of a prum equah the product of an edge and the ...perimeter of a right section.
Given the prism P ; a right section R with sides Si, *„ ; /i,/a, the faces of the prism; e, an edge.
To prove that the lateral area of P is e • (si -f «, -f ).
Proof. 1. '.'by definition of right section, R±e,.'.8i±e, § 339 2. \'fi, /a, are ZI7, Prop. V, cor. 2 .*. area/i = e-Si, V, prop. II, cor. 3 3. And '.* the edges are equal, Prop. V, cor. 3 .'. area f2 = e-Sz, and so for the other faces.
4. .'.lateral area = esi + 0-S2 + = e'(«i + «2+ ).
Ax. 2 Sec. 405.] THE MENSURATION OF THE PRISM, 299 405.
What to read after Solid Geometry?
You can find similar books in the "Read Also" column, or choose other free books by William Betz to read onlineMoreLess
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