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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q.e.d.
656. Cor. If the volume of a frustum of a triangular pyror mid is denoted by F, the lower base by 5, the upper base by &, and the altitude by JJ, V=-^Hx B-^iHxb-^iffx^Bxb = iHx(B-\-b-{- -y/Wxb).
320 BOOK VII. SOLID GEOMETRY.
Proposition XXI. Theorem.
657. The volume of the frustum of any pyramid is equal to the sum of the volumes of three pyramids whose corYvmon altitude is the altitude of the frustum, and whose bases are the lower base, the upper base, and the m£an proportional between ...the bases of the frustum.
i!
I Let B and b denote the lower and upper bases, H the altitude, and V the volume of the frustum ABCD-EF6I.
To prove that r = i H{B -\-h-\- VJ5 X h).
Proof. Let T-KLM be a triangular pyramid having the same altitude as S-ABCD and its base KLM equivalent to ABCD, and lying in the same plane. Then T-KLM ^ S-ABCD. § 653 Let the plane EFGI cut T-KLM in NOP.
Then NOP =o= EFGL § 648 Hence, T-NOP S-EFGL § 650 Hence, if we take away the upper pyramids, we have left the equivalent frustums NOP-KLM and EFGLABCD.
What to read after Solid Geometry?
You can find similar books in the "Read Also" column, or choose other free books by George Albert Wentworth to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
q.e.d.
656. Cor. If the volume of a frustum of a triangular pyror mid is denoted by F, the lower base by 5, the upper base by &, and the altitude by JJ, V=-^Hx B-^iHxb-^iffx^Bxb = iHx(B-\-b-{- -y/Wxb).
320 BOOK VII. SOLID GEOMETRY.
Proposition XXI. Theorem.
657. The volume of the frustum of any pyramid is equal to the sum of the volumes of three pyramids whose corYvmon altitude is the altitude of the frustum, and whose bases are the lower base, the upper base, and the m£an proportional between ...the bases of the frustum.
i!
I Let B and b denote the lower and upper bases, H the altitude, and V the volume of the frustum ABCD-EF6I.
To prove that r = i H{B -\-h-\- VJ5 X h).
Proof. Let T-KLM be a triangular pyramid having the same altitude as S-ABCD and its base KLM equivalent to ABCD, and lying in the same plane. Then T-KLM ^ S-ABCD. § 653 Let the plane EFGI cut T-KLM in NOP.
Then NOP =o= EFGL § 648 Hence, T-NOP S-EFGL § 650 Hence, if we take away the upper pyramids, we have left the equivalent frustums NOP-KLM and EFGLABCD.
What to read after Solid Geometry?
You can find similar books in the "Read Also" column, or choose other free books by George Albert Wentworth to read onlineMoreLess
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