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" Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is to say, as the products of their three dimensions. "
Elements of Geometry: With Practical Applications to Mensuration - Page 199
by Benjamin Greenleaf - 1863 - 320 pages
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Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 431 pages
...multiplied by their common altitude ; or ABODE x H. That is, V = B x H. QED 639 COROLLARY. Prisms are to each other as the products of their bases by their altitudes ; prisms having equivalent bases are to each other as their altitudes ; prisms having equal altitudes...
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Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 440 pages
...multiplied by their common altitude ; or ABCDE x H. That is, V = B x H. 0, ED 639 COROLLARY. Prisms are to each other as the products of their bases by their altitudes ; prisms having equivalent bases are to each other as their altitudes ; prisms having equal altitudes...
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Plane Geometry

Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...equal bases are to each other as their altitudes. Proof: CO377. THEOREM. Any two parallelograms are to each other as the products of their bases by their altitudes. Proof: (?). 378. THEOREM. The area of a triangle is equal to half the product of its base by its altitude....
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Geometry: Plane Trigonometry. Chain Surveying. Compass Surveying. Transit ...

International Correspondence Schools - Building - 1906
...rectangles having equal bases are to each other as their altitudes. 41. The areas of any two rectangles are to each other as the products of their bases by their altitudes. Let A and B, Fig. 27, be two rectangles whose altitudes are a and a' and whose bases are b and 6',...
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Plane and Solid Geometry

Edward Rutledge Robbins - Geometry - 1907 - 412 pages
...equal bases are to each other as their altitudes. Proof: (?). 377. THEOREM. Any two parallelograms are to each other as the products of their bases by their altitudes. Proof: (?). 378. THEOREM. The area of a triangle is equal to half the product of its base by its altitude....
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New Plane and Solid Geometry

Webster Wells - Geometry - 1908 - 338 pages
...bases. 3. Two prisms having equivalent bases are to each other as their altitudes. 4. Any two prisms are to each other as the products of their bases by their altitudes. ' Ex. 18. The volume of a right prism whose base is a regular hexagon is 600. One side of the base...
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New Plane Geometry

Webster Wells - Geometry, Plane - 1908 - 208 pages
...having equal bases are to each other as their altitudes. PROP. II. THEOREM 277. Any two rectangles are to each other as the products of their bases by their altitudes. If a y a R L _j PLANE GEOMETRY — BOOK IV Draw any two rectangles M and N. We then have : Given M...
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Wentworth's Plane Geometry

George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...parallelograms having equal altitudes are to each other as their bases; any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM 325. The area of a triangle is equal to half the product of its base by its...
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College Entrance Examination Papers in Plane Geometry

Geometry, Plane - 1911 - 192 pages
...a tangent is measured by one-half the difference of the intercepted arcs. 6. Any two rectangles are to each other as the products of their bases by their altitudes. 7. The area of a circle is equal to one-half the product of its circumference and radius. 8. A regular...
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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 500 pages
...limit. OAF as AP varies in value and Case1 QED are to PROPOSITION II. THEOREM 318. Two rectangles are to each other as the products of their bases by their altitudes. b' b Given the rectangles R and R', having for the numerical measure of their bases b and b', and of...
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