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" Two rectangles having equal altitudes are to each other as their bases. "
Elements of Geometry and Trigonometry: With Practical Applications - Page 77
by Benjamin Greenleaf - 1862 - 490 pages
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School Science and Mathematics, Volume 18

Education - 1918 - 990 pages
...and not a vague largeness. It is a very common inconsistency a little later to attempt to prove that "Two rectangles having equal altitudes are to each other as their bases" in the following manner: Call the two rectangles R and S, respectively. Assuming the bases commensurable,...
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Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 440 pages
...triangle, rectangle, etc., are frequently used for area of triangle, etc. PROPOSITION I. THEOREM 395 Two rectangles having equal altitudes are to each other as their bases. DE HYPOTHESIS. The rectangles ABCD and EFGH have equal altitudes, AB and EF. CONCLUSION. ABCD : EFGH...
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Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 431 pages
...triangle, rectangle, etc., are frequently used for area of triangle, etc. PROPOSITION I. THEOREM 395 Two rectangles having equal altitudes are to each other as their bases. DE HYPOTHESIS. The rectangles ABCD and EFGH have equal altitudes, AB and EF. CONCLUSION. ABCD : EFGH...
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New Plane Geometry

Webster Wells - Geometry, Plane - 1908 - 206 pages
...the radical sign ; then, 2x=mV5—m; and x (or AC) = BOOK IY ABBAS OP POLYGONS PROP. I. THEOREM 275. Two rectangles having equal altitudes are to each other as their bases. The words "rectangle," "parallelogram," "triangle," etc., in the propositions of Book IV, mean the...
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New Plane and Solid Geometry

Webster Wells - Geometry - 1908 - 338 pages
...the radical sign ; then, 2a;=mV5-m; and x (or AC) = BOOK TY AREAS OF POLYGONS PROP. I. THEOREM 275. Two rectangles having equal altitudes are to each other as their bases. The words "rectangle," "parallelogram," "triangle," etc., in the propositions of Book IV, mean the...
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Elements of Plane Geometry

William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...equal. 275 EFGH EH ABCD AD' QED 417. COE. Because any side of a rectangle may be taken as the base, two rectangles having equal altitudes are to each other as their bases. Ex. 347. Find the bisectors of the triangle whose sides are, respectively, 18, 20, and 22 ft. Ex. 348....
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Wentworth's Plane Geometry

George Albert Wentworth, David Eugene Smith - Geometry, Plane - 1910 - 287 pages
...identically equal," the word equal is often used to mean "equivalent." PROPOSITION I. THEOREM 316. Two rectangles having equal altitudes are to each other as their bases. A x BAX F Given the rectangles AC and AF, having equal altitudes AD. To prove that D AC: D AF = base...
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Plane Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 328 pages
...~^-- 480. Cor. m. (a) Two rectangles having equal bases are to each other as their altitudes, and (6) two rectangles having equal altitudes are to each other as their bases. — . — — OUTLINE OF PROOF — fr ' ft _ ft ~ ^ ' ft Sf~bh'~h'- ~B>~V~^h~VEx. 803. Draw a rectangle...
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The Teaching of Geometry

David Eugene Smith - Geometry - 1911 - 358 pages
...the vicinity offers all the outdoor work that is needed to make Book IV seem very important. THEOREM. Two rectangles having equal altitudes are to each other as their bases. Euclid's statement (Book VI, Proposition 1) was as follows: Triangles and parallelograms which are...
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College Entrance Examination Papers in Plane Geometry

Geometry, Plane - 1911 - 192 pages
...circle the product of the segments of one chord is equal to the product of the segments of the other. 5. Two rectangles having equal altitudes are to each other as their bases. 6. Two similar polygons are to each other as the squares of their homologous sides. 7. The line joining...
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