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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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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 346 pages
...CB, and the same altitude AO : for the rectangle BCEF is equivalent to the parallelogram ABCD. 170. Cor. 2. All triangles, which have equal bases and altitudes, are equivalent. THEOREM. 171. Two rectangles having the same altitude, are to each other as their bases. Let ABCD,...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1837 - 359 pages
...same altitude AH : for the rectangle ABGH is equivalent to the parallelogram ABCD (Prop. I. Cor.). Cor. 2. All triangles, which have equal bases and altitudes, are equivalent, being halves of equivalent parallelograms. PROPOSITION III. THEOREM. Two rectangles having the name...
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - Geometry - 1844 - 237 pages
...same altitude. EB AO : for the rectangle BCEF is equivalent to the parallelogram ABCD. (1.4. Cor.) Cor. 2. All triangles, which have equal bases and...altitudes, are equivalent. PROPOSITION III. THEOREM. Two rectangles ABCD, AEFD having the same altitude AD, are to each other as their bases, AB, AE. Suppose,...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 894 pages
...base CB, and the same altitude AO: for the rectangle BCEF is equivalent to the parallelogram ABCD. Cor. 2. All triangles, which have equal bases and altitudes, are equivalent. Cor. 3. Hence triangles having equal altitudes are to each other as their bases; conversely, triangles...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 384 pages
...same altitude AH : for the rectangle ABGH is equivalent to the parallelogram ABCD (Prop. I. Cor.). Cor. 2. All triangles, which have equal bases and altitudes, are equivalent, being halves of equivalent parallelograms. PROPOSITION HI. THEOREM. Two rectangles having the same...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...proportion cannot be less than AE; therefore, being neither greater nor less, it is equal to AE. Hence, any two rectangles having equal altitudes, are to each other as their bases. PROPOSITION IV. THEOEEM. Any two rectangles are to each other as the products of their bases and altitudes....
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...proportion cannot be less than AE; therefore, being neither greater nor less, it is equal to AE. Hence, any two rectangles having equal altitudes, are to each other as their bases. PROPOSITION IV. THEOREM. Any two rectangles are to each other as the products of their bases and altitudes....
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre ...

Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 444 pages
...proportion cannot be less than AE; therefore, being neither greater nor less, it is equal to AE. Hence, any two rectangles having equal altitudes, are to each other as their bases. PROPOSITION IV. THEOREM. Any two rectangles are to each other as the products of the'r bases and altitudes....
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 514 pages
...to half a rectangle having the same base and altitude, or to a rectangle cither having the same base and half of the same altitude, or having the same...two rectangles having the common altitude AD ; they are to each other as their bases AB, A E. AEB First. Suppose that the bases AB, AE are commensurable,...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 628 pages
...to half a rectangle having the same base and altitude, or to a rectangle either having the same base and half of the same altitude, or having the same...equal altitudes are to each other as their bases. Let ABCD, AEFD be DF c two rectangles having the common altitude AD ; they are to each other as their...
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