 | Adrien Marie Legendre - 1828 - 346 ページ
...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,... | |
 | Adrien Marie Legendre - 1837 - 376 ページ
...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... | |
 | James Bates Thomson - 1844 - 268 ページ
...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,... | |
 | Nathan Scholfield - 1845 - 894 ページ
...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... | |
 | Charles Davies - 1849 - 372 ページ
...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... | |
 | Adrien Marie Legendre - 1852 - 436 ページ
...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.... | |
 | Charles Davies - 1854 - 436 ページ
...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.... | |
 | Adrien Marie Legendre, Charles Davies - 1857 - 442 ページ
...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.... | |
 | Benjamin Greenleaf - 1862 - 532 ページ
...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,... | |
 | Benjamin Greenleaf - 1861 - 638 ページ
...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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Two rectangles having equal altitudes are to each other as their bases. 
