| 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,... | |
| 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... | |
| 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,... | |
| 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... | |
| 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... | |
| 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.... | |
| 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.... | |
| 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.... | |
| 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,... | |
| 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... | |
| |