| 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 - 442 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 - 1861 - 638 pages
...All triangles which have equal bases and altitudes are equivalent. PROPOSITION III. — THEOREM. 222. **Two rectangles having 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... | |
| Benjamin Greenleaf - Geometry - 1862 - 518 pages
...All triangles which have equal bases and altitudes are equivalent. PROPOSITION III. — THEOREM. 222. **Two rectangles having equal altitudes are to each other as their bases.** LetABCD, AEFD be DF c two rectangles having the common altitude AD ; they arc to each other as their... | |
| Benjamin Greenleaf - Geometry - 1863 - 504 pages
...All triangles which have equal bases and altitudes are equivalent. PROPOSITION III. — THEOREM. 222. **Two rectangles having equal altitudes are to each other as their bases.** Let ABCD, AEFD be D * c two rectangles having the common altitude AD ; they are to each other as their... | |
| Benjamin Greenleaf - Geometry - 1868 - 340 pages
...triangles which have equal bases and altitudes are equivalent. V PROPOSITION III. — THEOREM. 222. **Two rectangles having equal altitudes are to each other as their bases.** Let ABCD, AEFD be DFC two rectangles having the common altitude AD ; tbcy are to each other as their... | |
| Charles Davies - Geometry - 1870 - 392 pages
...squares on equal lines are equal. For a square is but a rectangle having its sides equal. THEOREM V. **Two rectangles having equal altitudes are to each other as their bases.** Let AEFD&nAEBCF be two JD rectangles having the common altitude AD ; then will they be to each other... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...unit. 2. Definition. Equivalent figures are those whose areas are equal. PROPOSITION I— THEOREM. 3. **Two rectangles having equal altitudes are to each other as their bases.** Let ABCD, AEFD, be two rectangles having equal altitudes, AB and AE their bases ; then, ABCD _AB AEFD... | |
| William Chauvenet - Geometry - 1872 - 382 pages
...unit. 2. Definition. Equivalent figures are those whose areas are equal. PROPOSITION I.— THEOREM. 3. **Two rectangles having equal altitudes are to each other as their bases.** Let ABCD, AEFD, be two rectangles having equal altitudes, AB and AE their bases ; then, ABCD _ AB AEFD... | |
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