 | 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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The areas of two rectangles having equal altitudes are to each other as their bases. 
