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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: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 320 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 D * c two rectangles having the common altitude AD ; they are to each other as their...
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Elements of Geometry and Trigonometry;: With Practical Applications

Benjamin Greenleaf - Geometry - 1863 - 502 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 bases and altitudes are equivalent. PROPOSITION III.—THEOREM. 222. Two rectangles having equal altitudes are to each other as their bases. Let ABCD,...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1866 - 328 pages
...the parallelogram ABEP (Prop. XXXI. Cor. 1, Bk. I.) ; hence the triangle ABE is equivalent to hah0 the parallelogram ABCD (Art. 34, Ax. 7). 220. Cor....equal altitudes are to each other as their bases. Let ABC D, AEFD be DF c two rectangles having the common altitude AD ; they are to each other as their...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - 1868 - 338 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...which have equal bases and altitudes are equivalent. V PROPOSITION III. — THEOREM. 222. Two rectangles having equal altitudes are to each other as their...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1869 - 516 pages
...half a rectajigle having tlie same base and altitude, or to a rectangle either having the same base and half of the same altitude, or having the same...having equal altitudes are to each other as their basest LetABCD, AEFD be D rc two rectangles having the common altitude AD; they are to each other as...
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Elements of Geometry and Trigonometry: With Applications in Mensuration

Charles Davies - Geometry - 1870 - 319 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...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

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...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

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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New Elementary Geometry: With Practical Applications ; a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1873 - 202 pages
...triangle ABE is equivalent to half the parallelogram ABCD (26, Ax. 7). BOOK IV. having the same base and half of the same altitude, or having the same altitude and half of the same base. 183. Cor. 2. All triangles which have equal bases and altitudes are equivalent. THEOREM III. 184. Two...
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New Elementary Geometry: With Practical Applications : a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1874 - 206 pages
...hence the triangle ABE is equivalent to half the parallelogram A BCD (26, Ax. 7). having the same base and half of the same altitude, or having the same altitude and half of the same base. 183. Cor. 2. All triangles which have equal bases and altitudes are equivalent. THEOREM III. 184. Two...
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