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