 | John Playfair - 1819 - 354 pages
...it but AD ; AD is therefore parallel to BF. Wherefore eqaal triangles, tc. Q, ED PROP. XLI. THEOR. If a parallelogram and a triangle be upon the same base, and between the same parallels ; the parallelogram is double of the triangle. Let the parallelogram ABCD and the triangle... | |
 | George Lees - 1826 - 276 pages
...parallelograms ; hence triangles upon the same base, and between the same parallels, are equivalent. Cor. 2. If a parallelogram and a triangle be upon the same base, and between the same parallels, the parallelogram is double of the triangle. Cor. 3. Equivalent triangles upon the same... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...to it but AD: AD is therefore parallel to BF. Wherefore equal triangles, &c. QED PROP. XLI. THEOR. If a parallelogram and a triangle be upon the same base, and bet-ween the same parallels ; the parallelogram shall be double of the triangle. Let the parallelogram A BCD and the... | |
 | Euclides - 1834 - 518 pages
...; AD is therefore parallel to BF. Wherefore, equal triangles, &c. 9. ED PROPOSITION XLI. THEOR. — If a parallelogram and a triangle be upon the same base, and between the same parallels, the parallelogram shall be double of the triangle. Let the parallelogram ABCD and the triangle... | |
 | Mathematics - 1835 - 684 pages
...The squares of equal straight lines are equal to one another: and conversely. PROP. 26. (Eue. i. 41.) If a parallelogram and a triangle be upon the same base and between the same parallels, the parallelogram shall be double of the triangle. Let the parallelogram ABCD and the triangle... | |
 | George Darley - Euclid's Elements - 1836 - 172 pages
...way, it may be proved that BG is not greater than EH. Hence BG and EH are equal. This, &c. ART. 31. If a parallelogram and a triangle be upon the same base, and between the same parallels, the parallelogram is double of the triangle. on the same base AC as the triangle ABC, and... | |
 | Mathematics - 1836 - 488 pages
...side of bases, which are equal and in the same straight line, are between the same parallels. XLI. If a parallelogram and a triangle be upon the same base, and between the same parallels; the parallelogram is double of the triangle. XLIII. The complements of the parallelograms... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...parallel to BF, but AD: AD is therefore parallel to BF. Wherefore equal triangles, &c. PROP. XLI. THEOR. IF a parallelogram and a triangle be upon the same base, and between the same parallels ; the parallelogram is double of the triangle. Let the parallelogram A BCD and the triangle... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...= greater, which shows the supposition to be false, 3. that .'. AD || BF. PROPOSITION XLI. Theorem. If a parallelogram and a triangle be upon the same base, and between the same parallels; the parallelogram shall be double of the triangle. Proved by showing that C3m BD = 2 A ABC,... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...are equal ; and if the areas and altitudes be equal, the bases are equal. PROPOSITION XLI. THEOREM. If a parallelogram and a triangle be upon the same base, and between the same parallels, the parallelogram shall be double of the triangle. X 3<5 ELEMENTS OF PLANE GEOMETRY. AE,... | |
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If a parallelogram and a triangle be upon the same base, and between the same parallels; the parallelogram shall be double of the triangle. 
