| Robert Simson - Geometry - 1838 - 434 pages
...therefore parallel to BF. Wherefore, equal triangles, &c. QED PROP. XLJ. THEOR. IF a paralellogram and 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 EBC be upon the same base... | |
| Euclides - 1840 - 82 pages
...side of it, are between the same parallels. PROP. XLI. THEOR. If a parallelogram and a triangle are upon the same base and between the same parallels, the parallelogram is double of the triangle. DF PROP. XLII. PROB. To construct a parallelogram equal to a given triangle, and having an angle equal... | |
| London city mission - Christian socialism - 1840 - 620 pages
...themsehes are unknown." We know, for example, that if a parallelogram and a triangle be constructed on the same base, and between the same parallels, the parallelogram is double of the triangle : (Euc. 1.41 :) though we may know nothing more, whatever, about either of the figures. 2. " Two lines... | |
| Euclides - Geometry - 1841 - 378 pages
...parallelogram and a triangle be upon the same bose, and between the same parallels; the parallelogram shall be double of the triangle. Let the parallelogram ABCD...and the triangle EBC be upon the same base BC, and between the same parallels BC, AE; the parallelogram ABCD shall be double of the triangle EBC. Join... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...demonstrated that there is no other parallel to it but AD ; AD is therefore parallel to BF. PROP. XLI. THEOR. If a parallelogram and a triangle be upon the same base, and between the same parallel ; the parallelogram is double of the triangle. ID Let the parallelogram ABCD and the triangle... | |
| Euclides - 1842 - 316 pages
...therefore, parallel to BF. Wherefore equal triangles, &c. QED PROP. XLI. THEOR. IF a parallelogram and 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 EBC be upon the same base... | |
| William Pease - Geometry - 1843 - 80 pages
...BK equal to A B. Join DK, when ADK will be the triangle required. Reason : " If a parallelogram and triangle be upon the same base, and between the same...parallels, the parallelogram is double of the triangle." But the base AB is only half of the base AK ; therefore ADK is equal to ABC D. PROBLEM LXm. Any isosceles... | |
| John Playfair - Euclid's Elements - 1844 - 338 pages
...XLI. THEOR. If a parallelogram and a triangle be upon the same base, and between the same parallel; the parallelogram is double of the triangle. Let the...and the triangle EBC be upon the same base BC and between the same parallels BC, AE ; the parallelogram ABCD is double of the triangle EBC. ID PROP.... | |
| Euclid, James Thomson - Geometry - 1845 - 382 pages
...BF, but AD : AD is therefore parallel to BF. Wherefore, if equal triangles, &c. PROP. XLI. THEOR. — If a parallelogram and a triangle be upon the same...and the triangle EBC be upon the same base BC, and between the same parallels BC, AE ; the parallelogram is double of the triangle. • In this proposition... | |
| Euclid - Geometry - 1845 - 218 pages
...AD : AD is therefore parallel to BF. Wherefore equal triangles, &c. QED PROPOSITION XLI. THEOB. — If a parallelogram and a triangle be upon the same...and between the same parallels; the parallelogram shall be double of the triangle. Let the parallelogram ABCD and the triangle EBC be upon the same base... | |
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