| George Darley - Euclid's Elements - 1836 - 172 pages
...; and by the same ART. CGHD is also equal to CABD. Hence, EABF is equal to CGHD. This, &c. ART. 25. **Triangles upon the same base and between the same parallels are equal.** on the same base AC, and between —-77 the same parallels AC, DF. Then these triangles are equal.... | |
| John Playfair - Geometry - 1837 - 332 pages
...equal to the same EBCH : Therefore also the parallelogram ABCD is equal to EFGH. P PROP. XXXVII. THEOR. **Triangles upon the same base, and between the same...parallels, are equal to one another. Let the triangles ABC,** DBC be upon the same base BC, and between the same parallels, AD, BC : The triangle ABC is equal to... | |
| Euclid - Geometry - 1837 - 410 pages
...given, however, it is so useful, that the student should be early acquainted with it. PARALLELOGRAMS **upon the same base, and between the same parallels, are equal to one another. Let the** parallelograms ABCD, EBCF (figs. 2. and 3.) be upon the same base BC, and between the same parallels... | |
| Andrew Bell - Euclid's Elements - 1837 - 240 pages
...line, they are between the same parallels. (1. 33, Cor.) PBOPOSITION XXXV. THEOREM. Parallelograms **upon the same base and between the same parallels, are equal to one another. Let the** parallelograms ABCD, EBCF (see the 2d and 3d figures), be upon the same base BC, and between the same... | |
| Euclides - Euclid's Elements - 1837 - 112 pages
...3. that whole Z ^BD = whole Z DCA, 4. that A ABC = A BCD. PROPOSITION XXXV. Theorem. Parallelograms **upon the same base, and between the same parallels, are equal to** each other. (In Jig. 1, the ams are equal, because each is double of A BDC.) Steps of the Demonstration,... | |
| Charles Reiner - Geometry - 1837 - 246 pages
...are about the diagonal of a square are, likewise, squares. 6. Parallelograms and triangles which are **upon the same base and between the same parallels are equal to** each other. 7. Parallelograms and triangles which are upon equal bases and between the same parallels... | |
| Euclides - 1838 - 264 pages
...diameter BC divides the parallelogram ACDB into two equal parts. QKD PROP. XXXV. THEOR. Parallelograms **upon the same base, and between the same parallels, are equal to one another. Let the** parallelograms ABCD, EBCF be upon the same base BC, and between the same parallels AF, BC : the parallelogram... | |
| Thomas Holliday - Surveying - 1838 - 404 pages
...figure be equal, they will alto be parallel, and the figure will be a parallelogram. 3. Parallelograms **upon the same base and between the same parallels are equal to one another.** 4. A parallelogram is double the area of a triangle of the same base and altitude. See fig. 22, plate... | |
| Euclides - 1840 - 82 pages
...Parallelograms on equal bases and between the. same parallels, are equal. DG _H a )•: PROP. XXXVII. THEOR. **Triangles upon the same base and between the same parallels, are equal.** BC__DP PROP. XXXVIII. THEOR. Triangles upon equal bases and between the same parallels, are equal.... | |
| Euclides - 1841 - 378 pages
...therefore the parallelogram ABCD is equal to EFGH. Wherefore parallelograms, &c. QED PROP. XXXVII. THEOR. **Triangles upon the same base, and between the same parallels, are equal to one another.** BC, and between the same parallels AD, BC: the triangle ABC shall be equal to the triangle DBC. Produce... | |
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