| Euclid, Robert Simson - Geometry - 1821 - 516 pages
...BCD, and the diameter BC divides the parallelogram ACDB into two equal parts. QED PROP. XXXV. THEOR. **PARALLELOGRAMS upon the same base, and between the...to one another.* "Let the parallelograms ABCD, EBCF** be upon the same base BC, and between the same parallels AF, BC; the parallelogram ABCD shall be equal... | |
| Peter Nicholson - Mathematics - 1825 - 372 pages
...triangle DBC. Wherefore triangles, &c. QED Propoķiķion XXXVIII. Theorem. Triangles upon equal bases, **and between the same parallels, are equal to one another. Let the** triangles ABC, DEF be upon equal bases BC, EF, and between the same parallels BF, AD : The triangle... | |
| Euclid - 1826 - 180 pages
...shall the two trapeziums be equal to one another. PROPOSITION XXXVII. THEOREM. Triangles constituted **upon the same base, and between the same parallels, are equal to one another. Let the** triangles ABC, DBC, be constituted upon the same base вс, and between the same parallels AD, вс.... | |
| Euclides - 1826
...shall the two trapeziums be equal to one another. PROPOSITION XXXVII. THEOREM. Triangles constituted **upon the same base, and between the same parallels, are equal to one another.** » 3i. i. parallel to сл, " and through c draw CF, parallel to в D. Therefore each of them EBCA,... | |
| Robert Simson - Trigonometry - 1827 - 513 pages
...and the diameter BC divides the parallelogram ACDB into two equal parts.' ei. ED PROP. XXXV. THEOR. **Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the** parnllelograms ABCD, EBCF be upon the same base BC, and between the same parallels AF, BC : the parallelogram... | |
| John Playfair - Geometry - 1829 - 186 pages
...to each other. Therefore, parallelograms &c. QED ED. PROPOSITION XXXVII. THEOREM, Triangles on the **same base, and between the same parallels, are equal to one another;** that is, their surfaces are equal. Let the triangles ABC, DBC be on the same base BC, and between the... | |
| Pierce Morton - Geometry - 1830 - 272 pages
...a rectangle of the same base and altitude. PROP. 25. (Eue. i. 36.) Parallelograms upon equal bases, **and between the same parallels, are equal to one another. Let the** parallelogramsABCD, E FGH, be upon equal bases BC, FG, and between the same parallels AH, BG. The parallelogram... | |
| John Martin Frederick Wright - Astronomy - 1831
...shall be equal to an nth part of the weight of the body. TRINITY COLLEGE, 1827. 1. PARALI/ELLOGRAMS **upon the same base, and between the same parallels, are equal to one another.** 2. If a straight line be divided in extreme and mean rate, the parts into which it is divided are incommensurable... | |
| Augustus De Morgan - 1831
...BGHA and BPKD are four- sided figures &c. (Construction.) .-. BGHA and BPKD are parallelograms. IX. **Parallelograms upon the same base and between the same parallels are equal.** (Proved.) EBAFandBGHA, are parallelograms &c. (Construction.) .•. EBAF and BGHA are equal. X. Parallelograms... | |
| Thomas Perronet Thompson - Euclid's Elements - 1833 - 150 pages
...parallelograms upon equal bases, &c. Which was to be demonstrated. PROPOSITION XXXVII. THEOREM. — Triangles **upon the same base, and between the same parallels, are equal to one another. Let the** triangles ABC, DEC be upon the same base BC, and between the same paral- EADF lels AD, BC. The triangle... | |
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