| Thomas Tate (mathematical master.) - 1848 - 284 pages
...ADGK = the parallelogram ADCB; therefore the triangle ADF is also = half the parallelogram ADCB. Cor. **Triangles upon the same base and between the same parallels are equal.** Application of this Theorem. 1. To show that the rectangle BCGF _—^— A o contains double the surface... | |
| Euclid, Thomas Tate - 1849 - 120 pages
...diameter BC divides the parallelogram ACDB into two equal parts. QED PROP. XXXV. THEOR. 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... | |
| American Association for the Advancement of Science - 1899 - 648 pages
...third part a strict treatment of equivalence. Even Euclid, in proving his I. 35, "Parallelograms on the **same base, and between the same parallels, are equal to one another,"** does not show that the parallelograms can be divided into pairs of pieces admitting of superposition... | |
| 582 pages
...possess in being situated as they are. EUCLID AND MECHANICS. First Year Student*. 1. Parallelograms **upon the same base and between the same parallels are equal to one another,** 2. If a straight line be divided into any two parts, the squares of the whol« line, and of one of... | |
| 1851
...Prove that the three angles of a triangle are equal to two right angles, .... — 10 3 2. Prove that **triangles, upon the same base, and between the same parallels, are equal,** 12 1 3. Describe a square upon a given straight line, . 11 2 4. Divide a given straight line in medial... | |
| Euclides - 1852 - 152 pages
...the sake of practice, be proved with the accompanying figure.] AB PROP. XXXV. THEOK. 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... | |
| Euclides - 1852 - 48 pages
...35.) ; therefore the parallelograms ABCD and EFGH are equal (Ax. 1.). WWD РBОР. XXXVП. ТнЕОB. **Triangles upon the same base and between the same parallels are equal.** Let the triangles в A c and в D c be on the same base в c, and between the same parallels в c and... | |
| Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...BC divides the parallellogram ACDB into two equal parts. QED PROPOSITION XXXV. THEOR. Parallelograms **upon the same base, and between the same parallels, are equal to one another. Let the** parallelograms ABCD, KBCF be upon the same base BC, and between the same parallels AF; BC : the parallelogram... | |
| Euclides - Geometry - 1853 - 176 pages
...divides the parallelogram a С db into two equal parts. QED PROPOSITION XXXV. — THEOREM. Parallelograms **upon the same base, and between the same parallels, are equal to one another. LET the** parallelograms abСd, ebСf (see the second figure) be upon the same base b С, andbetween the same... | |
| Euclides - 1853 - 146 pages
...diameter BC divides the parallelogram ACDB into two equal parts. QED PROP. XXXV. THEOREM. 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... | |
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