| J. Goodall, W. Hammond - 1848
...point out how the construction fails when that condition is not fulfilled. 2. Prove that parallelograms **upon the same base and between the same parallels are equal to one another.** Show hence that the area of a parallelogram is properly measured by the product of the numbers that... | |
| Great Britain. Committee on Education - 1848
...point out how the construction fails when that condition is not fulfilled. 2. Prove that parallelograms **upon the same base and between the same parallels are equal to one another.** Shew hence that the area of a parallelogram is properly measured by the product of the numbers that... | |
| Great Britain. Council on Education - 1848
...point out how the construction fails when that condition is not fulfilled. 2. Prove that parallelograms **upon the same base and between the same parallels are equal to one another.** Shew hence that the area of a parallelogram is properly measured by the product of the numbers that... | |
| Thomas Tate (mathematical master.) - 1848
...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 - 108 Seiten
...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
...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... | |
| ...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
...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
...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... | |
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