| Church schools - 1844 - 456 pages
...its central length is 21 f. 5 i. ; What is the quantity of wood in cubic yards ? 1843. GEOMETRY. 2. **Parallelograms on the same base, and between the same parallels are equal.** 3. If in a circle two chords eat one another, prove that the rectangle contained by the segments of... | |
| Education - 1844 - 688 pages
.... . II '. . JUNIOR MODERATOR AND SENIOR EXAMINER. [The Differential Calculut it not to be wed.] 1 . **Parallelograms on the same base and between the same parallels are equal** to one another. 2. From a given circle to cut off a segment containing an angle equal to a given rectilineal... | |
| William Whewell - History - 1847 - 716 pages
...himself with the first twenty-six propositions of Euclid, and not till then, it becomes evident to him, **that parallelograms on the same base and between the same parallels are equal** ^ and he cannot even conceive the contrary. When he has a little further cultivated his geometrical... | |
| Cambridge univ, exam. papers - 1847 - 40 pages
...and x both lie between 0 and 1, prove that >x. i — a 3. In the figure of Euclid, Book i. Prop. 35, **(Parallelograms on the same base and between the same parallels are equal,)** if two diagonals be drawn to the two parallelograms respectively, one from each extremity of the base,... | |
| J. Goodall, W. Hammond - 1848 - 390 pages
...angles, or 180°; if two be known, they must be deducted from 180°, to leave the third. 2. " Prove **that parallelograms on the same base and between the same parallels are equal** to one another." Euclid i. 35. Tate, Art. 48. 3. " In any right-angled triangle the square which js... | |
| American Association for the Advancement of Science - Science - 1899 - 648 pages
...geometry, and in the 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... | |
| James Elliot - 1851 - 152 pages
...any scale : inscribe a circle in it, and circumscribe a circle about it. PROPOSITION LVI. THEOREM. **Parallelograms on the same Base and between the same Parallels are equal.** Let the two parallelograms ABCD and CDEF stand on the same base CD, and have their sides opposite CD... | |
| William Somerville Orr - Science - 1854 - 534 pages
...rectangles of their containing sides (AB-BC and DE'EF). Draw AG, DH, perpendiculars to BC, EF. Then because **parallelograms on the same base and between the same parallels are equal,** AC=AG'BC, and DF=DH-EF. Also the rectangles AG-BC, AB-BC having the same altitude BC, are to each other... | |
| Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...also their other angles equal, each to each, namely, those to which the equal sides are opposite, 2. **Parallelograms on the same base and between the same parallels are equal** to one another. 3. In any triangle, if the square of one of the sides is equal to the squares of the... | |
| Cambridge univ, exam. papers - 1856 - 252 pages
...two equal and parallel right lines towards the same parts, are also themselves equal and parallel. 6. **Parallelograms on the same base and between the same parallels, are .equal** to each other. 7. If a right line be divided into any two parts, the square of the whole line is equal... | |
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