| Euclides - 1858 - 248 pages
...the opposite sides are parallel, and the diagonal joins opposite angles. DEMONSTRATION. — P. 35. **Parallelograms on the same base and between the same parallels are equal.** P. 34. The opposite sides and angles of parallelograms are equal, and the diameter bisects them. Ax.... | |
| War office - 1858 - 578 pages
...simple interest ? Euclid 1. The greater side of every triangle is opposite to the greater angle. 2. **Parallelograms on the same base and between the same parallels are equal** to one another. VOLUNTARY PORTION. (1 .) "When are two magnitudes said to be equimultiples of two other... | |
| William Whewell - Philosophy - 1860 - 604 pages
...himself with the first twenty-rix 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... | |
| Euclides - 1861 - 464 pages
...intervenes ; 5, to divide a / — 7 into two eq. pts. from a • in one of the sides, &c. 35. 113. **Parallelograms on the same base and between the same parallels are equal,** or rather equivalent, to one another. SCH. — The equality of / 7s proved by the Method of Indivisibles.... | |
| Dublin city, academic inst - 1862 - 32 pages
...line apply a parallelogram equal to a given triangle, and having an angle equal to a given one. 3. **Parallelograms on the same base and between the same parallels are equal.** 4. Suclid says the external angles of any rectilinear figure are together equal to two right angles... | |
| University of Oxford - Education, Higher - 1863 - 316 pages
...rectangle contained by the whole and one of the parts may be equal to the square on the other part. 9. **Parallelograms on the same base and between the same parallels are equal** to one another. 10. In any right-angled triangle, the square which is described on the side subtending... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...parallelogram ACDB into two equal parts. Wherefore, the opposite sides &c. QED PROPOSITION 35. THEOREM. **Parallelograms on the same base, and between the same parallels, are equal** to one another. Let the parallelograms ABCD, EBCF be on the same base BC, and between the sameparallels... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...parallelogram ACDB into two equal parts. Wherefore, the opposite aides &c. QED PROPOSITION 35. THEOREM. **Parallelograms on the same base, and between the same parallels, are equal** to one another. Let the parallelograms A BCD, EBCF be on the same base BC, and between the sameparallels... | |
| Alexander Bain - Logic - 1870 - 478 pages
...of Deduction. Let us assume that a certain proposition has been arrived at, "no matter how, say, ' **Parallelograms on the same base, and between the same parallels, are equal.'** Now any one considering this proposition might readily see, that the axiom of mediate equality applied... | |
| Euclides - 1871 - 136 pages
...the four triangles, into which a parallelogram is divided by its diagonals, are equal to each other. **Parallelograms on the same base and between the same parallels are equal.** Let the OĢ ABCD, EBCF be on the same base BC, and between the same \\s AF, BC. Then must rjABCD= CASE... | |
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