| Architecture - 1865 - 276 pages
...Given the vertical angle, and a side to construct the triangle. 3. Prop. 35. Theorem. Parallelograms **upon the same base and between the same parallels are equal to one another.** Shew this is equally true of triangles. 4. Prop. 44. — Problem. To a given straight line to apply... | |
| Euclides - 1865 - 402 pages
...BC divides the parallelogram ACI>B into two equal parts. QED PROP. XXXV.— THEOREM. Parallelograms **upon the same base, and between the same parallels, are equal to** each other. (References— Prop. I 4, 29, 34 ; ax. 1, 3, 6.) Let the parallelograms ABCD, EBCF, be... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...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 AF,BC: the parallelogram... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...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 AF, BC : the parallelogram... | |
| 1868 - 886 pages
...triangle be produced, the exterior nngle is greater than cither of the interior opposite angles 15 i 2. **Triangles upon the same base, and between the same parallels, are equal to one another** 15 3. In any right -angled triangle, the square \rhieh is described upon the side subtending the right... | |
| Robert Potts - 1868 - 434 pages
...Therefore, parallelograms upon equal, &c. QEJO. PROPOSITION XXXVII. THEOREM. Triangles upon the tame **base and between the same parallels, are equal to one another. Let the triangles ABC,** DBCbe upon the same base BC, and between the same parallels AD, BC. Then the triangle ABC shall be... | |
| Ellis A. Davidson - Mechanical drawing - 1869 - 140 pages
...not necessarily be of the same shape to be of equal area, and by Euclid* (Book I., prop, xxxvii.), " **Triangles upon the same base, and between the same parallels, are equal."** If, therefore, lines be drawn from ABCDE and F to G, five triangles will be formed, having the same... | |
| E. M. Reynolds - Geometry - 1868 - 172 pages
...the parallelogram A CBF. Then ACBF = DBCE. But ABC is half of ACBF; therefore of DBCE. THEOREM IV. **Triangles upon the same base and between the same parallels are equal.** For each is half of any parallelogram on that base and between those parallels. COR. 1. Triangles upon... | |
| Great Britain. Education Department. Department of Science and Art - 1869 - 98 pages
...Extract the square root of 141 • 7 to two places of decimals. (10.) *3. Show that parallelograms and **triangles upon the same base and between the same parallels are equal to one another.** (10.) 23 5. Angles in the same segment of a circle are equal to one another. *6. Divide a" — SaV... | |
| Euclides - 1870 - 270 pages
...points. P. 31. Through a given point to draw a st. line parallel to a given st. line. DEM. — P. 37. **Triangles upon the same base and between the same parallels are equal.** Ax. 1. Magnitudes equal to the same magnitude are equal. EXP. 1 HypConcl. Let the AS ABC, DEC, A be... | |
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