 | 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 - 876 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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Parallelograms upon the same base and between the same parallels, are equal to one another. 
