| Sandhurst roy. military coll - 1859 - 672 pages
...of any triangle be produced, the extorior angle is equal to the two interior and opposite angbs. k If a parallelogram and a triangle be upon the same base and between the same parallels, the parallelogran is double of the triangle. 3. Tf a straight line be divided into two equal parts, aid... | |
| Robert Potts - Geometry, Plane - 1860 - 380 pages
...AD is therefore parallel to BF. Wherefore, equal triangles upon, &c. QED PROPOSITION XLI. THEOREM. If a parallelogram and a triangle be upon the same...and between the same parallels ; the parallelogram shall be double of the triangle. Let the parallelogram ABCD, and the triangle EBC be upon the same... | |
| Euclides - 1860 - 288 pages
...equal ; and if the areas and altitudes be equal, the bases are equal. PROPOSITION XLI. THEOREM. . . .,, If a parallelogram and a triangle be upon the same...and between the same parallels, the parallelogram shall be double of the triangle: Given the parallelogram ABCD and the triangle EBC upon the same base... | |
| Euclides - 1862 - 140 pages
...is parallel to BF. Conclusion. — Therefore, equal triangles, &c. QED PROPOSITION 41.— THEORKM. If a parallelogram and a triangle be upon the same...and between the same parallels, the parallelogram shall be double of the triangle. (Ref erencea— Prop. I. 34, 37; ax. 1.) Hypothesis. — Let the parallelogram... | |
| Euclides - 1863 - 74 pages
...Thus saudre and -"""^-e rooi are corelative terms."— LAEDNER.S Euclid, p. 54. PROP. 41— THEOR. If a parallelogram and a triangle be upon the same...and between the same parallels ; the parallelogram shall be double of the triangle. Cos.— Pst. 1.— DEM.— P. 37, PM Let the / — 7 ABCD, and the... | |
| Euclides - 1864 - 262 pages
...parallelogram and a triangle be upon the same base, and between the same parallels ; the parallelogram shall be double of the triangle. Let the parallelogram ABCD,...and the triangle EBC be upon the same base BC, and between the same parallels BC, AE. Then the parallelogram AB CD shall be double of the triangle EBC.... | |
| Euclides - 1864 - 448 pages
...AD is therefore parallel to BF. Wherefore, equal triangles upon, &c. QED PROPOSITION XLI. THEOREM. If a parallelogram and a triangle be upon the same...and between the same parallels ; the parallelogram shall be double of the triangle, Let the parallelogram ABCD, and the triangle EBCbe upon the same base... | |
| Euclides - 1865 - 402 pages
...bases in the same straight line, and towards the same parts, are between the same parallels. Prop. 41. If a parallelogram and a triangle be upon the...and between the same parallels ; the parallelogram shall be double of the triangle. Prop. 42. To describe a parallelogram that shall be equal to a given... | |
| Robert Potts - 1865 - 528 pages
...is therefore parallel to BF. Wherefore, equal triangles upon, &c. QED PROPOSITION XLI. THEOREM. lf a parallelogram and a triangle be upon the same base,...and between the same parallels ; the parallelogram shall be double of the triangle. Let the parallelogram ABCD, and the triangle EBC be upon the same... | |
| Euclides - 1865 - 80 pages
...equal, their bases must be equal. PROPOSITION XL VII. THEOR. If a parallelogram and a triangle are upon the same base and between the same parallels, the parallelogram is double the triangle. Let the parallelogram ABCD and the triangle EBC be upon the same base BC, and between... | |
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