| Euclid, Thomas Tate - 1849 - 120 pages
...therefore parallel to BF. Wherefore equal triangles, &c. QED PROP. XLI. THEOR. If a parallelogram and 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... | |
| John Playfair - Euclid's Elements - 1849 - 332 pages
...XLl. THEOR. If a parallelogram and a triangle be upon the same base, and between the same parallel ; the parallelogram is double of the triangle. Let the parallelogram ABCD and the tri- A y» « angle EBC be upon the same base BC and =^- -*" between the same parallels BC, AE ; the... | |
| James Elliot - 1851 - 152 pages
...the given triangle. PROPOSITION LIX. THEOREM. If a Parallelogram and a Triangle are upon equal Bases, and between the same Parallels, the Parallelogram is double of the Triangle. EXERCISE 1. Draw any triangle, and make a parallelogram equal to it. 2. Make a triangle whose area... | |
| Euclides - 1852 - 152 pages
...triangles, &c. QED BOOK I. * xxxi. 1. b xxxviii. 1. BOOK I. PEOP. XLI. THEOR. If a parallelogram and 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 EEC be upon the same base... | |
| Euclides - 1853 - 146 pages
...but AD; therefore 4. AD is parallel to BF. Wherefore, equal triangles, &c. aED PROP. 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 base... | |
| Euclid - Geometry - 1853 - 176 pages
...area to half the same. PROPOSITION XII. THEOREM. — If a -parallelogram (ABCD) and, a triangle (E BC) be upon the same base, and between the same parallels, the parallelogram is double of the triangle. CONSTRUCTION. Draw the diagonal AC. DEMONSTRATION. Then, because the two triangles ABC and EBC are... | |
| Euclides - Geometry - 1853 - 334 pages
...and a triangle be on the same base and between the same parallels : then the parallelogram shall be double of the triangle. Let the parallelogram ABCD and the triangle EBC be on the same base BC, and between the same parallels BC, AE. Then the parallelogram ABCD shall be double... | |
| Euclides - Geometry - 1853 - 178 pages
...parallel to bf Wherefore equal triangles, ta. QED PROPOSITION XLI. — THEOREM. If a parallelogram and 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... | |
| Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...between the same parallels ; the parallelogram shall be double of the triangle. Let the paralellogram ABCD and the triangle EBC be upon the same base BC, and between the same parallels BC, AE ; the parallelogram ABCD is double of the triangle EBC. Join AC ;... | |
| Euclid, John Playfair - Geometry - 1853 - 336 pages
...that there is no other parallel to it bul AD ; AD is therefore parallel to BF. , / ' PROP. XLfTTHEOR. If a parallelogram and a triangle be upon the same base, and betioeen the same parallel ; the parallelogram is double of the triangle. D Let the parallelogram ABCD... | |
| |