 | John Playfair - Geometry - 1829 - 210 pages
...equal bases and between the same parallels, and therefore are equal. ED. PROPOSITION XLI. THEOREM. If a parallelogram and a triangle be on the same base, and between the same parallels, the parallelogram, is double of the triangle. Let the paral. A BCD and the triangle EBC... | |
 | Education - 1844 - 688 pages
...equal and parallel straight lines towards the same parts, are themselves also equal and parallel. 5. If a parallelogram and a triangle be on the same base, and between the same parallels, the parallelogram shall be double of the triangle. 6. If a straight line be divided into... | |
 | Euclides - Geometry - 1853 - 334 pages
...through A but AD is parallel to BF. Hence AD is parallel to BF. Which was to be proved. PEOP. XLI. THEOE. If a parallelogram 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... | |
 | 1856 - 422 pages
...is founded on the 41st proposition of Book I., Euclid's Elements, in which it is demonstrated that if a parallelogram and a triangle be on the same base and between the tame parallel», the parallelogram it double of the triangle. Now, since the rectangle formed by the... | |
 | Popular educator - 1860 - 424 pages
...is founded on the 41st proposition of Book I., Euclid's Elements, in which it is demonstrated that if a parallelogram and a triangle be on the same base and between the same parallels, the parallelogram is double of the triangle. Now, since the rectangle formed by the base... | |
 | University of Oxford - Education, Higher - 1863 - 316 pages
...angle. 5. Straight lines which are parallel to the same straight line are parallel to each other. 6. If a parallelogram and a triangle be on the same base and between the same parallels, the parallelogram shall be double of the triangle. 7. Describe a parallelogram equal to... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...to BF ; therefore AD is parallel to BF. Wherefore, equal triangles &c. QED PROPOSITION 41. THEOREM. If a parallelogram and a triangle be on the same base and between the same parallels, the parallelogram shall be double of the triangle. Let the parallelogram ABCD and the triangle... | |
 | Hugo Reid - Mathematics - 1872 - 148 pages
...often well to reserve the division to the last. 340. This rule depends on the geometrical truth, that if a parallelogram and a triangle be on the same base, and between the same parallels (that is, have the same altitude), the triangle is half of the parallelogram. Problem 8.... | |
 | Euclides - 1874 - 120 pages
...to BF ; therefore AD is parallel to BF. Therefore, equal triangles, &c. QED PROPOSITION 41. THEOREM. If a parallelogram and a triangle be on the same base and between the same parallels, the parallelogram shall be double of the triangle. . Let the parallelogram ABCD and the... | |
 | William Alexander Willock - Circle - 1875 - 196 pages
...AA, and CC ., being each equal to parallelogram AC,, are (Ax. 1) equal to each other, as stated. 8. If a Parallelogram and a Triangle be on the Same Base, and between the Same Parallels, the area of the triangle is Italf that of the parallelogram. Let ABA,B, be the parallelogram,... | |
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If a parallelogram and a triangle be on the same base and between the same parallels, the parallelogram shall be double of the triangle. 
