 | Geography - 1867 - 964 pages
...triangle о н в ; and this brings us to the foot, that when a square and a triangle happen to bo on the same base, and between the same parallels, the area of the square is double the area of the triangle. Now let us torn to the trapezoid o ELN, of which the sides... | |
 | 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 be on the same... | |
 | 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 two equal parts,... | |
 | 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... | |
 | 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 and the perpendicular... | |
 | 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 a given rectilineal... | |
 | Education - 1899 - 828 pages
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 | 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 EBC be on... | |
 | Henry William Watson - Geometry - 1871 - 320 pages
...ABC is half the rectangle of BC and AD. Corollary. — If a parallelogram and a triangle be upon the same base and between the same parallels, the area of the triangle will be half the area of the parallelogram. PROPOSITION 1r. If there be two straight lines, one of... | |
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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. 
