 | Euclides - Geometry - 1841 - 378 pages
...equal to the triangle CDE: and they are on the same base DE; but equal triangles on the same base, and on the same side of it, are between the same parallels ;* * 39. i therefore DE is parallel to BC. Wherefore, if a straight line, &c. QED PROP. III. THEOR.... | |
 | John Playfair - Euclid's Elements - 1844 - 338 pages
...ABC is equal to the triangle DEF. PROP. XXXIX. THEOR. Equal triangles upon the same base, and upon the same side of it, are between the same parallels. Join AD ; AD is parallel to BC ; for, if it is not, through the point A draw (31. 1.) AE parallel to BC, and... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...the straight line joining their vertices is parallel to the base. Let the equal triangles ABC, DBC be on the same base BC and on the same side of it ; join AD : AD is parallel to BC. For, if it be not, through A draw (I. 31 )AE parallel to BC, and... | |
 | Scottish school-book assoc - 1845 - 444 pages
...passing through A, except AD, which therefore is || to BF. QED Cor. 1. Equal triangles on the same base and on the same side of it, are between the same parallels. Cor. 2. In the same manner it might be shown that equal triangles between the same parallels are upon... | |
 | Euclides - 1845 - 546 pages
...proof depends on Theorem 66, p. 303. 58. Let ABC, EBC, DBC (DB being joined) be three equal triangles on the same base BC and on the same side of it (fig. Euc. i. 41). Join AD, DE. Then AD is parallel to BC, and DE .is parallel to BC. 59. The diameters... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...same base, and upon the same side of it, are between the same parallels. Let the = <£^s ABC, DEC, be on the same base BC, and on the same side of it ; then the will be between the same ||s. A B c For if not, Prop. so. draw AE || BC, and join EC. H,... | |
 | Dennis M'Curdy - Geometry - 1846 - 166 pages
...(4)p.36; (c) p. 34 ; (d) ox. 7. 89 Th. Equal triangles (ABC, DBC), upon the same base (BC), and upon the same side of it, are between the same parallels. Join AD; — AL> is parallel to BC: for if not, A through the point A draw AE parallel to BC (a), and join CE.... | |
 | Euclides - 1846 - 292 pages
...triangles upon S,c, QED PROP. XL. THEOR. Equal triangles upon equal bases, in the same straight line, and on the same side of it, are between the same parallels. Let the equal triangles, ABC, DEF, be upon equal bases BC, EF, in the same straight line BF, and on... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...ABC is equal to the triangle DEF. PROP. XXXIX. THEOR. Equal triangles upon the same base, and upon the same side of it, are between the same parallels. Join AD ; AD is parallel to BC ; for, if it is not, through the point A draw (31. 1.) AE parallel to BC, and... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...same base, and upon the same side of it, are between the name parallels. Let the = ^s ABC, DEC, be on the same base BC, and on the same side of it; then the .^s will be between the same ||s. AD B For if not, Prop. so. draw AE || BC, and join EC. H,p.... | |
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Equal triangles on the same base, and on the same side of it, are between the same parallels. 
