| Euclides - Geometry - 1841 - 351 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 - 317 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 - 352 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
...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
...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
...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 - 138 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
...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 - 317 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
...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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