 | Euclides - 1846 - 272 pages
...also equal (by Ax. 7.) PROPOSITION XXXIX. THEOREM. Equal triangles (BAC and BDC) on the same base, and on the same side of it, are between the same parallels. For if AD be not parallel to BC, draw through the point A the right line AF parallel to BC, cutting... | |
 | Euclid, Robert Potts - Euclid's Elements - 1847 - 118 pages
...proof depends on Theorem 6O, 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. Committee on Education - Education - 1847 - 624 pages
...two straight lines shall be in one and the same straight line. 3. Equal triangles on the same base and on the same side of it are between the same parallels. Section II. 1. In a given straight line find a point equally distant from two given points, one in... | |
 | Great Britain. Council on Education - Education - 1848 - 596 pages
...are parallel to the same right line are parallel to one another. 3. Equal triangles on the same base, and on the same side of it, are between the same parallels. Section 5. 1. If a right line be divided into any two parts, the squares of the whole line and one... | |
 | J. Goodall, W. Hammond - 1848 - 390 pages
...The greater side of every triangle subtends the greater angle. 3. Equal triangles on the same base and on the same side of it, are between the same parallels. Section 5. 1. If a right line be divided into any two parts, the squares of the whole line and one... | |
 | Euclides - Geometry - 1853 - 334 pages
...and on the same side of it shall be between the same parallels. Let the equal triangles ABC, DBC be on the same base BC, and on the same side of it. Then they shall be between the same parallels ; that is, if AD be joined, AD shall be parallel to BC.... | |
 | Robert Potts - 1855 - 1050 pages
...triangle by right lines drawn from a point given in one of its sides. 3. Equal triangles, on the same base and on the same side of it, are between the same parallels. 4. In any triangle the square of the side, subtending an acute angle, is less than the sum of the squares... | |
 | Euclides - 1855 - 270 pages
...the triangle СDE (V. 9) ; and they are on the same base D E. But equal triangles on the same base and on the same side of it, are between the same parallels (I. 39). Therefore DE is parallel to B С. Wherefore, if a straight line, &c. QED The necessity for... | |
 | Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...precaution is not taken, and give a proof in this case. Section 2. 1. Equal triangles on the same base, and on the same side of it, are between the same parallels. 2. If the square described upon one of the sides of a triangle be equal to the squares described upon... | |
 | 1856 - 428 pages
...figure, etc. QEBf PROPOSITION XL. THEOREM. Equal triangles upon equal bases in the same straight line, and on the same side of it, are between the same parallels. In fig. 40, let the equal triangles ABC and о в F be upon equal bases в с and в F, in the same... | |
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Equal triangles on the same base, and on the same side of it, are between the same parallels. 
