| Euclides - 1846
...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 - 478 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 - 1847
...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
...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
...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
...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
...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
...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
...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
...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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