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" Equal triangles on the same base, and on the same side of it, are between the same parallels. "
Euclid's Elements of Geometry: The Six First Books. To which are Added ... - Page 47
by Euclid, Rev. John Allen - 1822 - 494 pages
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Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

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...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson with ...

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...
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Minutes of the Committee of Council on Education, with Appendices

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...
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Report of the Committee of Council on Education (England and Wales ..., Issue 2

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...
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Solutions to the questions of the general examination at Easter, 1848 ...

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...
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The Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New Text ..., Book 1

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....
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

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...
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The Elements of geometry; or, The first six books, with the eleventh and ...

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...
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Minutes of the Committee of Council on Education

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...
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The Popular Educator, Volume 5

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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