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" A straight line drawn parallel to the base of a triangle, bisecting one of the sides, bisects the other also ; and the part intercepted between the two sides is equal to half the base. 72. Theorem. The median of a trapezoid is' parallel to the bases and... "
Wentworth & Hills's Exercise Manuals: Geometry - Page xiv
by George Albert Wentworth - 1889
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1863 - 464 pages
...equal to AB (D. 3) : hence, AB is greater than AD ; which was to be proved. PROPOSITION HI. THEOEEM. A straight line cannot meet a circumference in more than two points. Let AEBF be a circumference, and AB a straight line : then AB cannot meet the circumference in more...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1871 - 490 pages
...sum is equal to AB (D. 3) : hence, AB is greater than AD ; which was to be proved. PROPOSITION HI. THEOREM. A straight line cannot meet a circumference in more than two points. Let AEBF be a circumference, and AB a straight line : then AB cannot meet the circumference in more...
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The elements of geometry, in eight books; or, First step in applied logic

L J V. Gerard - 1874 - 428 pages
...their common point is convex to that point ; the other arc is concave to the same point. THEOREM 51. A straight line cannot meet a circumference in more than two points. For, otherwise, the centre could bo joined to the straight line by more than two equal straight lines,...
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Euclid simplified. Compiled from the most important French works, approved ...

John Reynell Morell - 1875 - 220 pages
...points unequally distant from the centre, which is contrary to the definition of a circle. THEOREM IL A straight line cannot meet a circumference in more than two points. For if it met it in three points, these three points would be equally distant from the centre. There...
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Wentworth & Hill's Exercise Manuals: Geometry, Issue 3

George Albert Wentworth - 1884 - 264 pages
...Equidistant parallels divide every secant into equal parts. BOOK II. THE CIRCLE. THE CIRCLE AND STKAIGHT LINES. 74. Definitions. Circumference, circle, radius,...circle can be circumscribed. 75. Theorem. A straight lino cannot meet a circumference in more than two points. 76. Theorem. Every diameter divides a circle...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...4 5. And -.-ZMOP2>ZMOB, .'. P20>BO. I, th. 20 6. .'. P2 is without the 0. Def. 0, cor. 4 COROLLABY. A straight line cannot meet a circumference in more than two points. For every other point on that line must be either between or not between those two points, and hence...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...cor. 4 5. And vZMOP2>ZMOB, .'.P20>BO. I, th. 20 6. .'. P2 is without the 0. Def. 0, cor. 4 COROLLARY. A straight line cannot meet a circumference in more than two points. For every other point on that line must be either between or not between those two points, and hence...
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Wentworth & Hill's Exercise Manuals: Geometry

George Albert Wentworth - 1898 - 266 pages
...from the ends of a straight line determine the perpendicular through the middle point of the line. 69. Theorem. Every point in the bisector of an angle is...circumference in more than two points. 76. Theorem. Everry diameter divides a circle and its circumference into two equal parts. 77. Theorem. The diameter...
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Wentworth & Hill's Exercise Manuals: Geometry

George Albert Wentworth - 1898 - 264 pages
...from the ends of a straight line determine the perpendicular through the middle point of the line. 69. Theorem. Every point in the bisector of an angle is...meet a circumference in more than two points. 76. Tlieorcm. Every diameter divides a circle and its circumference into two equal parts. 77. Theorem....
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New Plane Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 265 pages
...OP2 > Z MOB, .'.P2O>BO, I, prop. XX and .'. P2 is without the O. § 108, def. O, cor. 3 COROLLARY. A straight line cannot meet a circumference in more than two points. For every other point on that line must be either between or not between those two points, and hence...
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