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" THEOREM. A straight line cannot meet the circumference of a circle in more than two points. "
Elements of Geometry and Trigonometry: With Notes - Page 28
by Adrien Marie Legendre - 1830 - 316 pages
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 280 pages
...straight line JID < AC + CD, that is, AD < AB (91). 100. Corollary. Hence the greatest straight line that can be inscribed in a circle is equal to its diameter....circumference of a circle in more than two points. Demonstration. If it could meet it in three, these three points being equally distant from the centre,...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 pages
...straight line AD < AC + CD, that is, AD < AB (91). 100. Corollary. Hence the greatest straight line that can be inscribed in a circle is equal to its diameter....circumference of a circle in more than two points. Demonstration. If it could meet it in three, these three points being equally distant from the centre,...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 224 pages
...the greatest straight line that can be inscribed in a circle is equal to its diameter. THEOREM. ^y 101. A straight line cannot meet the circumference of a circle in more than two points. Demonstration. If it could meet it in three, these three points being equally distant from the centre,...
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A System of Popular Geometry: Containing in a Few Lessons So Much of the ...

George Darley - Euclid's Elements - 1836 - 128 pages
...which does not pass through the centre into equal parts, is perpendicular to it, ibid. ART. 53. A right line cannot meet the circumference of a circle in more than two points, ibid ART. 54. If a right line meet a circle in two points, that part of it between the points lies...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1837 - 359 pages
...diameter. , PROPOSITION III. THEOREM. A straight line cannot meet the circumference of a circle in mare than two points. For, if it could meet it in three,...drawn from the same point to the same straight line, winch is impossible (Book I. Prop. XV. Cr. 2.). PROPOSITION IV. THEOREM. In ihe same circle, or in...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 159 pages
...the greatest straight line which can be inscribed in a circle is equal to its diameter. 94. Theorem. A straight line cannot meet the circumference of a circle in more than two points. Demonstration. For, by arts. 38 and 41, only two equal straight lines can be drawn from the same point...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1838 - 359 pages
...Hence the greatest line which can be inscribed in a circle is its diameter. PROPOSITION III. THEOREM. A straight line cannot meet the circumference of a...from the centre ; and hence, there would be three equaF straight lines drawn from the same point to the same straight line, which is impossible (Book...
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A Treatise on Geometry and Its Application in the Arts

Dionysius Lardner - Curves, Plane - 1840 - 314 pages
...observations may be applied to every point of the line beyond A and B. (82.) Hence it follows, that a straight line cannot meet the circumference of a circle in more than two points, because every point of the line between these points will be within the circumference, and every other...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 235 pages
...straight line AD< AC + CD; that is, AD < AB (88). 100. Corollary. Hence the greatest straight line that can be inscribed in a circle is equal to its diameter....circumference of a circle in more than two points. Demonstration. If it could meet it in three, these three points being equally distant from the centre,...
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Arithmetical Spyglass and Teacher's Assistant: Intended as a Key and ...

Charles Waterhouse - Arithmetic - 1842 - 178 pages
...inward, and a saliant angle has its vertex directed outward. 6. Every chord is less than the diameter. 7. A straight line cannot meet the circumference of a circle in more than two points. 8. The circumference of a circle may be made to pass through any three points which are not in a right...
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