| 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,... | |
| 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,... | |
| 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,... | |
| 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... | |
| 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. C«r. 2.). PROPOSITION IV. THEOREM. In ihe same circle, or in... | |
| 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... | |
| 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... | |
| 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... | |
| 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,... | |
| 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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