 | James Bates Thomson - Geometry - 1844 - 268 pages
...greatest line which can be inscribed in a circle is equal to its diameter. PROPOSITION III. THEOREM. A straight line cannot meet the circumference of a circle in more than two points. to the same straight line, which is impossible. (Prop. 15. 1. Cor. 2.) Hence, A straight line, $c.... | |
 | Nathan Scholfield - 1845 - 894 pages
...shall then have AD< AC-fCD (Prop. XB II.); or AD<AB. PROPOSITION III. THEOREM. A right line cannot ment the circumference of a circle in more than two points....the centre ; and hence, there would be three equal right lines drawn from the same point to the same right line, which is impossible, (Prop. XVII. Cor.... | |
 | Charles Waterhouse - Arithmetic - 1844 - 232 pages
...an arc of 45 degrees, is equal in length to the radius of the circle of which the arc is a part. 22. A straight line cannot meet the circumference of a circle in more than two point*. 23. The circumference of a circle may be made to pass through any three points, which are not... | |
 | Benjamin Peirce - Geometry - 1847 - 204 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. Proof. For, by §§ 38 and 41, only two equal straight lines can be drawn from the same point to the... | |
 | Charles Davies - Trigonometry - 1849 - 372 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...drawn from the same point to the same straight line, wmch is impossible (Book I. Prop. XV. Cor. 2.). PROPOSITION IV. THEOREM. In the same circle, or in... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...definition of a circle. Therefore, every diameter, &c. PROPOSITION It. THEOREM. A straight line can not meet the circumference of a circle in more than two points. For, if it is possible, let the straight line ADB meet the circumference CDE in three points, C, D, E. Take F,... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...Hence, the greatest line which can be inscribed in a circle is a diameter. PROPOSITION III. THEOEEM. A straight line cannot meet the circumference of a...points would be equally distant from the centre; and there would be three equal straight lines drawn from the same point to the same straight line, which... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...Hence, the greatest line which can be inscribed in a circle is a diameter. PROPOSITION III. THEOREM. A straight line cannot meet the circumference of a...points would be equally distant from the centre; and there would be three equal straight lines drawn from the same point to the same straight line, which... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...Hence, the greatest line which can be inscribed in a circle is a diameter. PROPOSITION III. THEOREM. A. straight line cannot meet the circumference of...points would be equally distant from the centre ; and there would be three equal straight lines drawn from the same point to the same straight line, which... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...is a semi-circumference, and the included segmeut is a semicircle. PROPOSITION II. — THEOREM. 172. A straight line cannot meet the circumference of a circle in more than two points. For, if a straight line could meet the circumference ABD, in three points, A, B, D, join each of these points... | |
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THEOREM. A straight line cannot meet the circumference of a circle in more than two points. 
