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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 Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 638 pages
...semi-circumference, and the included segment 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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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 pages
...is a semi-circumference, and the included segment 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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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1868 - 340 pages
...is a semi-circumference, and the included segment 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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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1869 - 516 pages
...is a semi-circumference, and the included segment 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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New Elementary Geometry: With Practical Applications ; a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1873 - 202 pages
...ON REVIEW. 170. 1. The diameter is the longest straight line that can be inscribed in a circle. 2. A straight line cannot meet the circumference of a circle in more than two points. 3. Two parallel tangents meet the circumference at the extremity of the same ^\ T ~7j) \ diameter....
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New Elementary Geometry: With Practical Applications : a Shorter Course Upon ...

Benjamin Greenleaf - Geometry - 1874 - 206 pages
...ON REVIEW. 170. 1. The diameter is the longest straight line that can be inscribed in a circle. 2. A straight line cannot meet the circumference of a circle in more than two points. 3. Two parallel tangents meet the circumference at the extremity of the same diameter. 4. If two straight...
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Syllabus of Plane Geometry: (corresponding to Euclid, Books I-VI) ...

Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...given points is the straight line that bisects at right angles the line joining those points. THEOR. 9. A straight line cannot meet the circumference of a circle in more than two points. COR. A chord of a circle lies wholly within the circle. OBS. Hence the circumference of a circle is...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1877 - 458 pages
...in all respects. Therefore every diameter, etc. • PROPOSITION II. THEOREM. A straight line can not meet the circumference of a circle in more than two points. . For, if it be possible, let the straight line ABC meet the circumference of a circle in three points, DBE. Take...
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Elementary geometry

James Maurice Wilson - 1878 - 450 pages
...Identity that the one that bisects it is also the one that is perpendicular to it. . . - ..THEOREM 9. A straight line cannot meet, the circumference of a circle in more than two points. • Part. En, Let AB be. a straight line, O the centre of a circle; It is required to prove that the...
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Elements of Geometry, After Legendre, with a Selection of Geometrical ...

Charles Scott Venable - 1881 - 380 pages
...PROPOSITION III. THEOREM. A straight line cannot meet a circumference in more than two points. For, if it met it in three, those three points would be equally distant from the centre ; there would, therefore, be three equal straight lines drawn from the same point to the same straight...
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