 If, from a point without a circle, two secants are drawn, the product of one secant and its external segment is equal to the product of the other and its external segment.  New Plane Geometry - Page 126by Webster Wells - 1908 - 174 pagesFull view - About this book
 | Webster Wells - Geometry - 1886 - 392 pages
...tangent to the circumference at C; then by § 293, AP x ~ and A'Px. 139 That is, if any two secants are drawn through a fixed point without a circle, the...the product of the other and its external segment. 296. COROLLARY III. If any number of secants are drawn through a fixed point without a circle, the... | |
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...PEXPD. Therefore, if from a point without a circle two secants be drawn, the product of one secant and its external segment is equal to the product of the other and its external segment. Proposition 3 1 . Theorem. 343. If any angle of a triangle is bisected by a straight line which cuts... | |
 | Webster Wells - Geometry - 1894 - 400 pages
...the circle at C. Then, APXBP^CP*, and A'PX B'P = CP\ (§ 282.) Hence, AP X BP = A'PX B'P. That is, if any two secants be drawn through a fixed point...the product of the other and its external segment. 285. COR. III. If any two secants be drawn through a fixed point without a circle, the whole secants... | |
 | Webster Wells - Geometry - 1894 - 400 pages
...its external segment is equal to the product of the other and its external segment. 285. COR. III. If any two secants be drawn through a fixed point without a. circle, the whole secants and their external segments are reciprocally proportional (§ 281). PROPOSITION XXXIII.... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...PBxPA. Ax. i Hence, if from a point without a circle two secants be drawn, the product of one secant and its external segment is equal to the product of the other and its external segment. 323. Exercise. — Prove § 322 by drawing A'B and AB' '. 324. Def. — The projection of a straight... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...PBxPA, Ax. i Hence, if from a point without 0 circle two secants be drawn, the product of one secant and its external segment is equal to the product of the other and its external segment. 1 323. Exercise.— Prove § 322 by drawing A'B and AB'. 324. Def. — The projection of a straight... | |
 | Webster Wells - Geometry - 1898 - 264 pages
...the tangent is a mean proportional between the whole secant and its external segment. 284. Cor. II. If any two secants be drawn through a fixed point...the product of the other and its external segment. To Prove AP x BP = A'P x B'P. (We have AP x BP and A'P x B'P each equal to CP 2 .) 285. Cor. III. If... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...PC=PC'. EXERCISES. 1. If -from a point without a circle two secants be drawn, the product of one secant and its external segment is equal to the product of the other and its external segment. 2. If from a point without a circle any number of secants are drawn, the products of the whole secants... | |
 | Webster Wells - Geometry - 1898 - 250 pages
...respectively. To Prove AT x BP = A'P x B'P. (We have AP x BP and A'P x B'P each equal to OP*.) 285. Cor. III. If any two secants be drawn through a fixed point without a circle, the whole secants and their external segments are reciprocally proportional (§ 281). EXERCISES. 19. Find... | |
 | Webster Wells - Geometry - 1899 - 450 pages
...segment. To Prove AP x BP = A'P x B'P. (We have AP x BP and A'P x B'P each equal to CP\) 285. Cor. III. If any two secants be drawn through a fixed point without a circle, the whole secants and their external segments are reciprocally proportional (§ 281). EXERCISES. 19. Find... | |
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