 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.  Plane Geometry - Page 149by Arthur Schultze - 1901Full view - About this book
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...PE X PD = PC", (340) .-.PBX PA = PEXPD. Therefore, if from a point without a circle two secants be drawn, the product of one secant and its external...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... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...PS'xPA' = PC'. QED Therefore PB' xPA'=PSxPA. Ax. i Hence, if from a point without a circle two secants be drawn, the product of one secant and its external...the product of the other and its external segment. 323. Exercise.—Trove § 322 by drawing A'B and AB''. 324. Def.—The projection of a straight line... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...PB'xPA' = PC\ Therefore PB' xPA' = PBxPA, Ax. i Hence, if from a point without 0 circle two secants be drawn, the product of one secant and its external...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... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 376 pages
...Therefore PB'x PA' = PBxPA. Ax. i Hence, if from a point without a circle two secants be drawn, thc product of one secant and its external segment is...the product of the other and its external segment. 311, Def. — The projection of a straight line AB, upon another straight line MN, is the portion of... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...therefore (by 28), PC 2 = PC' 2 , or PC=PC'. EXERCISES. 1. If -from a point without a circle two secants be drawn, the product of one secant and its external...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 - 264 pages
...284. Cor. II. If any two secants be drawn through a fixed point without a circle, the product of one and its . external segment is equal to 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... | |
 | Webster Wells - Geometry - 1899 - 450 pages
...284. Cor. H. If any two secants be drawn through a fixed point without a circle, the product of one and its external segment is equal to 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\) 285. Cor. III. If any... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...284. Cor. n. If any two secants be drawn through a fixed point without a circle, the product of one and its . external segment is equal to 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 CP1.) 285. Cor. III. If... | |
 | William James Milne - Geometry, Modern - 1899 - 258 pages
...external segment compare with the rectangle formed by the other and its external segments? Theorem. If from a point without a circle two secants are drawn, the rectangle formed by one secant and its external segment is equivalent to the rectangle formed by the... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...whatever the direction of the secant. HINT. Draw BE and CD, and prove that &ABE and ACD are similar. COB. If from a point without a circle two secants are drawn, the whole secants and their external segments are reciprocally proportional. Proposition 158. Theorem.... | |
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