 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...their external segments are reciprocally proportional. Corollary. If a tangent and a secant intersect, the tangent is a mean proportional between the whole secant and its external segment. BOOK IV. THEOREMS. PROPOSITION I. Parallelograms having equal bases and equal altitudes are equivalent.... | |
 | James Wallace MacDonald - Geometry - 1889 - 80 pages
...Proposition XIX. A Theorem. 229. If from a point without a circle a secant and a tangent be drawn, the tangent is a mean proportional between the whole secant and its external segment How can this be proved by the Theory of Limits ? III. EXTREME AND MEAN RATIO. 230. What is dividing... | |
 | James Wallace MacDonald - Geometry - 1894 - 76 pages
...Proposition XIX. A Theorem. 229. If from a point without a circle a secant and a tangent be drawn, the tangent is a mean proportional between the whole secant and its external segment. How can this be proved by the Theory of Limits ? III. EXTREME AND MEAN RATIO. 230. What is dividing... | |
 | William Chauvenet - 1893 - 340 pages
...therefore similar. Consequently PB : PB' = PA': PA. 85. COROLLARY. If a tangent and a secant intersect, the tangent is a mean proportional between the whole secant and its external segment. Suggestion. Show that the triangles PA T and PTB are similar. r 36. Scholium. If the lengths of the... | |
 | George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...secant and its exterior segment. 235. Theorem. If from a point without a circle a tangent and a secant are drawn to the circle, the tangent is a mean proportional between the entire secant and its exterior segment. 236. Problem. To divide a given straight line into two parts... | |
 | Webster Wells - Geometry - 1894 - 400 pages
.... (§ 231.) 283. COR. I. If through a fixed point without a circle a secant and a tangent be drawn, the tangent is a mean proportional between the whole secant and its external fcgment. 284. COR. II. Let AP and A'P be any two secants of the circle ACB, intersecting without the... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...QED PROPOSITION XVII. THEOREM 321, If from a point without a circle a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and its external segment. GIVEN— a fixed point P outside of a circle, PC a tangent, and PR a secant (Fig. i). PB _PC PC ~ PA... | |
 | Joe Garner Estill - Geometry - 1896 - 168 pages
...each medial line in the ratio 1 : 2. 4. If from a point a tangent and a secant to a circle are drawn, the tangent is a mean proportional between the whole secant and its external segment. 5. Similar triangles are to each other as the squares of two homologous sides. 6. Divide a given straight... | |
 | Joe Garner Estill - 1896 - 186 pages
...each medial line in the ratio 1 : 2. 4. If from a point a tangent and a secant to a circle are drawn, the tangent is a mean proportional between the whole secant and its external segment. 5. Similar triangles are to each other as the squares of two homologous sides. 6. Divide a given straight... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...QED PROPOSITION XVII. THEOREM 321. If from a point without a circle a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and its external segment. GIVEN — a fixed point P outside of a circle, PC a tangent, and PB a secant (Fig. I). PB _PC PC~ PA... | |
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It follows from § 259 that if through a fixed point without a circle a secant and a tangent be drawn, the tangent is a mean proportional between the whole secant and its external segment. 
