 | Julius Petersen - Geometry, Modern - 1880 - 86 pages
...circle. and B coincide; here both Ob and OB are equal to the tangent; so that the proposition will be: The tangent is a mean proportional between the whole secant and the part outside the circle. These three propositions may be expressed under one, thus: When a circle cuts several... | |
 | George Albert Wentworth - 1881 - 266 pages
...for its altitude, is equivalent to R. For SB : SM : : SM : S С, § 292 (if from a point without aO,a secant and a tangent be drawn, the tangent is a mean...between the whole secant and the part without the O). Then S~M* = Я BXS С; § 259 and the difference between SB and S С is the diameter of the O,... | |
 | George Albert Wentworth - Geometry, Modern - 1879 - 262 pages
...the one, : 0 II, the shortest side of the other. QED PROPOSITION XIII. THEOREM. 292. If from a poin( without a circle a secant and a tangent be drawn,...the whole secant and the part without the circle. O C Let OB be a tangent and 0 C a secant drawn, from the point 0 to the circle MBC. We are to prove... | |
 | George Albert Wentworth - Geometry, Modern - 1882 - 268 pages
...division point of AB required. Por AD : AB : : AB : AE, § 292 (if from a point without the circumference a secant and a tangent be drawn, the tangent is a...between the whole secant and the part without the circumference). Then AD—AB:AB::AB—AE:AE. §265 Since AB = 2СB, Cons. and ED = 2CB, (the diameter... | |
 | George Albert Wentworth - Geometry - 1882 - 442 pages
...PROPOSITION .XIII. THEOREM. 292. If from a point without a circle a secant and, a tangent be drawn, ihe tangent is a mean proportional between the whole secant and the part without the circle. О С" Let OB be a tangent and 0С a secant drawn from the point О to the circle MBC. I , We are to... | |
 | George Albert Wentworth - Geometry - 1888 - 272 pages
...equivalent to R. Proof. SB:SM=SM: SC, § 348 (if from a point without a O a secant and a tangent are drawn, the tangent is a mean proportional between the whole secant and the part without the O). Then SM'-SBxSC, and the difference between SB and SC is the diameter of the O, that is, MN. . QE... | |
 | George Albert Wentworth - Geometry - 1888 - 264 pages
...mean ratio. Proof. AG : AB = AB : AF, § 348 (if from a point without a O a secant and a tangent are drawn, the tangent is a mean proportional between the whole secant and the external segment). Then by § 301 and § 300, AG-AB:AB = AB-AF: AF, (1) AG + AB: AG= AB + AF : AB.... | |
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...of CP and DP. Proposition 3O. Theorem. 339. 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 the external segment. Hyp. Let PC and PB be a tangent and a secant drawn from the point P to the O ABC.... | |
 | William Power Burnham - 1893 - 188 pages
...of the circle ? 5. From an exterior point a tangent and a secant are drawn to a circle : prove that the tangent is a mean proportional between the whole secant and the part without the circle. 6. Prove that the areas of similar triangles are to each other as the squares on their homologous sides.... | |
 | Examinations - 1893 - 408 pages
...intercepted arcs. (Two cases.) 8 6 Prove that 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 the external segment. 5 7 Solve the following and prove the correctness of each construction : (a) to circumscribe... | |
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Prove that, 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 the part without the circle. 
