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" If from a point without a circle a secant and a tangent are drawn, the tangent is the mean proportional between the whole secant and its external segment. "
Plane Geometry: A Complete Course in the Elements of the Science - Page 183
by Edward Brooks - 1901 - 266 pages
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A System of Popular Geometry: Containing in a Few Lessons So Much of the ...

George Darley - Euclid's Elements - 1836 - 172 pages
...under the segments of one is equal to the rectangle under the segments of the other, 110. ART. 156. If from a point without a circle a secant and a tangent be drawn to the circle, the square of the tangent is equal to the rectangle under the whole secant...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 pages
...rectangle GE- EH; therefore the rectangle AE'EC, is equal to the rectangle BE • ED. PROPOSITION XXXVI. THEOREM. If from a point without a circle a secant and a tangent to it be drawn, the rectangle under the secant and its external segment is equal to the square of the...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...give the proportion PA:PB::;PB':PA'. THEOREM When a secant and tangent are drawn from the same point, the tangent is a mean proportional between the secant and its external segment. This Theorem is in reality only a particular case of the preceding, when the points B, B' of the secant...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 pages
...the rectangle AE • EC is equal to the rectangle BE • ED. *»* See Appendix — Proposition (D). If from a point without a circle a secant and a tangent to it be drawn, the rectangle under the secant and its external segment is equal to the square on the...
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The Mathematical Monthly, Volume 3

John Daniel Runkle - Mathematics - 1861 - 490 pages
...then x -f- R and x-\-r will be the secants, and x — R and x — r the external segments ; and since the tangent is a mean proportional between the secant and its external segment, we have 2^(2* — R2) = \J(x* — r2), whence PRIZK SOLUTION OP PROBLEM П. By A. STANLEY, London,...
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The essentials of geometry, plane and solid, as taught in French and German ...

John Reynell Morell - Geometry - 1871 - 156 pages
...SB. s (rig. 39.) 55. If from a point outside the circumference you describe a tangent and a secant, the tangent is a mean proportional between the secant and its external segment. If the straight line OB is a tangent to the circumference at a point B, we shall have — OA : OB :...
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Euclidian Geometry

Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...rectangle (PX, PQ) = rectangle (RX, XS). (Ii. 2) Lastly, if neither of them pass through the centre, THEOREM (<?). If from a point without a circle a secant and a tangent be drawn, the rectangle contained by the parts of the secant between the given point and the circle...
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Annual Register of the United States Naval Academy, Annapolis, Md, Volumes 25-32

United States Naval Academy - 1874 - 888 pages
...triangle, or circle deribed upon the side as diameter ? Give reasons for your answer. I. Prove that if, from a point without a circle, a secant and a tangent bo drawn, a tangent ie a mean proportional between the whole secant and the part without i- circle....
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Elements of Geometry with Exercises for Students: An an Introduction to ...

Aaron Schuyler - Geometry - 1876 - 384 pages
...and equivalent to tlie square of the tangent drawn from the same point to the circumference; that is, the tangent is a mean proportional between the secant and its external segment. (?) 249. Exercises. 1. If two circles are tangent internally, chords of the greater, drawn from the...
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Proceedings

Scotland free church, gen. assembly - 1876 - 1124 pages
...equations : (1.) (2.) 4x-lly=9. 5. To draw a tangent to a circle from a given point without it. 6. If, from a point without a circle, a secant and a tangent to it be drawn, the square on the tangent is equal to - (complete the enunciation, and prove the theorem)....
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