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" If from a point without a circle, a tangent and a secant be drawn, the tangent will be a mean proportional between the secant and its external segment. "
The Eclectic School Geometry - Page 64
by Evan Wilhelm Evans - 1884 - 149 pages
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 394 pages
...demonstrated. PROPOSITION XXX. THEOREM. If from the same point O without a circle, a tangent OA and a secant OC be drawn, the tangent will be a mean proportional between the secant and its external segment ; that is, we shall have OC : OA : : OA : OD ; or, which is the same thing, OAZ=OC.OD. For,...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 346 pages
...regarded as a particular case of the proposition just demonstrated. THEOREM. 228. If from the same point without a circle, a tangent and a secant be...proportional between the secant, and its external segment. From the point O, let the tangent OA, and the secant OC be drawn ; then will, OC : OA : :...
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 138 pages
...This we shall find to be a very useful problem. 81. — If from a point without a circle a tangent and secant be drawn, the tangent will be a mean proportional between the entire .secant and the part without the circle — . Thus if O F48 (fig. 48) be the poiut, 0 A the...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 210 pages
...arches which they intercept is equal to half the circumference. PROPOSITION E. THEOREM. E». If from any point without a circle a tangent and a secant be drawn, the angle which they contain is equal to an angle at the circumference of the circle standing on an arch...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 394 pages
...a particular case of the proposition just demonstrated. PROPOSITION XXX. THEOREM. If from the same point without a circle, a tangent and a secant be...mean proportional between the secant and its external segment. From the point O, let the tangent OA, and the secant OC be be drawn ; then will OC : OA :...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1837 - 376 pages
...PROPOSITION XXX. THEOREM. If from the same point without a circle, a tangent and a secant be drawn,,the tangent will be a mean proportional between the secant and its external segment. From the point O, let the tangent OA, and the secant OC be be drawn ; then will • • OC...
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - Geometry - 1844 - 268 pages
...triangles are similar; consequently OC : OA : : OA : OD ; or, (5. 3 ;) OAa=OC.OD. Hence, If from the same point without a circle, a tangent and a secant be...mean proportional between the secant and its external segment. PROBLEMS RELATING TO THE FOURTH BOOK. PROBLEM I. To divide a given straight line into any...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 894 pages
...just demonstrated. PROPOSITION XXXVII. THEOREM. If from the same point without a circle, a tangent and secant be drawn, the tangent will be a mean proportional between the secant and its external segment. From the point 0, let the tangent OA, and the secant OC, be drawn ; then will OC : OA: :OA...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 326 pages
...progression. A PROPOSITION XXI. THEOREM. If, from the same point without a circle, a tangent and secant line be drawn, the tangent will be a mean proportional between the secant and its external segment. From the point B, let the tangent BA, and the secant BC, be drawn ; then will BC : BA : :...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 372 pages
...the rectangle OA.OB is equal to the rectangle OC.OD. 8" PROPOSITION XXX. THEOREM. If from the same point without a circle, a tangent and a secant be...mean proportional between the secant and its external segment. From the point O, let the tangent OA, and the secant OC be be drawn ; then will OC : OA :...
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