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" If } from a point without a circle, a tangent and a secant be drawn, the tangent is the mean proportional between the secant and its external segment. "
Plane Geometry - Page 146
by Arthur Schultze, Frank Louis Sevenoak - 1911 - 233 pages
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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 drawn, the tangent will be a mean proportional between the secant, and its external segment. From the point O, let 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. EĽ. 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 drawn, the tangent will be a mean proportional between the secant and its external segment. From the point O, let the...
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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 drawn, the tangent will be a mean proportional between the secant and its external segment. PROBLEMS RELATING TO THE FOURTH...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...in a circle are reciprocally proportional; that is, AE : DE : : EC:EB. PROPOSITION XXVIII. THEOREM. If from a point without a circle, a tangent and a secant be drawn, the square of the tangent will be equivalent to the rectangle contained by the whole secant and its external...
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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 drawn, the tangent will be a mean proportional between the secant and its external segment. From the point O, let the...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...may 'be regarded as a particular case of the proposition just demonstrated. PROPOSITION XXX. THEOEEM. 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. From the point 0, let the...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...be regarded as a particular case of the proposition just demonstrated. „ PROPOSITION XXX. THEOREM. 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. From the point O, let the...
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre ...

Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...be regarded as a particular case of the proposition just demonstrated. PROPOSITION XXX. THEOREM. Jf from a point without a circle, a tangent and a secant be drawn, the tangent will be a mean proportional between tht secant and its external segment. From the point O, let the...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 256 pages
...in a circle are reciprocally proportional ; that is, AE : DE : : EC:EB. PROPOSITION XXVIII. THEOREM. If from a point without a circle, a tangent and a secant be drawn, the square of the tangent will be equivalent to the rectangle contained by the whole secant and its external...
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