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" If from, a point without a circle a secant and a tangent are drawn, the tangent is a mean proportional between the whole secant and the external segment. "
Elements of Geometry: Including Plane, Solid, and Spherical Geometry - Page 176
by George Washington Hull - 1807 - 398 pages
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An Elementary Course of Plane Geometry

Richard Wormell - Geometry, Plane - 1870 - 304 pages
...arc is equal to the angle CAB. Fig. 211. 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 part without the circle. 230. We have seen that, if from a point 0 two secants be drawn (fig. 212)...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...is, if through a fixed point without a circle a tangent to the circle is drawn, and also any secant, the tangent is a mean proportional between the whole secant and its external segment. 60. Scholium I. When a secant, constantly passing through a fixed point, changes its direction, the...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Mathematics - 1872 - 382 pages
...is, if through a fixed point without a circle a tangent to the circle is drawn, and also any secant, the tangent is a mean proportional between the whole secant and its external segment. 60. Scholium I. When a secant, constantly passing through a fixed point, changes its direction, the...
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A Treatise on Special Or Elementary Geometry

Edward Olney - 1872 - 270 pages
...Theorem.—If from a point without a circle a tangent be drawn, and a secant terminating in the concave arc, the tangent is a mean proportional between the whole secant and its external seg° ment; whence the square of the tangent equals \P_ the product of the secant into its external...
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A Treatise on Special Or Elementary Geometry

Edward Olney - Geometry - 1872 - 472 pages
...— Jf from a point without a circle a tangent be drawn, and a secant terminating in the concave arc, the tangent is a mean proportional between the whole secant and its external seg° ment; whence the square of the tangent equals the product of the secant into its external segment....
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Annual Register of the United States Naval Academy, Annapolis, Md, Volumes 25-32

United States Naval Academy - 1874 - 888 pages
...and 6. 3. I'rove that if from a point without a circle a tangent and a secant be drawn, the angent is a mean proportional between the whole secant and its external segment. 'rove that in any triangle the product of two sides is equal to the product of the segnents of the...
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A Treatise on Special Or Elementary Geometry

Edward Olney - Geometry - 1876 - 354 pages
...Theorem.—If from a point without a circle a tangent be drawn, and a secant terminating in the concave arc, the tangent is a mean proportional between the whole secant and its external segment; whence the square of the tangent equals the product of the secant into its external segment. FIG, DEM.—OA...
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Annual Statement, Volumes 11-20

1876 - 646 pages
...their sum, and bisects the opposite side. 3. 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. 4. (a) Define a geometric locus. (b) If the base and vertical angle of...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 pages
...EC : EB; or, EA:EB = EC2. (4). Hence, if from a point w1tnout tne cIrcte a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and the part w1thout the circle. Secants of Two Circles. — In any two circles, the secants joining the...
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A Treatise on Special Or Elementary Geometry

Edward Olney - Geometry - 1877 - 272 pages
...Theorem.—If from a point without a circle a tangent be drawn, and a secant terminating in the concave arc, the tangent is a mean proportional between the whole secant and its external segment; whence the square of the tangent equals the product of the secant into its external seg~ ment. FIG....
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