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" 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 its external segment. "
High School Algebra Complete - Page 355
by Marquis Joseph Newell - 1920 - 401 pages
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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...
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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...
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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...
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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...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1863 - 464 pages
...that is, the rectangles of each secant and its external segment are equal. PROPOSITION XXX. THEOREM. If from a point without a circle, a tangent and a secant be drawn, the secant terminating in the concave arc, the tangent will be a mean proportional between...
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Primary Elements of Plane and Solid Geometry: For Schools and Academies

Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...Then, multiplying extremes and means, we get AExEC=BExED. Therefore, if two chords, etc. THEOREM XIII. 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 part. Let AB...
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An Elementary Course of Plane Geometry

Richard Wormell - Geometry, Modern - 1868 - 286 pages
...arc required. For every angle AMB inscribed in the arc is equal to the angle CAB. Fig. 211. Fig. 212. 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....
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Catalogue of the Officers and Students

Trinity College (Hartford, Conn.) - 1870 - 1008 pages
...formed by a tangent and a chord is measured by half the arc included between its sides. 4. Prove that If from a point without a circle a tangent and a secant are drawn, the square of the tangent is equivalent to the rectangle of the whole secant and its external segment....
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An Elementary Course of Plane Geometry

Richard Wormell - Geometry, Plane - 1870 - 304 pages
...contained by the segments of the one is equal to the rectangle contained by the segments of the other. 49. 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...
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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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