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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. "
Principles of Plane Geometry - Page 47
by James Wallace MacDonald - 1889 - 63 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 and its external...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 pages
...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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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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An Elementary Course of Plane Geometry

Richard Wormell - Geometry, Plane - 1870 - 304 pages
...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 (§230). Or, If from any point without a circle two straight lines be drawn,...
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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 - 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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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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Euclidian Geometry

Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...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 is tqual to the...
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Annual Register of the United States Naval Academy, Annapolis, Md, Volumes 25-32

United States Naval Academy - 1874 - 886 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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