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" X PB'; that 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. "
A Treatise on Elementary Geometry: With Appendices Containing a Collection ... - Page 115
by William Chauvenet - 1871 - 368 pages
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...tangent as a secant whose two points of intersection are coincident (II. 28), we shall have PT 2 = PA' X PB'; that is, if through a fixed point without...proportional, since their product is constant (2). point in the plane of a circle a straight line is drawn intersecting the circumference, the product...
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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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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 Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1875 - 466 pages
...tangent as a secant whose two points of intersection are coincident (II. 28), we shall have PT'^PA' X PB'; that is, if through a fixed point without a...proportional, since their product is constant (2). point in the plane of a circle a straight line is drawn intersecting the circumference, the product...
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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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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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A Treatise on Elementary Geometry, with Appendices Containing a Collection ...

William Chauvenet - Geometry - 1879 - 380 pages
...tangent as a secant whose two points of intersection are coincident (II. 28), we shall have PF = P4' X PB'; that is, if through a fixed point without a...between the whole secant and its external segment. 60. Se/ialium I. When a secant, constantly passing through a fixed point, changes its direction, the whole...
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Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with ...

Edward Olney - Geometry - 1883 - 352 pages
...— // from a point without a circle a tangent is 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. DEMONSTRATION....
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...homologous sides are proportional ; that is, AP: CP = CP:BP. Whence, AP x BP = UP. 294. COROLLARY I. The tangent is a mean proportional between the whole secant and its external segment. 295. COROLLARY II. Let AP and A'P be any two secants of the circle ACB, and draw CP tangent to the...
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