 | 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... | |
 | 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... | |
 | 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.... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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.... | |
 | 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.... | |
 | Albert Newton Raub - Education - 1894 - 782 pages
...diameter of the glass ball. . EF, the height of the pole, 100 ft. The line AE is secant and AC tangent to the circle. The tangent is a mean proportional between the whole ecant and the external segment. AE: AC :: AC : AH 9: AC :: AC : 5 AC2 = 45 AC = 6.708 In the right... | |
 | 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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It follows from § 259 that if through a fixed point without a circle a secant and a tangent be drawn, the tangent is a mean proportional between the whole secant and its external segment. 
