 | William Chauvenet - Geometry - 1872 - 382 pages
...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 a circle...proportional, since their product is constant (2). point in the plane of a circle a straight line is drawn intersecting the circumference, the product... | |
 | 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... | |
 | 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.... | |
 | 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.... | |
 | William Chauvenet - Geometry - 1879 - 380 pages
...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 circle...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... | |
 | 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.... | |
 | 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... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...their external segments are reciprocally proportional. Corollary. If a tangent and a secant intersect, the tangent is a mean proportional between the whole secant and its external segment. BOOK IV. THEOREMS. PROPOSITION I. Parallelograms having equal bases and equal altitudes are equivalent.... | |
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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. 
