 | George Roberts Perkins - Geometry - 1856 - 460 pages
...give the proportion PA:PB::;PB':PA'. THEOREM When a secant and tangent are drawn from the same point, the tangent is a mean proportional between the secant and its external segment. This Theorem is in reality only a particular case of the preceding, when the points B, B' of the secant... | |
 | John Daniel Runkle - Mathematics - 1861 - 490 pages
...then x -f- R and x-\-r will be the secants, and x — R and x — r the external segments ; and since the tangent is a mean proportional between the secant and its external segment, we have 2^(2* — R2) = \J(x* — r2), whence PRIZK SOLUTION OP PROBLEM П. By A. STANLEY, London,... | |
 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...B and D equal. Therefore, AE : EC : : DE : EB. 333. Corollary. — If from the same point there be a tangent and a secant, the tangent is a mean proportional between the secant and its exterior part. For the tangent is the limit of all the secants which pass through the point of meeting.... | |
 | Eli Todd Tappan - Geometry - 1868 - 432 pages
...at B and D equal. Therefore, AE : EC : : DE : EB. 333. Corollary — If from the same point there be a tangent and a secant, the tangent is a mean proportional between the secant and its exterior part. For the tangent is the limit of all the secants which pass through the point of meeting.... | |
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...at B and D equal. Therefore, AE : EC : : DE : EB. 333. Corollary — If from the same point there be a tangent and a secant, the tangent is a mean proportional between the secant and its exterior part. For the tangent is the limit of all the secants which pass through the point of meeting.... | |
 | Aaron Schuyler - Geometry - 1876 - 384 pages
...and equivalent to tlie square of the tangent drawn from the same point to the circumference; that is, the tangent is a mean proportional between the secant and its external segment. (?) 249. Exercises. 1. If two circles are tangent internally, chords of the greater, drawn from the... | |
 | William Henry Searles - 1899 - 604 pages
...rectangle of the secant tangent meet. and its external segment is equal to the square on the tangent. And the tangent is a mean proportional between the secant and its external segment. K If a straight line The sum of the squares on from the vertex the two sides is equal to of a triangle... | |
 | Franklin Ibach - Geometry - 1882 - 208 pages
...PLANE GEOMETRY. THEOREM XXVII. 287. If a tangent and a secant are drawn from a point without a circle, the tangent is a mean proportional between the secant and its external segment. Let the tangent PB and the secant PA be drawn from a point P without the O. and To prove that PA :... | |
 | Seth Thayer Stewart - Geometry, Modern - 1891 - 428 pages
...external segments. PROP. XVIII. If, from any point without a circle, a tangent and secant are drawn, the tangent is a mean proportional between the secant and its external segment. PROP. XIX. Circumferences of circles are proportional to the diameters or to their radii. 257 PROP.... | |
 | George Clinton Shutts - Geometry - 1894 - 412 pages
...the circle can be PROPOSITION XXVIII. 314. Theorem. // a secant and a tangent meet without a circle, the tangent is a mean proportional between the secant and its external segment. Let AC represent a tangent, and OC a secant meeting the tangent at the point C. ОС AC To prove that... | |
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If from the same point there be a tangent and a secant, the tangent is a mean proportional between the secant and its exterior part. 
