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" If } from a point without a circle, a tangent and a secant be drawn, the tangent is the mean proportional between the secant and its external segment. "
Plane Geometry - Page 146
by Arthur Schultze, Frank Louis Sevenoak - 1911 - 233 pages
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Catalogue - Harvard University

Harvard University - 1876 - 554 pages
...circle in terms of the segments AD and BD, into which it divides the diameter AB perpendicular to it. 4. If from a point, without a circle, a tangent and a secant are drawn, the tangent is a mean proportional between the entire secant and the part without the circle....
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Harvard Examination Papers

Robert Fowler Leighton - 1877 - 372 pages
...circle in terms of the segments AD and BD, into which it divides the diameter AB perpendicular to it. 4. If from a point, without a circle, a tangent and a secant are drawn, the tangent is a mean proportional between the entire secant and the part without the circle....
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Elements of Plane Geometry, Part 1

Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...and in like manner it can be proved of any other two homologous sides. PROPOSITION XVHL—THEOREM. If from a point without a circle a tangent and a secant be drawn, the tangent will be a mean proportional between the secant and its external segment. Let AC be a secant, and CB...
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First B.A. Examination, University of London: A Hand-book to the Study of ...

J. G - 1878 - 408 pages
...constant, and conversely." Hence, also, either as a separate theorem or as a corollary to " B : " " If from a point without a circle a tangent and a secant be drawn to it, the square on the tangent will be equal to the rectangle contained by the whole secant and the...
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Annual Report of the Superintendent of Public Instruction of the State of ...

Wisconsin. Department of Public Instruction - Education - 1879 - 380 pages
...difference of two quantities is equal to the difference of their squares. 3. Prove that, if from the same point without a circle a tangent and a secant be drawn, the tangent will be a mean proportional between the secant and its external segment. 4. If the faces of a square...
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Appendix to the Assembly Journal, Volume 2

Wisconsin - Wisconsin - 1879 - 1240 pages
...difference of two quantities is equal to the difference of their squares, 3. Prove that, if from the same point without a circle a tangent and a secant be drawn, the tangent will be a mean proportional between the secant and its external segment. 4. If the faces of a square...
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Harvard Examination Papers

Robert Fowler Leighton - 1880 - 428 pages
...other, what is the ratio of the areas ? State and prove the proposition on which your answer depends. 5. If from a point without a circle a tangent and a secant be drawn, the tangent will be a mean proportional between the whole secant and its external segment. Prove. 6. If two circles...
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Essentials of Geometry

Alfred Hix Welsh - Geometry - 1883 - 326 pages
...circle. Suggestion.—What kind of a triangle is ABC? How does AC cut DB? (See Th. VI.) THEOREM XIII. If from a point without a circle, a tangent and a secant be drawn, terminating in the circumference, 'the square of the tangent will equal the rectangle of the secant...
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The Eclectic School Geometry

Evan Wilhelm Evans - Geometry - 1884 - 242 pages
...point within a circle any chord . is drawn, the product of its two segments is constant. THEOREM XIX. If from a point without a circle a tangent and a secant be drawn, the tangent will be a mean proportional between the secant and its external part. Let AB be a tangent and AC a...
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Wentworth & Hill's Exercise Manuals: Geometry, Issue 3

George Albert Wentworth - 1884 - 264 pages
...secant and the external segment is constant in whatever direction the secant is drawn. 166. Theorem. If from a point without a circle a tangent and a secant are drawn, the tangent is a mean proportional between the entire secant and the external segment. PROBLEMS....
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