 | 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.... | |
 | 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...mean proportional between the secant and its external segment. Let AC be a secant, and CB a tangent, both drawn from the point C; then will CB 2 be equal... | |
 | 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... | |
 | 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,...mean proportional between the secant and its external segment. 4. If the faces of a square pyramid are equilateral triangles, prove that the height of the... | |
 | 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,...mean proportional between the secant and its external segment. 4. If the faces of a square pyramid are equilateral triangles, prove that the height of the... | |
 | 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...the tangent will be a mean proportional between the whole secant and its external segment. Prove. 6. If two circles intersect and from any point of their... | |
 | Vermont. Dept. of Education - 1880 - 216 pages
...point without a circle, v. tangent au'la secant be drawn, the secant terminating in the concave arc, the tangent will be a mean proportional between the secant and its external s«gment 5. How inscribe a regular hexagon ? An equilateral triangle ? A regular decagon ? Pentagon... | |
 | 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... | |
 | 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.... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...that is, the rectangles of each secant and its external segment arc equal. PROPOSITION XXX. THEOREM. If from a point without a circle, a tangent and a secant are drawn, the secant terminating in the concave arc, the tangent is a t1tfan proportional between... | |
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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. 
