| George Darley - Euclid's Elements - 1836 - 172 pages
...under the segments of one is equal to the rectangle under the segments of the other, 110. ART. 156. **If from a point without a circle a secant and a tangent be drawn** to the circle, the square of the tangent is equal to the rectangle under the whole secant and its external... | |
| Andrew Bell - Euclid's Elements - 1837 - 290 pages
...EH; therefore the rectangle AE'EC, is equal to the rectangle BE • ED. PROPOSITION XXXVI. THEOREM. **If from a point without a circle a secant and a tangent** to it be drawn, the rectangle under the secant and its external segment is equal to the square of the... | |
| Euclides - 1860 - 288 pages
...the rectangle AE • EC is equal to the rectangle BE • ED. *»* See Appendix — Proposition (D). **If from a point without a circle a secant and a tangent** to it be drawn, the rectangle under the secant and its external segment is equal to the square on the... | |
| Richard Wormell - Geometry, Plane - 1870 - 304 pages
...contained by the segments of the other. 49. If from a point without a circle a tangent and a secant **be drawn, the tangent is a mean proportional between the whole secant and** the part without the circle (§230). Or, If from any point without a circle two straight lines be drawn,... | |
| 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... | |
| Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...PQ) = rectangle (RX, XS). (Ii. 2) Lastly, if neither of them pass through the centre, THEOREM (<?). **If from a point without a circle a secant and a tangent be drawn, the** rectangle contained by the parts of the secant between the given point and the circle is tqual to the... | |
| United States Naval Academy - 1874 - 886 pages
...triangle, or circle deribed upon the side as diameter ? Give reasons for your answer. I. Prove that **if, from a point without a circle, a secant and a tangent** bo drawn, a tangent ie a mean proportional between the whole secant and the part without i- circle.... | |
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