...segments between the vertex and the cutting line, may be equal to a given square. (VI.) If from a given point, without a circle, two straight lines be drawn to the concave circumference, they shall be reciprocally proportional to the parts of them between the given point...

...intercepted by two lines drawn from its other extremity to the former intersections of the circle. 79- If from a point without a circle two straight lines be drawn touching it, and from one point of contact a perpendicular be drawn to that diameter which passes through...

...be equal to twice the rectangle contained by this cutting line and the part without the Circle. 10. If from a point without a circle two straight lines be drawn, one through the centre to the circumference, and the other perpendicular to it, and on the former a...

...: AB : : AB : AE ; .-. {E. 17. 6.) DA X AE = AB*. PROP. XLIX. ' ' ' ' 58. THEOREM. If from a given point, without a circle, two straight lines be drawn to the concave - circumference, they shall be reciprocally pro.' fortional to the parts of them bet-ween the given...

...equal, therefore (Eucl. iii. 29.) the straight lines AG, В F arc also equal. (2.) If from a paint without a circle, two straight lines be drawn to the...with the line joining the same point and the centre, t he parts of t he lines which are intercepted within the circle are equal. From the point P without...

...circumference. If FG be parallel to AB ; the arc EF= EG, whence AG = BF. GEOMETRICAL PKOBLEMS. (2.) If from a point without a circle, two straight lines...joining the same point and the centre, the parts of the lines which are intercepted within the circle are equal. From the point P without the circle ABC...

...cut the circle. 9. Two tangents from the same point, without a circle, are equal to each other. 10. If, from a point without a circle, two straight lines be drawn whereof one is a tangent and the other cuts the circle, the rectangle contained by the line which cuts...

...«Cor. 16. touches the circle ABC. Wherefore, if from a point, '' &c. UED COR. Hence it is evident, that if from a point without a circle, two straight lines be drawn to touch the circle, these two straight lines are equal to one another. THE ELEMENTS OF EUCLID. BOOK IV....

...triangle. Q. XXIII. If, from a point P, without the circle ABC, two straight lines Fig. 314. PB, PD, he drawn to the concave part of the circumference, making equal angles with PO, the line joining P and the centre, the parts of the lines, AB, CD, which are intercepted within...

...equiangular to one another, the sides which are opposite to equal angles are proportional. (Euc. VI. 4.) 7. If from a point without a circle two straight lines be drawn cutting it, and be continued to meet the remote part of its circumference, the rectangle contained...