...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...cuts the circle and the part of it without the circle is equal to the square of the tangent. 50. The line joining the centres of two circumferences is perpendicular...

...enunciation, so as to extend it to the case where the parallelograms are on opposite sides of the bases. 5. If from any point without a circle two straight lines...the circle, and the part of it without the circle, is equal to the square of the line which touches it. 6. Prove that similar triangles are to one another...

...rectangle of EC and ED becomes the square of EF, and therefore we have this proposition, viz. If from a point without a circle two straight lines be drawn, one of which cuts and the other touches the circle, then the rectangle of the segments of the cutting line shall be equal...

...AB; shew that the rectangle CP, CQ is equal to the rectangle CP", CQ.' PROPOSITION XXXVI. THEOREM. If, from any point without a circle, two straight...it; the rectangle contained by the whole line which cute the circle, and the part of it without the circle, must be equal to the square on the line which...

...circle, their four extremities shall all -. in the circumference of a circle. PROPOSITION XXXVI. THEOREM. If, from any point without a circle, two straight...and the other touches it ; the rectangle contained 6y the whole line which cuts the circle, and the part of it without the. circle, must be equal to the...

...respectively, shew that the quadrilateral KLMN is equal in all respects to the quadrilateral ABCD. IX. If from any point without a circle two straight lines be drawn, one of which cuts the circle, bui does not pass through the centre, and the other touches it ; prove that the rectangle contained...

...The following results are frequently required in the investigation of the properties of triangles. If from any point without a circle two straight lines be drawn touching the circle, they are equal. This follows immediately from Euclid in. 37. For if DBj DE be...

...that AB bisects the angle between PA and QA produced. Prove that the chords .SPand BQ are equal. 7. If from any point without a circle two straight lines...of which cuts the circle, and the other touches it j the rectangle contained by the whole line which cuts the circle, and the part of it without the circle,...

...circle there be drawn two straight lines, one of which cuts the circle, and the other meets it; if the rectangle contained by the whole line which cuts...the circle, and the part of it without the circle, be equal to the square on the line which, meets it, the line which meets, shall touch the circle. Let...

...circle there be drawn two 10 straight linos one of which cuts the circle and tho other meets it, and if the rectangle contained by the whole line which cuts the circle and the part of it without the circle be equal to tho square of the lino which meets it, then the line which meets the circle shall bo a...