Elements of analytical geometry and the differential and integral calculus . -l= THE CIRCLE. 31 This last equation shows that the two lines are perpendicularto each other, as proved by (Cor. 2, Prop. V, Chap. I.)* Because a and a are indefinite, we conclude that an infinitenumber of supplemental chords may be drawn in the semicircle,which is obviously true. Scholium. As BDX is a right angled triangle, and BX itshypotenuse, it follows that the diameter is greater than any one chord increases, its supplementary chord decreases. From the center A let fall the perpendiculars AH, AF. Th
Elements of analytical geometry and the differential and integral calculus . -l= THE CIRCLE. 31 This last equation shows that the two lines are perpendicularto each other, as proved by (Cor. 2, Prop. V, Chap. I.)* Because a and a are indefinite, we conclude that an infinitenumber of supplemental chords may be drawn in the semicircle,which is obviously true. Scholium. As BDX is a right angled triangle, and BX itshypotenuse, it follows that the diameter is greater than any one chord increases, its supplementary chord decreases. From the center A let fall the perpendiculars AH, AF. Thenthe two triangles XAH and XBD are equiangular and similar ;therefore, as A is the middle point of XB, His the middle pointof XD, and F is the middle point of BD. AH=^(BD), andAF=^[XD). That is, the distance of any chord frmn the centeris equal to half its supplementary chord. PROPOSITION III. To find the equation of a straight line which shall be tangentto the circumference of a circle. Draw a line cutting the curve inany two points, as P and Q. De-signate the co-ordinates of
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