Elements of analytical geometry and the differential and integral calculus . is 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 the pointP by x\ y\ and of the point Q byx, y, and of any other point in theline as H by x, y. Now the equation of any linepassing through point
Elements of analytical geometry and the differential and integral calculus . is 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 the pointP by x\ y\ and of the point Q byx, y, and of any other point in theline as H by x, y. Now the equation of any linepassing through point H may beexpressed by y=ax-\-h. (I) * This condition of the perpendicularity of the twolines may be more satisfactory to some when they readthe more direct demonstration. Let AB be one line, and AT) another line at rightangles to it. Join BD, and from A draw AX perpen-dicular to BD, and conceive ^Athe axis. The tangentof the angle BAX=a, and XAD=^—a\ AX=l, andit is the mean proportion between a and -—a. There-fore a : 1 : : 1 : —a. Whence —aa=l or O(i-fl=0. Q. B, D.
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Keywords: ., bookauthorrobinson, bookcentury1800, bookdecade1850, bookyear1856
