 | Benjamin Williamson - Calculus, Differential - 1872 - 372 pages
...0 + -= о ; hence find when they are real and when imaginary. 26. Show geometrically that the first pedal of a circle with respect to a point on its circumference is a cardioide. 27. In the figure of Art. 25о prove that the square of the arc BPi& equal to 8 a. PN'.... | |
 | Benjamin Williamson - Calculus - 1873 - 394 pages
...+ - = о ; hence find when they are real and when imaginary. id. Show geometrically that the first pedal of a circle with respect to a point on its circumference is a cardioid. 27. Show in like manner that the Limaçon is the first pedal of a circle with respect to... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...which it is measured in the opposite direction as exercises to the student. PROPOSITION. The inverse of a circle with respect to a point on its circumference is a straight line perpendicular to the diameter through the point. Let A be the other end of the diamr.... | |
 | Electronic journals - 1922 - 560 pages
...1718, at twenty years of age, was not only the first to show that the cardioid is the first positive pedal of a circle, with respect to a point on its circumference, but also the first to find the equations of the positive and negative pedals of the cardioid with respect... | |
 | Edwin Bidwell Wilson - Calculus - 1911 - 302 pages
...reflected rays is called the caustic of the curve with respect to the point. Show that the caustic of a circle with respect to a point on its circumference is a cardioid. 16. The curve which is the envelope of the characteristic lines, that is, of the rulings,... | |
 | University of Aberdeen - 1915 - 944 pages
...the three internal bisectors of the angles of a triangle are concurrent. 3. — Show that the inverse of a circle with respect to a point on its circumference is a straight line. Prove that this line is the radical axis of the given circle and the circle of inversion.... | |
 | Edinburgh Mathematical Society - Electronic journals - 1887 - 162 pages
...PK be the normal, we Let OK bisect the angle FOB. The OK = KP, and we have 20KcosJ0 = OP = 2acos2J0. Hence OK = acos£0 ; and it follows that K lies on...circle. For M is a point on the pedal of the circle OKB ; and OM = MP. Hence the locus of M is a cardioid similar to OPA, the ratio of similarity being... | |
 | Edward Harrington Lockwood - Curves - 1967 - 290 pages
...base-circle. A curve drawn in this way is called the pedal of the base-curve; thus the cardioid is said to be the pedal of a circle with respect to a point on its circumference. (See ch. 18, p. 153.) If P is a point on the cardioid corresponding to a point Q on the base-circle,... | |
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We have, incidentally, a proof that the pedal of a circle with respect to a point on its circumference is... 