Constructive Geometry of Plane Curves With Numerous Examples
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The centre of the auxiliary circle is frequently called the origin. The advantage of using a circle for the auxiliary conic chiefly arises from the two following theorems, which enable us to trans- form by this method, not only theorems of position, but also theorems involving the magnitude of lines and angles. Theorem. The distance of any point P from the origin is the reciprocal of the distance Ot from the origin of the cor- responding line pt ; i. E. OP. Ot = r\ where Ot is perpendicular to ...pt and r is the radius of the auxiliary circle. Theorem. The angle TQT^ between any two lines TQ^ T^Q is equal to the angle subtended at the origin by the corresponding points 27, p^ ; for Op is perpendicular to TQ and Op^ to T^Q. Problem 119. To find the polar reciprocal of one circle, centre C, radius GA, with regard to another, centre 0, radius OM, i. E. To find the locus of the pole p with regard to the circle (0) of any tangent PT to the circle C. (Fig. 116. ) Find iT/if, the polar with respect to the auxiliary circle (centre 0) of C, the centre of the circle to be reciprocated ; i.
What to read after Constructive Geometry of Plane Curves With Numerous Examples?
You can find similar books in the "Read Also" column, or choose other free books by T H Thomas Henry Eagles to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
The centre of the auxiliary circle is frequently called the origin. The advantage of using a circle for the auxiliary conic chiefly arises from the two following theorems, which enable us to trans- form by this method, not only theorems of position, but also theorems involving the magnitude of lines and angles. Theorem. The distance of any point P from the origin is the reciprocal of the distance Ot from the origin of the cor- responding line pt ; i. E. OP. Ot = r\ where Ot is perpendicular to ...pt and r is the radius of the auxiliary circle. Theorem. The angle TQT^ between any two lines TQ^ T^Q is equal to the angle subtended at the origin by the corresponding points 27, p^ ; for Op is perpendicular to TQ and Op^ to T^Q. Problem 119. To find the polar reciprocal of one circle, centre C, radius GA, with regard to another, centre 0, radius OM, i. E. To find the locus of the pole p with regard to the circle (0) of any tangent PT to the circle C. (Fig. 116. ) Find iT/if, the polar with respect to the auxiliary circle (centre 0) of C, the centre of the circle to be reciprocated ; i.
What to read after Constructive Geometry of Plane Curves With Numerous Examples?
You can find similar books in the "Read Also" column, or choose other free books by T H Thomas Henry Eagles to read onlineMoreLess
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