Download PDF by William J. M'Clelland: A treatise on the geometry of the circle and some extensions

By William J. M'Clelland

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New PDF release: A treatise on the geometry of the circle and some extensions

Leopold is thrilled to put up this vintage booklet as a part of our huge vintage Library assortment. a number of the books in our assortment were out of print for many years, and as a result haven't been available to most of the people. the purpose of our publishing application is to facilitate quick entry to this tremendous reservoir of literature, and our view is this is an important literary paintings, which merits to be introduced again into print after many many years.

Extra resources for A treatise on the geometry of the circle and some extensions to conic sections by the method of reciprocation, with numerous examples.

Example text

Segments and there remains the quadrilateral y A'B'C'D' (Ex. ]* of a quadrilateral are given in magnitude, the fourth side d is the diameter of maximum when the circle through the vertices and generally, When all the sides but one of a polygon of any order are given in magnitude, the area is a maximum when the circle on the ; closing side as diameter passes through the remaining vertices. ] 5. of a quadrilateral the diagonals S Having given pair of opposite sides is parallel to AD. BC and AD, its area is a and &' and a maximum when BC [Take any position of the quadrilateral and through and equal to 8.

The triangles ACD and BB'C are equal in every respect (Euc. I. 4), hence AA'C> BB'C] therefore A'B'C > ABC; therefore, etc. Let COR. 2. When the curve is a AB circle touching the sides ABC are each arid area of the angle the tangent is isosceles. the minima when triangle MAXIMUM AND MINIMUM. COR. Cor. 2, 3. we If which is 25 consider the portion of the circle in (7, the intercept of a variable convex to tangent made by the sides of the angle subtends a constant angle a at the centre of the circle (2a = 7r C).

From P : : OQ is the Centre of Similitude. is a point invariably connected with a Thus since variable inscribed triangle PQR of given species, the MAXIMUM AND MINIMUM. , points invariably connected with the describe triangle, right lines which can at once be constructed by the above method. all other Moreover, circle, we know that and the variable if is line or fixed and P describes a Radius Vector OP be divided in Q, in a given ratio, the locus of Q is a circle. Now if Q be turned around through any given angle the locus is the same circle displaced through the same angle.

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A treatise on the geometry of the circle and some extensions to conic sections by the method of reciprocation, with numerous examples. by William J. M'Clelland


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