This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1884 Excerpt: ...through which the circle can be drawn. 83. From these principles follow the tables below, which include the fundamental problems already given. The problems of a straight line through two explicit points, and of a circle througn three such points, are omitted, as they are not problems of tan gency. a---Tangent Straight ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1884 Excerpt: ...through which the circle can be drawn. 83. From these principles follow the tables below, which include the fundamental problems already given. The problems of a straight line through two explicit points, and of a circle througn three such points, are omitted, as they are not problems of tan gency. a---Tangent Straight Lines. / Prob. 52. To draw a Tangent at a given point, on a circl- whose centre is known. The solution here given is a useful application of Prob. 43. Thus (Fig. 21): Fia. 21. 1st. Lay off the radius AC, each way from A, and on the circumference. 2d. Through C, and the points p and q thus found, draw indefinite lines, not shown. 3d. From j- and q as centres, and radius, AC, of the given circle, draw arcs, and note their intersections with the lines just described. 4th. Join the points thus found, by a straight line, and it will be the required tangent at A. Principles.--These will be perfectly obvious on making the construction. Prob. 53. To draw a Tangent at a given point, on a circle whose centre is not known. Let abc, Fig. 48, be the circle, and T the given point. Take any arc, la, on one side of T, and a double arc, Tc, on the other side Draw cad, making ad equal to Ta. Then c?T will be the tangeni required. Remark.--By finding the centre, and drawing the radii at T and a, the principles of the solution will be obvious. Pkob. 54. To draw a Tangent to a given circle, from an exterior point. Let C be the centre of the given circle, and let A be the given point. (Fig. 49.) Fio. 49. 1st. Join A and C. 2d. Find by trial, or by construction, B, the middle point of AC. 3d. With B as a centre, and with BA as a radius, describe the arc deA. 4th. Draw Ae and Ad, and they will both be tangents, answering the given conditions. Principles.--...
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