Read A treatise on the geometry of the circle and some extensions to conic sections by the method of reciprocation; with numerous examples

A treatise on the geometry of the circle and some extensions to conic sections by the method of reciprocation; with numerous examples

William J. M'Clelland

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Description: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. 1891 ...of t, F2, F& These and many other excellent illustrations of the theory of three directly similar figures are to be found in Casey's Sequel to Euclid, to which the student is referred. See fifth edition, Miscellaneous Examples, pp. 231-248. CHAPTER X. Section I. Centres Of Similitude. 109. If A, rx; B, r2 be any two non-intersecting circles, P and Q the points of intersection of the direct and transverse common tangents, it is easily proved that A, B, P, Q are collinear, and that AP/BP = AQ/BQ = rjr2; hence the centres of similitude of two circles are the points of intersection of the direct and transverse common tangents In the case of intersecting circles, if G be a point of intersection, we infer from these equations that the bisectors of the angle between the circles meet the line of centres in P and Q (Euc. VI. 3). For the in-and ex-circles of a triangle taken in pairs the twelve centres of similitude are the vertices and the points where the bisectors of the angles meet the opposite sides. The centres of similitude of a line L and circle A are the extremities of the diameter perpendicular to L. For the common tangents to the circle and line are Therefore the common tangents, real or imaginary, to any two circles always intersect in real points. parallel to the latter, and the line of centres is the diameter at right angles to L; therefore, etc. 110. It has been seen as a particular case of a general property of coaxal circles (Art. 93) that any line AlA2B1B2 through 0, a, cuts the circles at equal angles and, /3, that the intercepted chords A1A2&d BlBl are in the ratio of the radii. These are obvious by the following AA1 and BBV Since GA/GB=rJr2 = AAJBB1 the triangles CAA1 and CBBt are similar (Euc. VI. 7); therefore AAX is paral...We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with A treatise on the geometry of the circle and some extensions to conic sections by the method of reciprocation; with numerous examples. To get started finding A treatise on the geometry of the circle and some extensions to conic sections by the method of reciprocation; with numerous examples, you are right to find our website which has a comprehensive collection of manuals listed.
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ISBN: 1130752712

Description: 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. 1891 ...of t, F2, F& These and many other excellent illustrations of the theory of three directly similar figures are to be found in Casey's Sequel to Euclid, to which the student is referred. See fifth edition, Miscellaneous Examples, pp. 231-248. CHAPTER X. Section I. Centres Of Similitude. 109. If A, rx; B, r2 be any two non-intersecting circles, P and Q the points of intersection of the direct and transverse common tangents, it is easily proved that A, B, P, Q are collinear, and that AP/BP = AQ/BQ = rjr2; hence the centres of similitude of two circles are the points of intersection of the direct and transverse common tangents In the case of intersecting circles, if G be a point of intersection, we infer from these equations that the bisectors of the angle between the circles meet the line of centres in P and Q (Euc. VI. 3). For the in-and ex-circles of a triangle taken in pairs the twelve centres of similitude are the vertices and the points where the bisectors of the angles meet the opposite sides. The centres of similitude of a line L and circle A are the extremities of the diameter perpendicular to L. For the common tangents to the circle and line are Therefore the common tangents, real or imaginary, to any two circles always intersect in real points. parallel to the latter, and the line of centres is the diameter at right angles to L; therefore, etc. 110. It has been seen as a particular case of a general property of coaxal circles (Art. 93) that any line AlA2B1B2 through 0, a, cuts the circles at equal angles and, /3, that the intercepted chords A1A2&d BlBl are in the ratio of the radii. These are obvious by the following AA1 and BBV Since GA/GB=rJr2 = AAJBB1 the triangles CAA1 and CBBt are similar (Euc. VI. 7); therefore AAX is paral...We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with A treatise on the geometry of the circle and some extensions to conic sections by the method of reciprocation; with numerous examples. To get started finding A treatise on the geometry of the circle and some extensions to conic sections by the method of reciprocation; with numerous examples, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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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

A treatise on the geometry of the circle and some extensions to conic sections by the method of reciprocation; with numerous examples

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