A Treatise on the Geometry of the Circle and Some Extensions to Conic Sections by the Method of Reciprocation: With Numerous ExamplesMacmillan, 1891 - 299 σελίδες |
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Σελίδα xiv
... INTERSECTION OF FIGURES AND OF THEIR INVERSES . 123. General Relations between a Circle and its Inverse from any 124. Problem . Corollary , 125. Theorem , 243 • 245 246 246 • 126. Angle between two Curves remains unaltered by Inversion ...
... INTERSECTION OF FIGURES AND OF THEIR INVERSES . 123. General Relations between a Circle and its Inverse from any 124. Problem . Corollary , 125. Theorem , 243 • 245 246 246 • 126. Angle between two Curves remains unaltered by Inversion ...
Σελίδα 6
... intersection of two circles is that between the tangents drawn to them at either point of intersection ; it is therefore equal to the angle between 6 INTRODUCTION . Limiting Cases, 0 and ∞,
... intersection of two circles is that between the tangents drawn to them at either point of intersection ; it is therefore equal to the angle between 6 INTRODUCTION . Limiting Cases, 0 and ∞,
Σελίδα 7
... intersection . EXAMPLES . 1. To find the angles between the circum- and ex - circles of a triangle ABC . [ Since 82 R2 + 2Rr , etc. , we easily obtain 2 cos 01 = with similar expressions for 02 and 03. ] 2. To find the angle of intersection ...
... intersection . EXAMPLES . 1. To find the angles between the circum- and ex - circles of a triangle ABC . [ Since 82 R2 + 2Rr , etc. , we easily obtain 2 cos 01 = with similar expressions for 02 and 03. ] 2. To find the angle of intersection ...
Σελίδα 9
... secutive , their point of intersection is on the curve . A curve touched by a variable line is called the Envelope of the line . Thus the envelope of a line which varies according to any law is the locus of the. INTRODUCTION . 9 Envelopes,
... secutive , their point of intersection is on the curve . A curve touched by a variable line is called the Envelope of the line . Thus the envelope of a line which varies according to any law is the locus of the. INTRODUCTION . 9 Envelopes,
Σελίδα 21
... Let fall a perpendicular BL and make B'L - BL . Join AB and let C be its intersection with L. Take any other point P on the line and join AP and B'P . The triangles BCL and B'CL are equal in every respect. MAXIMUM AND MINIMUM . 21.
... Let fall a perpendicular BL and make B'L - BL . Join AB and let C be its intersection with L. Take any other point P on the line and join AP and B'P . The triangles BCL and B'CL are equal in every respect. MAXIMUM AND MINIMUM . 21.
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Άλλες εκδόσεις - Προβολή όλων
A Treatise on the Geometry of the Circle: And Some Extensions to Conic ... William J. M'Clelland Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
A Treatise on the Geometry of the Circle and Some Extensions to Conic ... William J. M'Clelland Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD bisected bisector Brocard points centre of similitude centres of perspective circum-centre circum-circle coaxal system coincide common tangents concurrent concurrent lines conic constant corresponding cyclic polygon cyclic quadrilateral denote diagonals diameter distances equal equation equianharmonic ex-circles fixed point given circles hence hexagon in-circle infinity inscribed inverse points Isogonal Conjugates isosceles limiting points line at infinity lines joining locus maximum mean centre median median triangle meet middle point minimum multiples opposite sides orthocentre orthogonally pair of inverse parallel pedal triangle perpendiculars point of intersection points of contact polar polygon prove r₁ radical axis radius reciprocal rectangle right angles segments sides of ABC similar triangles Similarly Simson lines species squares subtend symmedian point system of points tangents Theorem transversal triangle ABC triangle PQR vertex vertical angle
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