A Treatise on the Geometry of the Circle and Some Extensions to Conic Sections by the Method of Reciprocation: With Numerous ExamplesMacmillan, 1891 - 299 páginas |
Dentro del libro
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Página xi
... 159 SECTION III . RECIPROCATION . 80. Reciprocal Polar Curves . Their Elementary Properties , 81. Reciprocation of a Circle from any Origin , Examples , · 162 · 164 167 ARTICLE CHAPTER VIII . COAXAL CIRCLES . SECTION I. COAXAL CONTENTS .
... 159 SECTION III . RECIPROCATION . 80. Reciprocal Polar Curves . Their Elementary Properties , 81. Reciprocation of a Circle from any Origin , Examples , · 162 · 164 167 ARTICLE CHAPTER VIII . COAXAL CIRCLES . SECTION I. COAXAL CONTENTS .
Página xiv
... • 245 246 246 • 126. Angle between two Curves remains unaltered by Inversion ,. 127. Important Considerations arising from the Theorem of 247 Art . 126 , 248 ARTICLE SECTION III . ANHARMONIC RATIOS UNALTERED by INVERSION . xiv CONTENTS .
... • 245 246 246 • 126. Angle between two Curves remains unaltered by Inversion ,. 127. Important Considerations arising from the Theorem of 247 Art . 126 , 248 ARTICLE SECTION III . ANHARMONIC RATIOS UNALTERED by INVERSION . xiv CONTENTS .
Página 9
... curve of which A is fixed and X variable , and TA and TX tangents . It appears as before that as X approaches A the ... curve AX . Hence in the limiting position , i.e. , when the tangents are con- secutive , their point of intersection ...
... curve of which A is fixed and X variable , and TA and TX tangents . It appears as before that as X approaches A the ... curve AX . Hence in the limiting position , i.e. , when the tangents are con- secutive , their point of intersection ...
Página 18
... curve of given perimeter is of greatest area when its form is a circle . A M N B [ Let A be any point on the curve , and take B such that AMB and ANB are equal in length . Then the areas AMB and ANB are each a maximum when AB is the ...
... curve of given perimeter is of greatest area when its form is a circle . A M N B [ Let A be any point on the curve , and take B such that AMB and ANB are equal in length . Then the areas AMB and ANB are each a maximum when AB is the ...
Página 23
... curve concave to its vertex C. The tangent AB which forms with the sides of the angle a triangle ABC of minimum area ... curve is concave to C , A'B'C < XYC ; a fortiori ABC < XYC . COR . 1. In the particular case when the curve is a ...
... curve concave to its vertex C. The tangent AB which forms with the sides of the angle a triangle ABC of minimum area ... curve is concave to C , A'B'C < XYC ; a fortiori ABC < XYC . COR . 1. In the particular case when the curve is a ...
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Otras ediciones - Ver todas
A Treatise on the Geometry of the Circle: And Some Extensions to Conic ... William J. M'Clelland Sin vista previa disponible - 2017 |
A Treatise on the Geometry of the Circle and Some Extensions to Conic ... William J. M'Clelland Sin vista previa disponible - 2018 |
Términos y frases comunes
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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