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 1
... direction . Thus AB = == - BA or AB + BA = 0 . Similarly for three collinear points A , B , C : AB + BC - AC - CA , therefore BC + CA + AB = 0 . 2. If four points A , B , C , D , be taken in alphabetical order on a circle , we have by ...
... direction . Thus AB = == - BA or AB + BA = 0 . Similarly for three collinear points A , B , C : AB + BC - AC - CA , therefore BC + CA + AB = 0 . 2. If four points A , B , C , D , be taken in alphabetical order on a circle , we have by ...
Página 8
... direction of the infinitesimal chord at its point of contact , or is the chord joining two indefinitely near points . Again , let the tangent T and its point of contact be fixed and the chord AX given in length . As the radius of the ...
... direction of the infinitesimal chord at its point of contact , or is the chord joining two indefinitely near points . Again , let the tangent T and its point of contact be fixed and the chord AX given in length . As the radius of the ...
Página 28
... direction such that the area of the quadrilateral ABXY , where AB is a given diameter , is a maximum . [ Draw a diameter YX ' , and AYBX ' is a rectangle , hence AX ' is equal and parallel to BY . Join BX and XX ' , and draw BC parallel ...
... direction such that the area of the quadrilateral ABXY , where AB is a given diameter , is a maximum . [ Draw a diameter YX ' , and AYBX ' is a rectangle , hence AX ' is equal and parallel to BY . Join BX and XX ' , and draw BC parallel ...
Página 33
... direction around P , according as PB recedes from the perpendicular from P on BC , the segments AP and BP approach an equality , and the triangle ABC is a minimum when AP - BP . 18. The several parts , of a geometrical figure which ...
... direction around P , according as PB recedes from the perpendicular from P on BC , the segments AP and BP approach an equality , and the triangle ABC is a minimum when AP - BP . 18. The several parts , of a geometrical figure which ...
Página 34
... example , that a variable chord XY of a circle moves parallel to a certain direction ; it gradually increases in length as it approaches the centre and if XY be a diameter and X'Y ' a consecutive chord ;. 34 MAXIMUM AND MINIMUM . SECTION ...
... example , that a variable chord XY of a circle moves parallel to a certain direction ; it gradually increases in length as it approaches the centre and if XY be a diameter and X'Y ' a consecutive chord ;. 34 MAXIMUM AND MINIMUM . SECTION ...
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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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