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
Resultados 1-5 de 54
Página 13
... points ? Ptolemy's Theorem . 2. Express a condition that the circum - circle ... middle points of the sides and the in - circle are four circles satisfying ... point of contact of the tangent . Then BC . AP + CA . BP + AB . CP = 0 . But ...
... points ? Ptolemy's Theorem . 2. Express a condition that the circum - circle ... middle points of the sides and the in - circle are four circles satisfying ... point of contact of the tangent . Then BC . AP + CA . BP + AB . CP = 0 . But ...
Página 15
... point , after which they begin to diminish . This point is obviously the middle point of the seg- ment - the vertex of the isosceles triangle with the given parts - or the point at which the tangent to the arc is parallel to the base ...
... point , after which they begin to diminish . This point is obviously the middle point of the seg- ment - the vertex of the isosceles triangle with the given parts - or the point at which the tangent to the arc is parallel to the base ...
Página 16
... middle point M of the arc AB . On the other hand it is manifest that the difference of base angles ( A - B ) and difference of sides ( a - b ) both diminish as the vertex C approaches M and vanish at that point ; and after C passes ...
... middle point M of the arc AB . On the other hand it is manifest that the difference of base angles ( A - B ) and difference of sides ( a - b ) both diminish as the vertex C approaches M and vanish at that point ; and after C passes ...
Página 17
... mid - way between the other two , or the area and perimeter would both be increased by removing any vertex to the middle point . ] 2. A regular polygon of n sides inscribed in a circle has a greater area and perimeter than any other ...
... mid - way between the other two , or the area and perimeter would both be increased by removing any vertex to the middle point . ] 2. A regular polygon of n sides inscribed in a circle has a greater area and perimeter than any other ...
Página 25
... point of contact P , is the middle point of A , B1 . Therefore , having given a circle and two fixed tangents , the portion of a variable tangent intercepted by the fixed tangents becomes a minimum in two positions , viz . , when its point ...
... point of contact P , is the middle point of A , B1 . Therefore , having given a circle and two fixed tangents , the portion of a variable tangent intercepted by the fixed tangents becomes a minimum in two positions , viz . , when its point ...
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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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