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 41
Página 11
... inscribed circle . ] 4. Mannheim's Theorem . - Having given the vertical angle and radius of the in- or corresponding ex - circle , the envelope of the circum - circle is a circle . [ By Ex . 3. ] 7. We shall conclude the present ...
... inscribed circle . ] 4. Mannheim's Theorem . - Having given the vertical angle and radius of the in- or corresponding ex - circle , the envelope of the circum - circle is a circle . [ By Ex . 3. ] 7. We shall conclude the present ...
Página 13
... inscribed in a circle , and λ , μ , v the distances of its vertices from any tangent , show that the equation in Ex . 2 reduces to a√x + b√μ + c√v = 0.t 5. More generally if λ , μ , denote the distances from any line , give the ...
... inscribed in a circle , and λ , μ , v the distances of its vertices from any tangent , show that the equation in Ex . 2 reduces to a√x + b√μ + c√v = 0.t 5. More generally if λ , μ , denote the distances from any line , give the ...
Página 17
... inscribed in a circle is equilateral . [ For each vertex must lie 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 ...
... inscribed in a circle is equilateral . [ For each vertex must lie 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 ...
Página 20
... In the particular case when a = b = c , the equation for d reduces to hence ( d - 2a ) ( d + a ) 2 = 0 ; d = 2a , thus showing that the quadrilateral is half the regular inscribed hexagon . B C d D E Now , ABDE is a 20 MAXIMUM AND MINIMUM .
... In the particular case when a = b = c , the equation for d reduces to hence ( d - 2a ) ( d + a ) 2 = 0 ; d = 2a , thus showing that the quadrilateral is half the regular inscribed hexagon . B C d D E Now , ABDE is a 20 MAXIMUM AND MINIMUM .
Página 22
... inscribed in a given one is formed by joining the feet X , Y , Z of the perpendiculars * let fall from the vertices on the opposite sides . [ For the joining lines are equally inclined to sides on which they intersect ( Euc . III . 21 ) ...
... inscribed in a given one is formed by joining the feet X , Y , Z of the perpendiculars * let fall from the vertices on the opposite sides . [ For the joining lines are equally inclined to sides on which they intersect ( Euc . III . 21 ) ...
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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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