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 6
... coincides with the centre 1 ΣΤΑ PA ' = 0 . [ Through P draw the line parallel to one of the sides , etc. ] 10. If parallels be drawn through any point O to the four lines in Ex . 4 , the relation may be written sin ẞ ' sin y sin ẞ sin y ...
... coincides with the centre 1 ΣΤΑ PA ' = 0 . [ Through P draw the line parallel to one of the sides , etc. ] 10. If parallels be drawn through any point O to the four lines in Ex . 4 , the relation may be written sin ẞ ' sin y sin ẞ sin y ...
Σελίδα 8
... coincide with the tangent . Hence a tangent to a circle is in 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 ...
... coincide with the tangent . Hence a tangent to a circle is in 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 ...
Σελίδα 44
... coincide , and PQR is the minimum triangle of given species that can be inscribed in ABC . 23. It is manifest that a given triangle ABC may be escribed to another PQR . For having determined the point O , the triangles BOC , COA , and ...
... coincide , and PQR is the minimum triangle of given species that can be inscribed in ABC . 23. It is manifest that a given triangle ABC may be escribed to another PQR . For having determined the point O , the triangles BOC , COA , and ...
Σελίδα 48
... coincide alternately with A and B the locus is seen to be the line joining the middle points of the perpendiculars from the extremities of the base of the triangle ABC . ] A M X N B 8. The sides of the pedal triangle PQR are in the ...
... coincide alternately with A and B the locus is seen to be the line joining the middle points of the perpendiculars from the extremities of the base of the triangle ABC . ] A M X N B 8. The sides of the pedal triangle PQR are in the ...
Σελίδα 49
... coincides with the in- or ex- centres of the triangle ABC , the formula in Ex . 11 reduces to 82 = R2-2Rr or d12 = R2 + 2Rr , etc. 24. Theorem . — When three points P , Q , R are taken collinearly on the sides of a triangle , the ...
... coincides with the in- or ex- centres of the triangle ABC , the formula in Ex . 11 reduces to 82 = R2-2Rr or d12 = R2 + 2Rr , etc. 24. Theorem . — When three points P , Q , R are taken collinearly on the sides of a triangle , the ...
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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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