A Treatise on the Geometry of the Circle and Some Extensions to Conic Sections by the Method of Reciprocation: With Numerous Examples |
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Page 4
... equal to AB cos 0 , where 0 is the angle between AB and L. EXAMPLES . 1. The sum of the projections of the sides of a polygon on any right line = 0 ; and generally if lines be drawn equally inclined and proportional to the sides of a ...
... equal to AB cos 0 , where 0 is the angle between AB and L. EXAMPLES . 1. The sum of the projections of the sides of a polygon on any right line = 0 ; and generally if lines be drawn equally inclined and proportional to the sides of a ...
Page 10
... equal chords in a circle is a concentric circle ( Euc . III . 14 ) . 2. Bobillier's Theorem . — If two sides of a given triangle touch fixed circles the third side also touches , or envelopes , a circle . [ Let ABC be the given triangle ...
... equal chords in a circle is a concentric circle ( Euc . III . 14 ) . 2. Bobillier's Theorem . — If two sides of a given triangle touch fixed circles the third side also touches , or envelopes , a circle . [ Let ABC be the given triangle ...
Page 15
... equal to the vertical angle . ( Euc . III . 21. ) Let a number of tri- angles be constructed satisfying the given conditions , and it will be observed that as the vertex recedes from either extremity of the base the altitude and area ...
... equal to the vertical angle . ( Euc . III . 21. ) Let a number of tri- angles be constructed satisfying the given conditions , and it will be observed that as the vertex recedes from either extremity of the base the altitude and area ...
Page 18
... 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 diameter of semicircles. 18 MAXIMUM AND MINIMUM .
... 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 diameter of semicircles. 18 MAXIMUM AND MINIMUM .
Page 20
... equal parts and there remains the quadrilateral ABCD greater than A'B'C'D ' . ] * 4. If three sides a , b , c , of a ... equal to 8. Join BE and AE . The triangles BDE and BCD are equal ( Euc . I. 37 ) ; to each add ABD , therefore ABCD ...
... equal parts and there remains the quadrilateral ABCD greater than A'B'C'D ' . ] * 4. If three sides a , b , c , of a ... equal to 8. Join BE and AE . The triangles BDE and BCD are equal ( Euc . I. 37 ) ; to each add ABD , therefore ABCD ...
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Other editions - View all
A Treatise on the Geometry of the Circle: And Some Extensions to Conic ... William J. M'Clelland No preview available - 2017 |
A Treatise on the Geometry of the Circle and Some Extensions to Conic ... William J. M'Clelland No preview available - 2018 |
Common terms and phrases
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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