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 3
... divided harmonically or such that AB | BC = AD / CD , then BC . AD = AB.CD ; hence by ( 3 ) the pencil is divided harmonically , i.e. , the angle COA is divided internally in B and externally in D in the same ratio of sines . Defs . The ...
... divided harmonically or such that AB | BC = AD / CD , then BC . AD = AB.CD ; hence by ( 3 ) the pencil is divided harmonically , i.e. , the angle COA is divided internally in B and externally in D in the same ratio of sines . Defs . The ...
Σελίδα 18
... divided at A to be rigidly attached to the lines AB and AC . If the angle at A is not right , by rotating AC around A until it is perpendicular to AB , the area of the triangle ABC , and therefore also of the whole figure , is increased ...
... divided at A to be rigidly attached to the lines AB and AC . If the angle at A is not right , by rotating AC around A until it is perpendicular to AB , the area of the triangle ABC , and therefore also of the whole figure , is increased ...
Σελίδα 27
... divided into any two parts a and b , their rectangle is a maximum when the line is bisected . For Euc . ( II . 5 ) - 2 2 ab + ( a - b ) 2 = ( a + b ) 2 = const . , 2 hence ab is a maximum when a - b = 0 or when a = COR . The continued ...
... divided into any two parts a and b , their rectangle is a maximum when the line is bisected . For Euc . ( II . 5 ) - 2 2 ab + ( a - b ) 2 = ( a + b ) 2 = const . , 2 hence ab is a maximum when a - b = 0 or when a = COR . The continued ...
Σελίδα 29
... divided into any number of parts a , b , c ... ; to find when a b c ... is a maximum , where a , ß , y are given ... divided ; hence ( a / a ) a is the product of the equal subdivisions . Similarly ( b / B ) is the product of the ẞ equal ...
... divided into any number of parts a , b , c ... ; to find when a b c ... is a maximum , where a , ß , y are given ... divided ; hence ( a / a ) a is the product of the equal subdivisions . Similarly ( b / B ) is the product of the ẞ equal ...
Σελίδα 30
... divided into any number of parts a , b , c ... , to find when a2 + b2 c2 + - + ... is minimum α β ' γ where a , ẞ , y are known quantities . B , Let the segment a be divided into a equal parts ; each part is therefore a / a and the sum ...
... divided into any number of parts a , b , c ... , to find when a2 + b2 c2 + - + ... is minimum α β ' γ where a , ẞ , y are known quantities . B , Let the segment a be divided into a equal parts ; each part is therefore a / a and the sum ...
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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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