Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 3
... opposite these sides only one can be the greater . Then , if it is proved that the greater side is opposite the greater angle it follows that the greater angle is opposite the greater side . In this example there is but one X ( the ...
... opposite these sides only one can be the greater . Then , if it is proved that the greater side is opposite the greater angle it follows that the greater angle is opposite the greater side . In this example there is but one X ( the ...
Page 4
... opposite ) Y , therefore Y is ( corresponds to or is opposite ) X. 8 ° . A Corollary is a theorem deduced from some other theorem , usually by some qualification or restriction , and occasionally by some amplification of the hypothesis ...
... opposite ) Y , therefore Y is ( corresponds to or is opposite ) X. 8 ° . A Corollary is a theorem deduced from some other theorem , usually by some qualification or restriction , and occasionally by some amplification of the hypothesis ...
Page 7
... opposite direction , " etc. , for these express relations between directions , and such relations are as readily comprehended as relations between lengths or other magnitudes . The most prominent property , and in fact the distinctive ...
... opposite direction , " etc. , for these express relations between directions , and such relations are as readily comprehended as relations between lengths or other magnitudes . The most prominent property , and in fact the distinctive ...
Page 17
... each pair is a straight angle ( 36 ° ) . q.e.d. Cor . 1. The angle between the opposite directions of a line is a straight angle . B Cor . 2. If a radius vector be rotated until RELATIONS OF TWO LINES . - ANGLES . 17.
... each pair is a straight angle ( 36 ° ) . q.e.d. Cor . 1. The angle between the opposite directions of a line is a straight angle . B Cor . 2. If a radius vector be rotated until RELATIONS OF TWO LINES . - ANGLES . 17.
Page 18
... opposite A ' , and B being opposite B ' . 40 ° . Theorem . - The opposite angles of a pair formed by two intersecting lines are equal to one another . Proof.- and :: and = LA + LB a straight angle LA ' + LB a straight angle . LA = LA ...
... opposite A ' , and B being opposite B ' . 40 ° . Theorem . - The opposite angles of a pair formed by two intersecting lines are equal to one another . Proof.- and :: and = LA + LB a straight angle LA ' + LB a straight angle . LA = LA ...
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Common terms and phrases
ABCD Algebra altitude becomes bisects c.p.-circles centre of similitude chord of contact circles touch circumcircle co-axal coincide collinear concurrent concurrent lines concyclic congruent cut the circle denote diagonals diameter divided double points end-points equal angles equianharmonic equilateral triangle excircles external bisector fixed point geometric given circles given line given point harmonic range Hence hexagram homographic homologous hypothenuse incircle internal angles inverse points isosceles joins LAOB line-segment locus median middle point nine-points circle opposite sides orthogonally pair parallel parallelogram passes pencil perpendicular perspective plane point of contact point of intersection polar reciprocal Proof quadrangle radical axis radical centre radii radius rectangle rectilinear figure regular polygon rhombus right angle right bisector rotation secant similar Similarly square straight angle symbol tangent tensor theorem Theorem.-The three circles transversal vertex vertices