Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page vi
... relations but also conduces to greater generality . In dealing with proportion the method of measures is employed in preference to that of multiples as being equally accurate , easier of comprehension , and more in vi PREFACE .
... relations but also conduces to greater generality . In dealing with proportion the method of measures is employed in preference to that of multiples as being equally accurate , easier of comprehension , and more in vi PREFACE .
Page 2
... greater than any one of its parts . ii . Things equal to the same thing are equal to one another . iii . If equals be added to equals the sums are equal . iv . If equals be taken from equals the remainders are equal . v . If equals be ...
... greater than any one of its parts . ii . Things equal to the same thing are equal to one another . iii . If equals be added to equals the sums are equal . iv . If equals be taken from equals the remainders are equal . v . If equals be ...
Page 3
... greater , and of the two angles 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 ...
... greater , and of the two angles 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 ...
Page 4
Nathan Fellowes Dupuis. In this example there is but one X ( the greater side ) and one Y ( the greater angle ) , and as X is ( corresponds to or is opposite ) Y , therefore Y is ( corresponds to or is opposite ) X. 8 ° . A Corollary is ...
Nathan Fellowes Dupuis. In this example there is but one X ( the greater side ) and one Y ( the greater angle ) , and as X is ( corresponds to or is opposite ) Y , therefore Y is ( corresponds to or is opposite ) X. 8 ° . A Corollary is ...
Page 14
... greater . Thus , if B moves into the position of C , the angle between EA and EC is greater than the angle between EA and EB . Similarly , if the stars appear to approach one another , the angle at E becomes smaller ; and if the stars ...
... greater . Thus , if B moves into the position of C , the angle between EA and EC is greater than the angle between EA and EB . Similarly , if the stars appear to approach one another , the angle at E becomes smaller ; and if the stars ...
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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