Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page v
... taken as the geometric elements of Plane Geometry , and any one of these or any combination of them is defined as a geometric plane figure . Thus a triangle is not the three - cornered portion of the plane inclosed within its sides ...
... taken as the geometric elements of Plane Geometry , and any one of these or any combination of them is defined as a geometric plane figure . Thus a triangle is not the three - cornered portion of the plane inclosed within its sides ...
Page 2
... taken from unequals the results are unequal . vi . If unequals be taken from equals the remainders are unequal . vii . Equal multiples of equals are equal ; so also equal submultiples of equals are equal . The axioms which belong ...
... taken from unequals the results are unequal . vi . If unequals be taken from equals the remainders are unequal . vii . Equal multiples of equals are equal ; so also equal submultiples of equals are equal . The axioms which belong ...
Page 11
... taken as a physical line . By separating these as far as possible , the thread takes the form which we call straight , or tends to take that form . Therefore a straight finite line has its end - points further apart than a curved line ...
... taken as a physical line . By separating these as far as possible , the thread takes the form which we call straight , or tends to take that form . Therefore a straight finite line has its end - points further apart than a curved line ...
Page 12
... taken away equal in length to the shorter . Thus , if AC and DE be two segments of which AC is the longer , and if BC is equal to DE , then AB is the difference between AC and DE . This is expressed symbolically by writing AB - AC - DE ...
... taken away equal in length to the shorter . Thus , if AC and DE be two segments of which AC is the longer , and if BC is equal to DE , then AB is the difference between AC and DE . This is expressed symbolically by writing AB - AC - DE ...
Page 18
... taken to be the angle between the lines . These four angles consist of two pairs of opposite or vertical angles , viz . , A , A ' , and B , B ' , A being opposite A ' , and B being opposite B ' . 40 ° . Theorem . - The opposite angles ...
... taken to be the angle between the lines . These four angles consist of two pairs of opposite or vertical angles , viz . , A , A ' , and B , B ' , A being opposite A ' , and B being opposite B ' . 40 ° . Theorem . - The opposite angles ...
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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