Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 2
... put into the form— If C is not D then A is not B , which is called the contrapositive of the former . The truth of a theorem establishes the truth of its contra- positive , and vice versa , and hence if either 2 SYNTHETIC GEOMETRY .
... put into the form— If C is not D then A is not B , which is called the contrapositive of the former . The truth of a theorem establishes the truth of its contra- positive , and vice versa , and hence if either 2 SYNTHETIC GEOMETRY .
Page 3
... hence a theorem and its converse have in general to be proved separately . But on account of the peculiar relation existing between the two , a relation exists also between the modes of proof for the two . These are known as the direct ...
... hence a theorem and its converse have in general to be proved separately . But on account of the peculiar relation existing between the two , a relation exists also between the modes of proof for the two . These are known as the direct ...
Page 5
... Hence we may consider the geometric line as being the limit towards which a physical line approaches as its breadth is continually diminished . We may consequently consider a geometric line as length abstracted from every other ...
... Hence we may consider the geometric line as being the limit towards which a physical line approaches as its breadth is continually diminished . We may consequently consider a geometric line as length abstracted from every other ...
Page 6
... hence arguments in regard to geometric lines may be replaced by arguments in regard to physical lines , if from such arguments we exclude everything that would involve the idea of breadth . The diagrams employed to direct and assist us ...
... hence arguments in regard to geometric lines may be replaced by arguments in regard to physical lines , if from such arguments we exclude everything that would involve the idea of breadth . The diagrams employed to direct and assist us ...
Page 9
... hence , in imagination , we may follow a line as far as we please without coming to any necessary termination . This property is conveniently expressed by saying that a line extends to infinity . 3. — The hypothetical end - points of ...
... hence , in imagination , we may follow a line as far as we please without coming to any necessary termination . This property is conveniently expressed by saying that a line extends to infinity . 3. — The hypothetical end - points of ...
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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