Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page vi
... determining the consequent geometric interpretation which is to be given to each interpretable algebraic form . The use of such forms and symbols not only shortens the statements of geometric relations but also conduces to greater ...
... determining the consequent geometric interpretation which is to be given to each interpretable algebraic form . The use of such forms and symbols not only shortens the statements of geometric relations but also conduces to greater ...
Page ix
... Determined Points - The Triangle . SECTION IV . - Parallels . SECTION V. - The Circle . SECTION VI . - Constructive Geometry , . PAGE PART II . SECTION I. — Comparison of Areas . SECTION II .-- Measurement of Lengths and Areas . SECTION ...
... Determined Points - The Triangle . SECTION IV . - Parallels . SECTION V. - The Circle . SECTION VI . - Constructive Geometry , . PAGE PART II . SECTION I. — Comparison of Areas . SECTION II .-- Measurement of Lengths and Areas . SECTION ...
Page 8
... determine it . A similar nomenclature applies to other geometric ele- ments . The statement that a point or line lies in a plane does not give it , but a point or line placed in the plane for future reference is considered as being ...
... determine it . A similar nomenclature applies to other geometric ele- ments . The statement that a point or line lies in a plane does not give it , but a point or line placed in the plane for future reference is considered as being ...
Page 10
... determine one finite point . For , if they determined two , they would each pass through the same two points , which , from Cor . 2 , is impossible . Cor . 4. Another statement of Cor . 2 is - Two lines which have two points in common ...
... determine one finite point . For , if they determined two , they would each pass through the same two points , which , from Cor . 2 , is impossible . Cor . 4. Another statement of Cor . 2 is - Two lines which have two points in common ...
Page 22
... determine at most three lines ; and three lines determine at most three points . Proof 1. - Since ( 24 ° , Cor . 2 ) two points determine one line , three points determine as many lines N A M B as we can form groups from three points ...
... determine at most three lines ; and three lines determine at most three points . Proof 1. - Since ( 24 ° , Cor . 2 ) two points determine one line , three points determine as many lines N A M B as we can form groups from three points ...
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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