Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 8
... considered as being given . Such a point is usually called an origin , and such a line a datum line , an initial line , a prime vector , etc. 21 ° . Def . 1.- A line considered merely as a geometric element , and without any limitations ...
... considered as being given . Such a point is usually called an origin , and such a line a datum line , an initial line , a prime vector , etc. 21 ° . Def . 1.- A line considered merely as a geometric element , and without any limitations ...
Page 10
... considered , C is said to divide the segment internally and C ' to divide it externally in the same manner . 24 ° . Axiom . - Through a given point only one line can pass in a given direction . Let A be the given point , and let the ...
... considered , C is said to divide the segment internally and C ' to divide it externally in the same manner . 24 ° . Axiom . - Through a given point only one line can pass in a given direction . Let A be the given point , and let the ...
Page 91
... considered with respect to its extent only , and without respect to form . A closed figure of any form may contain an area of any given extent , and closed figures of different forms may con- tain areas of the same extent , or equal ...
... considered with respect to its extent only , and without respect to form . A closed figure of any form may contain an area of any given extent , and closed figures of different forms may con- tain areas of the same extent , or equal ...
Page 92
... considered from two points of view . 1. With respect to the character and disposition of the lines which form it . When thus considered , figures group themselves into triangles , squares , circles , etc. , where the members of each ...
... considered from two points of view . 1. With respect to the character and disposition of the lines which form it . When thus considered , figures group themselves into triangles , squares , circles , etc. , where the members of each ...
Page 104
Nathan Fellowes Dupuis. In all cases where a u.l. and a u.a. are considered together , they are supposed to be connected by the relation of 150 ° , 3 and 4 . 152 ° . Theorem .-- The number of unit - areas in a rectangle is the product of ...
Nathan Fellowes Dupuis. In all cases where a u.l. and a u.a. are considered together , they are supposed to be connected by the relation of 150 ° , 3 and 4 . 152 ° . Theorem .-- The number of unit - areas in a rectangle is the product 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