Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page v
... common plane are 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 ...
... common plane are 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 ...
Page 1
... common word , or it may introduce some technical term to be used in a particular sense . Some terms , such as space , straight , direction , etc. , which express elementary ideas cannot be defined . 2. Def . - A Theorem is the formal ...
... common word , or it may introduce some technical term to be used in a particular sense . Some terms , such as space , straight , direction , etc. , which express elementary ideas cannot be defined . 2. Def . - A Theorem is the formal ...
Page 6
... common to all the parts of the line , the line is straight . The word " direction " is not in itself definable , and when applied to a line in the absolute it is not intelligible . But every person knows what is meant by such ...
... common to all the parts of the line , the line is straight . The word " direction " is not in itself definable , and when applied to a line in the absolute it is not intelligible . But every person knows what is meant by such ...
Page 7
... common example of a curve is a circle or portion of a circle . Henceforward , the word " line , " unless otherwise qualified , will mean a straight line . 16 ° . The " rule " or " straight - edge " is a strip of wood , metal , or other ...
... common example of a curve is a circle or portion of a circle . Henceforward , the word " line , " unless otherwise qualified , will mean a straight line . 16 ° . The " rule " or " straight - edge " is a strip of wood , metal , or other ...
Page 10
... , which , from Cor . 2 , is impossible . Cor . 4. Another statement of Cor . 2 is - Two lines which have two points in common coincide and form virtually but one line . 25 ° . Axiom . — A straight line is ΙΟ SYNTHETIC GEOMETRY .
... , which , from Cor . 2 , is impossible . Cor . 4. Another statement of Cor . 2 is - Two lines which have two points in common coincide and form virtually but one line . 25 ° . Axiom . — A straight line is ΙΟ SYNTHETIC GEOMETRY .
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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