Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page v
... lying in a 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 ...
... lying in a 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 ...
Page 5
... lying without it . This surface can have no thickness , as in such a case it would include a part of the board or of ... lie in or on a plane . Some such figures are known to every person under such names as " triangle , " " square ...
... lying without it . This surface can have no thickness , as in such a case it would include a part of the board or of ... lie in or on a plane . Some such figures are known to every person under such names as " triangle , " " square ...
Page 8
... lie in it and form a plane figure . But where more than one plane is concerned , or where a curved surface is concerned ... lies in a plane does not give it , but a point or line placed in the plane for future reference is considered as ...
... lie in it and form a plane figure . But where more than one plane is concerned , or where a curved surface is concerned ... lies in a plane does not give it , but a point or line placed in the plane for future reference is considered as ...
Page 9
... lies between A and B. 23 ° . In dealing with a line - segment , we frequently have to consider other portions of the indefinite line of which the segment is a part . As an example , let it be required to divide THE LINE AND POINT . 9.
... lies between A and B. 23 ° . In dealing with a line - segment , we frequently have to consider other portions of the indefinite line of which the segment is a part . As an example , let it be required to divide THE LINE AND POINT . 9.
Page 10
... lie along and coincide with AP so as to form with it virtually but one line . Cor . 1. A finite point and a direction determine one line . Cor . 2. Two given finite points determine one line . For , if A and P be the points , the ...
... lie along and coincide with AP so as to form with it virtually but one line . Cor . 1. A finite point and a direction determine one line . Cor . 2. Two given finite points determine one line . For , if A and P be the points , the ...
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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