Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 4
... lines never meet . 4. Every point equidistant from the end - points of a line- segment is on the right bisector of that segment . SECTION I. THE LINE AND POINT . 9 ° . Space may be defined to be that which admits of length or distance ...
... lines never meet . 4. Every point equidistant from the end - points of a line- segment is on the right bisector of that segment . SECTION I. THE LINE AND POINT . 9 ° . Space may be defined to be that which admits of length or distance ...
Page 8
... line , the curve , the plane and the curved surface are the elements which go to make up geo- metric figures . Where a single plane is the only surface concerned , the point and line ... segment , or simply a segment . That absolute sameness ...
... line , the curve , the plane and the curved surface are the elements which go to make up geo- metric figures . Where a single plane is the only surface concerned , the point and line ... segment , or simply a segment . That absolute sameness ...
Page 9
... line leads directly to the following conclusions : - ( 1 ) No distinction can be made between any two segments of the same line ... segment is denoted by naming its end points , as the ' segment AB , " where A and B are the end points . This ...
... line leads directly to the following conclusions : - ( 1 ) No distinction can be made between any two segments of the same line ... segment is denoted by naming its end points , as the ' segment AB , " where A and B are the end points . This ...
Page 10
... segment , A say , as it is from the other , B. But on the indefinite line through A and B we may place C ' so as to be twice as far from A as from B. So that we have two points , C and C ' , both satisfying the condition of being twice ...
... segment , A say , as it is from the other , B. But on the indefinite line through A and B we may place C ' so as to be twice as far from A as from B. So that we have two points , C and C ' , both satisfying the condition of being twice ...
Page 11
... line of equal length . Or , a less length of line will reach from one given point to another when the line is straight than when it is curved . Def . — The distance between two points is the length of the segment which connects them or ...
... line of equal length . Or , a less length of line will reach from one given point to another when the line is straight than when it is curved . Def . — The distance between two points is the length of the segment which connects them or ...
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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