Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 8
... placed in the plane for future reference is 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 ...
... placed in the plane for future reference is 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 ...
Page 12
... placed in line with one end - point in each coincident . D E Let AB and DE be two segments , and on the line of which AB is a segment let BC be equal to DE . Then AC is the sum of AB C and DE . A B This is expressed symbolically by ...
... placed in line with one end - point in each coincident . D E Let AB and DE be two segments , and on the line of which AB is a segment let BC be equal to DE . Then AC is the sum of AB C and DE . A B This is expressed symbolically by ...
Page 15
... placed at the vertex , as the 40 , or by a letter with or without an arch of dots , as 48 ; or by three letters of which the A extreme ones denote points upon the arms of the angle and the middle one denotes the vertex , as LAOB . 3 ...
... placed at the vertex , as the 40 , or by a letter with or without an arch of dots , as 48 ; or by three letters of which the A extreme ones denote points upon the arms of the angle and the middle one denotes the vertex , as LAOB . 3 ...
Page 16
... placed upon O , and O'A ' is made to lie along OA , O'B ' can also be made to lie along OB , the LA'O'B ' is equal to LAOB . This equality is symbolized thus : LA'O'B ' LAOB . B B ' A ' Where the sign = is to be interpreted as ...
... placed upon O , and O'A ' is made to lie along OA , O'B ' can also be made to lie along OB , the LA'O'B ' is equal to LAOB . This equality is symbolized thus : LA'O'B ' LAOB . B B ' A ' Where the sign = is to be interpreted as ...
Page 25
... placed between two figures capable of congruence denotes that the figures are congruent . Closed figures , like triangles , admit of comparison in two ways . The first is as to their capability of perfect coinci- dence ; when this is ...
... placed between two figures capable of congruence denotes that the figures are congruent . Closed figures , like triangles , admit of comparison in two ways . The first is as to their capability of perfect coinci- dence ; when this is ...
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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