Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 7
... coincides wholly with the surface . The planarity of a surface may be tested by applying the rule to it . If the rule touches the surface at some points and not at others the surface is not a plane . But if the rule touches the surface ...
... coincides wholly with the surface . The planarity of a surface may be tested by applying the rule to it . If the rule touches the surface at some points and not at others the surface is not a plane . But if the rule touches the surface ...
Page 10
... 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 direction AP is ...
... 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 direction AP is ...
Page 11
... coincide with the latter in every part , the two figures are necessarily and identically equal , and become virtually one figure by the superposition . 27 ° . Two line - segments can be compared with respect to length only . Hence a ...
... coincide with the latter in every part , the two figures are necessarily and identically equal , and become virtually one figure by the superposition . 27 ° . Two line - segments can be compared with respect to length only . Hence a ...
Page 12
Nathan Fellowes Dupuis. made to coincide with the end - points of the other by super- position . 28 ° . Def . — The sum of two segments is that segment which is equal to the two when placed in line with one end - point in each coincident ...
Nathan Fellowes Dupuis. made to coincide with the end - points of the other by super- position . 28 ° . Def . — The sum of two segments is that segment which is equal to the two when placed in line with one end - point in each coincident ...
Page 16
... coincide in direction respec- tively with the arms of the other ; or when the angles are described by the same rotation . Thus , if , when O ' is placed upon O , and O'A ' is made to lie along OA , O'B ' can also be made to lie along OB ...
... coincide in direction respec- tively with the arms of the other ; or when the angles are described by the same rotation . Thus , if , when O ' is placed upon O , and O'A ' is made to lie along OA , O'B ' can also be made to lie along OB ...
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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