Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page vi
... congruence and equality are accord- ingly carefully distinguished . The principle of motion in the transformation of geometric figures , as recommended by Dr. Sylvester , and as a consequence the principle of continuity are freely ...
... congruence and equality are accord- ingly carefully distinguished . The principle of motion in the transformation of geometric figures , as recommended by Dr. Sylvester , and as a consequence the principle of continuity are freely ...
Page 25
... congruent . Congruent figures are distinguishable from one another only by their position in space and are said to be identically equal . Congruence is denoted by the algebraic symbol of identity , = ; and this symbol placed between two ...
... congruent . Congruent figures are distinguishable from one another only by their position in space and are said to be identically equal . Congruence is denoted by the algebraic symbol of identity , = ; and this symbol placed between two ...
Page 26
... congruent . ( 51 ° ) q.e.d. Cor . Since two congruent triangles can be made to coin- cide in all their parts , therefore- When two triangles have two sides and the included angle in the one respectively equal to two sides and the ...
... congruent . ( 51 ° ) q.e.d. Cor . Since two congruent triangles can be made to coin- cide in all their parts , therefore- When two triangles have two sides and the included angle in the one respectively equal to two sides and the ...
Page 29
... congruent . If A'B ' AB ) the As ABC B'C ' = BC and A'B'C'are C'A ' CA ) congruent . Proof . Turn the △ A'B'C ' over and place A ' on A , and A B A'C ' along AC , and let B ' fall at some point D. = A'C ' AC , C ' falls at C , and ADC ...
... congruent . If A'B ' AB ) the As ABC B'C ' = BC and A'B'C'are C'A ' CA ) congruent . Proof . Turn the △ A'B'C ' over and place A ' on A , and A B A'C ' along AC , and let B ' fall at some point D. = A'C ' AC , C ' falls at C , and ADC ...
Page 30
... congruent . 60 ° . Theorem . - An external angle of a triangle is greater than an internal opposite angle . B C D E The external angle BCD is greater than the internal opposite angle ABC or BAC . Proof . Let BF be a median produced ...
... congruent . 60 ° . Theorem . - An external angle of a triangle is greater than an internal opposite angle . B C D E The external angle BCD is greater than the internal opposite angle ABC or BAC . Proof . Let BF be a median produced ...
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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