Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 155
... homologous side in each equal : I. If the angle is opposite the longer of the two sides the triangles are similar . 2. If the angle is opposite the shorter of the two sides the triangles may or may not be similar . AB BC A'B ' B'C ' and ...
... homologous side in each equal : I. If the angle is opposite the longer of the two sides the triangles are similar . 2. If the angle is opposite the shorter of the two sides the triangles may or may not be similar . AB BC A'B ' B'C ' and ...
Page 156
... homologous sides in each equal . If in 4 the equal angles are opposite the shorter sides in each the triangles are not necessarily similar unless some other condition is satisfied . By comparing this article with 66 ° we notice that ...
... homologous sides in each equal . If in 4 the equal angles are opposite the shorter sides in each the triangles are not necessarily similar unless some other condition is satisfied . By comparing this article with 66 ° we notice that ...
Page 160
... homologous lines of the figures . 207 ° . Theorem .-- Two similar rectilinear figures have any two line - segments from the one proportional to the homolo- gous segments from the other . Proof . By definition △ P ~ ^ P ' , and they are ...
... homologous lines of the figures . 207 ° . Theorem .-- Two similar rectilinear figures have any two line - segments from the one proportional to the homolo- gous segments from the other . Proof . By definition △ P ~ ^ P ' , and they are ...
Page 161
... homologous sides of two similar regular polygons , and let r and r ' be their circumradii . Then and r ' are homologous , r a b - a - b - с = = a + b + c + ... a + b + c + ... perimeter of P perimeter of P ' ( 195 ° , 3 ) But at the ...
... homologous sides of two similar regular polygons , and let r and r ' be their circumradii . Then and r ' are homologous , r a b - a - b - с = = a + b + c + ... a + b + c + ... perimeter of P perimeter of P ' ( 195 ° , 3 ) But at the ...
Page 168
... homologous lines in GM and HN is AD : DB . The three points E , D , and F being all adjustable the ratio can be changed at pleasure . Altogether the Pantagraph is a highly important instrument , and when so adjusted that E , D , and F ...
... homologous lines in GM and HN is AD : DB . The three points E , D , and F being all adjustable the ratio can be changed at pleasure . Altogether the Pantagraph is a highly important instrument , and when so adjusted that E , D , and F ...
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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