Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
From inside the book
Results 1-5 of 20
Page 122
... proportional or the geometric mean between the sides of the rectangle . Thus the altitude to the hypothenuse of a right - angled △ is a geometric mean between the segments into which the altitude divides the hypothenuse . ( 169 ° , Cor ...
... proportional or the geometric mean between the sides of the rectangle . Thus the altitude to the hypothenuse of a right - angled △ is a geometric mean between the segments into which the altitude divides the hypothenuse . ( 169 ° , Cor ...
Page 155
... proportional and the included angles equal , the triangles are similar . AB AC and △ A = LA ' , A'B ' A'C " then AABCAA'B'C ' . B с E B Proof . - Place A ' on A , and let A'C ' lie along AB , and A'B ' lie along AC , so that C ' falls ...
... proportional and the included angles equal , the triangles are similar . AB AC and △ A = LA ' , A'B ' A'C " then AABCAA'B'C ' . B с E B Proof . - Place A ' on A , and let A'C ' lie along AB , and A'B ' lie along AC , so that C ' falls ...
Page 156
... proportional . 3. Two sides proportional and the included angles equal . 4. Two sides proportional and the angles opposite the longer of the homologous sides in each equal . If in 4 the equal angles are opposite the shorter sides in ...
... proportional . 3. Two sides proportional and the included angles equal . 4. Two sides proportional and the angles opposite the longer of the homologous sides in each equal . If in 4 the equal angles are opposite the shorter sides in ...
Page 157
... proportional to the correspond- ing segments from the second figure . Def . - Two line - segments are divided similarly when , being divided into the same number of parts , any two parts from one of the segments and the corresponding ...
... proportional to the correspond- ing segments from the second figure . Def . - Two line - segments are divided similarly when , being divided into the same number of parts , any two parts from one of the segments and the corresponding ...
Page 160
... proportional to the homolo- gous segments from the other . Proof . By definition △ P ~ ^ P ' , and they are similarly placed , ... AE : A'E ' = AD : A'D ' . For like reasons , AD : A'D ' AC : A'C ' = AB : A'B ' . AE AD AC AB = = = etc ...
... proportional to the homolo- gous segments from the other . Proof . By definition △ P ~ ^ P ' , and they are similarly placed , ... AE : A'E ' = AD : A'D ' . For like reasons , AD : A'D ' AC : A'C ' = AB : A'B ' . AE AD AC AB = = = etc ...
Other editions - View all
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