Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
From inside the book
Results 1-5 of 62
Page 18
... cut one another four angles are formed about the point of intersection , any one of which may be taken to be the angle between the lines . These four angles consist of two pairs of opposite or vertical angles , viz . , A , A ' , and B ...
... cut one another four angles are formed about the point of intersection , any one of which may be taken to be the angle between the lines . These four angles consist of two pairs of opposite or vertical angles , viz . , A , A ' , and B ...
Page 27
... cut AP ; and similarly it does not cut BP ; therefore it passes through P , or P is on the right bisector . q.e.d. This form of proof should be compared with that of Art . 53 ° , they being the kinds indicated in 6 ° . This latter or ...
... cut AP ; and similarly it does not cut BP ; therefore it passes through P , or P is on the right bisector . q.e.d. This form of proof should be compared with that of Art . 53 ° , they being the kinds indicated in 6 ° . This latter or ...
Page 28
... cut the right bisector in Q. QA QB , and 4QAB = LQBA . ( 53 ° and Cor . 1 ) LPBA = LQAB ; LPBA = 4QBA , which is not true unless P and Q coincide . ( hyp . ) Therefore if P is not on the right bisector of AB , the LPAB cannot be equal ...
... cut the right bisector in Q. QA QB , and 4QAB = LQBA . ( 53 ° and Cor . 1 ) LPBA = LQAB ; LPBA = 4QBA , which is not true unless P and Q coincide . ( hyp . ) Therefore if P is not on the right bisector of AB , the LPAB cannot be equal ...
Page 43
... All other triangles are called acute - angled triangles , and have three acute angles . 6. The acute angles in a right - angled triangle are comple- mentary to one another . 78 ° . Theorem . — If a line cuts PARALLELS , ETC. 43.
... All other triangles are called acute - angled triangles , and have three acute angles . 6. The acute angles in a right - angled triangle are comple- mentary to one another . 78 ° . Theorem . — If a line cuts PARALLELS , ETC. 43.
Page 44
... cuts every parallel to the given line . N Р M Let L cut M , and let N be any parallel to M. Then L cuts N. Proof . If L does not cut N it is || to N. But M is to N. Therefore through the same point P two lines L and M pass which are ...
... cuts every parallel to the given line . N Р M Let L cut M , and let N be any parallel to M. Then L cuts N. Proof . If L does not cut N it is || to N. But M is to N. Therefore through the same point P two lines L and M pass which are ...
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