Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 14
... Similarly , if the stars appear to approach one another , the angle at E becomes smaller ; and if the stars become coinci- dent , or situated in the same line through E , the angle at E vanishes . Hence an angle is capable of continuous ...
... Similarly , if the stars appear to approach one another , the angle at E becomes smaller ; and if the stars become coinci- dent , or situated in the same line through E , the angle at E vanishes . Hence an angle is capable of continuous ...
Page 16
... Similarly , LAOP LAOP ' - ¿ POP ' . Def . - When two angles , as AOP and POP ' , have one arm in common lying between the remaining arms , the angles are adjacent angles . 36 ° . Def . — A radius vector which starts from any given ...
... Similarly , LAOP LAOP ' - ¿ POP ' . Def . - When two angles , as AOP and POP ' , have one arm in common lying between the remaining arms , the angles are adjacent angles . 36 ° . Def . — A radius vector which starts from any given ...
Page 27
... 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 indirect form ...
... 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 indirect form ...
Page 30
... Similarly , and LACE is > < BAC . < BCD is > < ABC , LBCD = LACE . ( 40 ° ) Therefore the Ls BCD and ACE are each greater than each of the LS ABC and BAC . q.e.d. 61 ° . Theorem .-- Only one perpendicular can be drawn to a line from a ...
... Similarly , and LACE is > < BAC . < BCD is > < ABC , LBCD = LACE . ( 40 ° ) Therefore the Ls BCD and ACE are each greater than each of the LS ABC and BAC . q.e.d. 61 ° . Theorem .-- Only one perpendicular can be drawn to a line from a ...
Page 37
... since they have two sides and an angle opposite the longer equal in each ( 65 ° , 1 ) ; .. ¿ POA = LPOB , and PO bisects the LAOB . Similarly , if the perpendiculars from Q upon OA and THREE OR MORE POINTS AND LINES . 37.
... since they have two sides and an angle opposite the longer equal in each ( 65 ° , 1 ) ; .. ¿ POA = LPOB , and PO bisects the LAOB . Similarly , if the perpendiculars from Q upon OA and THREE OR MORE POINTS AND LINES . 37.
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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