Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 8
... similar nomenclature applies to other geometric ele- ments . The statement that a point or line lies in a plane does not give it , but a point or line placed in the plane for future reference is considered as being given . Such a point ...
... similar nomenclature applies to other geometric ele- ments . The statement that a point or line lies in a plane does not give it , but a point or line placed in the plane for future reference is considered as being given . Such a point ...
Page 10
... similar relations held by C and C ' to the end- points of the segment , it is convenient and advantageous to consider both points as dividing the segment AB . When thus considered , C is said to divide the segment internally and C ' to ...
... similar relations held by C and C ' to the end- points of the segment , it is convenient and advantageous to consider both points as dividing the segment AB . When thus considered , C is said to divide the segment internally and C ' to ...
Page 37
... similar manner that the perpendiculars from Q upon the arms of the angle AOB are equal . q.e.d. 2. If PA is to OA and PB is 1 to OB , and PA = PB , then PO is a bisector of the angle AOB . Proof . The As POA and POB are congruent ...
... similar manner that the perpendiculars from Q upon the arms of the angle AOB are equal . q.e.d. 2. If PA is to OA and PB is 1 to OB , and PA = PB , then PO is a bisector of the angle AOB . Proof . The As POA and POB are congruent ...
Page 43
... similar . 5. A triangle can have but one obtuse angle ; it is then called an obtuse - angled triangle . A triangle can have but one right angle , when it is called a right - angled triangle . All other triangles are called acute ...
... similar . 5. A triangle can have but one obtuse angle ; it is then called an obtuse - angled triangle . A triangle can have but one right angle , when it is called a right - angled triangle . All other triangles are called acute ...
Page 130
... similar relation holds for any polygon . 19. AA1 , BB1 are the diagonals of a rectangle and P any point . Then PA2 + PB2 + PA12 + PB12 = AA , 2 + 4PO2 , where O 2 is the intersection of the diagonals . 20. ABC is a triangle , AD , BE ...
... similar relation holds for any polygon . 19. AA1 , BB1 are the diagonals of a rectangle and P any point . Then PA2 + PB2 + PA12 + PB12 = AA , 2 + 4PO2 , where O 2 is the intersection of the diagonals . 20. ABC is a triangle , AD , BE ...
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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