Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page vii
... centre , of inverse figures , of pole and polar , of harmonic division , etc. , as applied to the line and circle ; and it is believed that a student who becomes acquainted with these geometric extensions in this their simpler form will ...
... centre , of inverse figures , of pole and polar , of harmonic division , etc. , as applied to the line and circle ; and it is believed that a student who becomes acquainted with these geometric extensions in this their simpler form will ...
Page ix
... SECTION V. - Constructive Geometry , PART III . SECTION I. Proportion amongst Line - Segments . SECTION II . - Functions of Angles and their Applications in Geometry , 91 147 PART IV . SECTION 1. - Geometric Extensions . Centre ix.
... SECTION V. - Constructive Geometry , PART III . SECTION I. Proportion amongst Line - Segments . SECTION II . - Functions of Angles and their Applications in Geometry , 91 147 PART IV . SECTION 1. - Geometric Extensions . Centre ix.
Page x
Nathan Fellowes Dupuis. PART IV . SECTION 1. - Geometric Extensions . Centre of Mean Position . linearity and Concurrence . SECTION II.— SECTION III . — Col- SECTION IV - Inver- sion and Inverse Figures . SECTION V. - Pole and Polar ...
Nathan Fellowes Dupuis. PART IV . SECTION 1. - Geometric Extensions . Centre of Mean Position . linearity and Concurrence . SECTION II.— SECTION III . — Col- SECTION IV - Inver- sion and Inverse Figures . SECTION V. - Pole and Polar ...
Page 6
... centre the centre of the circle ; stretched cords become straight lines , etc. 13 ° . The Point . A point marks position , but has no size . The intersection of one line by another gives a point , called the point of intersection . If the ...
... centre the centre of the circle ; stretched cords become straight lines , etc. 13 ° . The Point . A point marks position , but has no size . The intersection of one line by another gives a point , called the point of intersection . If the ...
Page 49
... line , ( 70 ° , Ax . ) Ę and FB = BD . ( 81 ° , 1 ) and EAF is one line and EA = AF . Similarly , DCE is one line and DC = CE , Now , AC is || to FD , the altitude to AC is to FD and passes through B the middle point of FD . ( 72 ...
... line , ( 70 ° , Ax . ) Ę and FB = BD . ( 81 ° , 1 ) and EAF is one line and EA = AF . Similarly , DCE is one line and DC = CE , Now , AC is || to FD , the altitude to AC is to FD and passes through B the middle point of FD . ( 72 ...
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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