Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page vii
... ratio I have ventured , when comparing two finite lines , to introduce Hamilton's word tensor as seeming to me to express most clearly what is meant . After treating of proportion I have not hesitated to employ those special ratios ...
... ratio I have ventured , when comparing two finite lines , to introduce Hamilton's word tensor as seeming to me to express most clearly what is meant . After treating of proportion I have not hesitated to employ those special ratios ...
Page x
... Ratio . SECTION III . —Anharmonic Properties . SECTION IV . — Polar Reciprocals and Reciprocation . SECTION V. - Homography and Involution , PAGE 178 252 PART I. GENERAL CONSIDERATIONS . 1o . A statement which X CONTENTS .
... Ratio . SECTION III . —Anharmonic Properties . SECTION IV . — Polar Reciprocals and Reciprocation . SECTION V. - Homography and Involution , PAGE 178 252 PART I. GENERAL CONSIDERATIONS . 1o . A statement which X CONTENTS .
Page 141
... ratio , or in median section . Ex . 2. To describe a square when the sum of its side and diagonal is given . Analysis . — If AB is the side of a square , AB / 2 is its diagonal , ( 180 ° ) ... AB ( 1 + √2 ) is a given CONSTRUCTIVE ...
... ratio , or in median section . Ex . 2. To describe a square when the sum of its side and diagonal is given . Analysis . — If AB is the side of a square , AB / 2 is its diagonal , ( 180 ° ) ... AB ( 1 + √2 ) is a given CONSTRUCTIVE ...
Page 147
... ratio of m to n , and in Geometry it is called the ratio of AB to CD . Now n has to m the same ratio as unity has to the fraction But if CD be taken as u.l. its measure becomes unity , m n while that of AB becomes m n Therefore the ...
... ratio of m to n , and in Geometry it is called the ratio of AB to CD . Now n has to m the same ratio as unity has to the fraction But if CD be taken as u.l. its measure becomes unity , m n while that of AB becomes m n Therefore the ...
Page 148
... ratio of the segments , but it introduces a different idea . Hence in the case of com- mensurable segments the tensor is arithmetically expressible , but in the case of incommensurable ones the tensor may be symbolically denoted , but ...
... ratio of the segments , but it introduces a different idea . Hence in the case of com- mensurable segments the tensor is arithmetically expressible , but in the case of incommensurable ones the tensor may be symbolically denoted , but ...
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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