Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page vi
... relations but also conduces to greater generality . In dealing with proportion the method of measures is employed in preference to that of multiples as being equally accurate , easier of comprehension , and more in vi PREFACE .
... relations but also conduces to greater generality . In dealing with proportion the method of measures is employed in preference to that of multiples as being equally accurate , easier of comprehension , and more in vi PREFACE .
Page ix
... Measurement of Lengths and Areas . SECTION III . - Geometric Interpretation of Algebraic Forms . SECTION IV . - Areal Relations - Squares and Rect- angles . SECTION V. - Constructive Geometry , PART III . SECTION I. Proportion amongst ...
... Measurement of Lengths and Areas . SECTION III . - Geometric Interpretation of Algebraic Forms . SECTION IV . - Areal Relations - Squares and Rect- angles . SECTION V. - Constructive Geometry , PART III . SECTION I. Proportion amongst ...
Page 14
... measured . 2. If B is moved to B ' , any point on EB , and A to A ' , any point on EA , the angle at E is not changed . Hence increas- ing or diminishing one or both of the segments which form an angle does not affect the magnitude of ...
... measured . 2. If B is moved to B ' , any point on EB , and A to A ' , any point on EA , the angle at E is not changed . Hence increas- ing or diminishing one or both of the segments which form an angle does not affect the magnitude of ...
Page 83
... measured in two directions along the line SX , two squares can have their sides passing through the same four points P , Q , R , S , and having P and Q on opposite sides . Also , since P may be first connected with R or S , two squares ...
... measured in two directions along the line SX , two squares can have their sides passing through the same four points P , Q , R , S , and having P and Q on opposite sides . Also , since P may be first connected with R or S , two squares ...
Page 92
... measures the distance of the farthest point of a figure from a side taken as base . The terms base and altitude are thus correlative . A tri- angle may have three different bases and as many corre- sponding altitudes . ( 87 ° ) In the ...
... measures the distance of the farthest point of a figure from a side taken as base . The terms base and altitude are thus correlative . A tri- angle may have three different bases and as many corre- sponding altitudes . ( 87 ° ) In the ...
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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