Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page vi
... Algebraic forms and symbols , ( 1 ) by an elementary study of the modes of representing geometric ideas in the symbols of Algebra , and ( 2 ) by determining the consequent geometric interpretation which is to be given to each ...
... Algebraic forms and symbols , ( 1 ) by an elementary study of the modes of representing geometric ideas in the symbols of Algebra , and ( 2 ) by determining the consequent geometric interpretation which is to be given to each ...
Page ix
... Algebraic Forms . SECTION IV . - Areal Relations - Squares and Rect- angles . SECTION V. - Constructive Geometry , PART III . SECTION I. Proportion amongst Line - Segments . SECTION II . - Functions of Angles and their Applications in ...
... Algebraic Forms . SECTION IV . - Areal Relations - Squares and Rect- angles . SECTION V. - Constructive Geometry , PART III . SECTION I. Proportion amongst Line - Segments . SECTION II . - Functions of Angles and their Applications in ...
Page 12
... AB = AC - DE we can write AC AB + DE . We thus see that in using these algebraic symbols , = , + , and , a term , as DE , may be transferred from one side of the equation to another by changing its sign from + 12 SYNTHETIC GEOMETRY .
... AB = AC - DE we can write AC AB + DE . We thus see that in using these algebraic symbols , = , + , and , a term , as DE , may be transferred from one side of the equation to another by changing its sign from + 12 SYNTHETIC GEOMETRY .
Page 13
... algebra must apply to them as a matter of necessity . It must be remembered , however , that the formal rules of algebra are founded upon the properties of numbers , and that we should not assume , without examination , that these rules ...
... algebra must apply to them as a matter of necessity . It must be remembered , however , that the formal rules of algebra are founded upon the properties of numbers , and that we should not assume , without examination , that these rules ...
Page 25
... algebraic symbol of identity , = ; and this symbol placed between two figures capable of congruence denotes that the figures are congruent . Closed figures , like triangles , admit of comparison in two ways . The first is as to their ...
... algebraic symbol of identity , = ; and this symbol placed between two figures capable of congruence denotes that the figures are congruent . Closed figures , like triangles , admit of comparison in two ways . The first is as to their ...
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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