Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page ix
... 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 Line - Segments ...
... 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 Line - Segments ...
Page 4
... length or distance in every direction ; so that length and direction are fundamental ideas in studying the geometric properties of space . Every material object exists in , and is surrounded by 4 SYNTHETIC GEOMETRY .
... length or distance in every direction ; so that length and direction are fundamental ideas in studying the geometric properties of space . Every material object exists in , and is surrounded by 4 SYNTHETIC GEOMETRY .
Page 5
... as its breadth is continually diminished . We may consequently consider a geometric line as length abstracted from every other consideration . This theoretic relation of a geometric line to a physical THE LINE AND POINT . 5.
... as its breadth is continually diminished . We may consequently consider a geometric line as length abstracted from every other consideration . This theoretic relation of a geometric line to a physical THE LINE AND POINT . 5.
Page 7
... length . Def . - A plane figure made up of straight lines only is called a rectilinear figure . 15 ° . A Curve is a line of which no part is straight ; or a curve is a line of which no two adjacent parts have the same direction . The ...
... length . Def . - A plane figure made up of straight lines only is called a rectilinear figure . 15 ° . A Curve is a line of which no part is straight ; or a curve is a line of which no two adjacent parts have the same direction . The ...
Page 8
... 2. - A limited portion of a line , especially when any refer- ence is had to its length , is a finite line , or a line - segment , or simply a segment . That absolute sameness ( 14 ° ) which characterizes every 8 SYNTHETIC GEOMETRY .
... 2. - A limited portion of a line , especially when any refer- ence is had to its length , is a finite line , or a line - segment , or simply a segment . That absolute sameness ( 14 ° ) which characterizes every 8 SYNTHETIC GEOMETRY .
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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