Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page vi
... given to each interpretable algebraic form . The use of such forms and symbols not only shortens the statements of geometric relations but also conduces to greater generality . In dealing with proportion the method of measures is ...
... given to each interpretable algebraic form . The use of such forms and symbols not only shortens the statements of geometric relations but also conduces to greater generality . In dealing with proportion the method of measures is ...
Page vii
... given of the more important geometric drawing - instruments , having special reference to the geometric principles of their actions . Parts IV . and V. contain a synthetic treatment of the theories of the mean centre , of inverse ...
... given of the more important geometric drawing - instruments , having special reference to the geometric principles of their actions . Parts IV . and V. contain a synthetic treatment of the theories of the mean centre , of inverse ...
Page 8
... Given Point and Line . A point or line is said to be given when we are made to know enough about it to enable us to distinguish it from every other point or line ; and the data which give a point or line are commonly said to determine ...
... Given Point and Line . A point or line is said to be given when we are made to know enough about it to enable us to distinguish it from every other point or line ; and the data which give a point or line are commonly said to determine ...
Page 10
... given direction . Let A be the given point , and let the segment AP mark the given direction . Then , of all the lines P Р A that can pass through the point A , only one can have the direction AP , and this one must lie along and ...
... given direction . Let A be the given point , and let the segment AP mark the given direction . Then , of all the lines P Р A that can pass through the point A , only one can have the direction AP , and this one must lie along and ...
Page 11
... given points . Although it is possible to give a reasonable proof of this axiom , no amount of proof could make its truth more apparent . The following will illustrate the axiom . Assume any two points on a thread taken as a physical ...
... given points . Although it is possible to give a reasonable proof of this axiom , no amount of proof could make its truth more apparent . The following will illustrate the axiom . Assume any two points on a thread taken as a physical ...
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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