Elementary Synthetic Geometry of the Point, Line and Circle in the PlaneElementary Synthetic Geometry of the Point, Line and Circle in the Plane by Nathan Fellowes Dupuis, first published in 1889, is a rare manuscript, the original residing in one of the great libraries of the world. This book is a reproduction of that original, which has been scanned and cleaned by state-of-the-art publishing tools for better readability and enhanced appreciation. Restoration Editors' mission is to bring long out of print manuscripts back to life. Some smudges, annotations or unclear text may still exist, due to permanent damage to the original work. We believe the literary significance of the text justifies offering this reproduction, allowing a new generation to appreciate it. |
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Page 8
... A similar nomenclature applies to other geometric ele- ments . The statement that a point or line lies in a plane does not give it , but a point or line placed in the plane for future reference is considered as being given . Such a point ...
... A similar nomenclature applies to other geometric ele- ments . The statement that a point or line lies in a plane does not give it , but a point or line placed in the plane for future reference is considered as being given . Such a point ...
Page 10
... a given point only one line can pass in a given direction . Let A be the given point , and let the segment AP mark the given direction . Then , of all the lines P that can pass through the point A , only one can have the direction AP ...
... a given point only one line can pass in a given direction . Let A be the given point , and let the segment AP mark the given direction . Then , of all the lines P that can pass through the point A , only one can have the direction AP ...
Page 11
... a straight finite line has its end - points further apart than a curved line of equal length . Or , a less length of line will reach from one given point to another when the line is straight than when it is curved . Def . - The distance ...
... a straight finite line has its end - points further apart than a curved line of equal length . Or , a less length of line will reach from one given point to another when the line is straight than when it is curved . Def . - The distance ...
Page 13
... A given line - segment has but one middle point . 4. In Art . 23 ° , if C becomes the middle point of AB , what becomes of C ' ? 5. In Art . 30 ° the internal point of bisection is spoken of . What meaning can you give to the " external ...
... A given line - segment has but one middle point . 4. In Art . 23 ° , if C becomes the middle point of AB , what becomes of C ' ? 5. In Art . 30 ° the internal point of bisection is spoken of . What meaning can you give to the " external ...
Page 19
... a right angle , and less than two right angles . 41 ° . From ( 36 ° ) we have I circumangle = 2 straight angles = 4 right angles . In estimating an angle numerically it may be expressed in any one of the given units . If a right angle ...
... a right angle , and less than two right angles . 41 ° . From ( 36 ° ) we have I circumangle = 2 straight angles = 4 right angles . In estimating an angle numerically it may be expressed in any one of the given units . If a right angle ...
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Common terms and phrases
ABCD algebraic altitude apothem bisects c.p.-circles centre of similitude centre-line chord of contact circles touch circumcircle co-axal coincide collinear concurrent concurrent lines concyclic congruent corresponding cut the circle denote diagonals diameter divided 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