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 2
... equal . v . If equals be added to or taken from unequals the results are unequal . vi . If unequals be taken from equals the remainders are unequal . vii . Equal multiples of equals are equal ; so also equal submultiples of equals are equal ...
... equal . v . If equals be added to or taken from unequals the results are unequal . vi . If unequals be taken from equals the remainders are unequal . vii . Equal multiples of equals are equal ; so also equal submultiples of equals are equal ...
Page 11
... equal length . Or , a less length of line will reach from one given point to another when the line is straight than ... equal , and become virtually one figure by the superposition . 27 ° . Two line - segments can be compared with ...
... equal length . Or , a less length of line will reach from one given point to another when the line is straight than ... equal , and become virtually one figure by the superposition . 27 ° . Two line - segments can be compared with ...
Page 12
... equal to DE . Then AC is the sum of AB Cand DE . This is expressed symbolically by writing AC = AB + DE , where ... equal in length to AB and DE together . 29 ° . Def.- The difference between two segments is the segment which remains ...
... equal to DE . Then AC is the sum of AB Cand DE . This is expressed symbolically by writing AC = AB + DE , where ... equal in length to AB and DE together . 29 ° . Def.- The difference between two segments is the segment which remains ...
Page 16
... equal when the arms of the one may be made to coincide in direction respec- tively with the arms of the other ; or when the angles are described by the same rotation . Thus , if , when O ' is placed upon O , and O'A ' is made to lie ...
... equal when the arms of the one may be made to coincide in direction respec- tively with the arms of the other ; or when the angles are described by the same rotation . Thus , if , when O ' is placed upon O , and O'A ' is made to lie ...
Page 18
... equal , and each is a right angle ( 36 ° ) . Therefore , if two adjacent angles formed by two intersect- ing lines are equal to each other , all four of the angles so formed are equal to one another , and each is a right angle . Def . 2 ...
... equal , and each is a right angle ( 36 ° ) . Therefore , if two adjacent angles formed by two intersect- ing lines are equal to each other , all four of the angles so formed are equal to one another , and each is a right angle . Def . 2 ...
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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