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. |
From inside the book
Results 1-5 of 45
Page 1
... proved , or it may be deduced from some previous course of reasoning . In the former case it is called a Proposition , that is , some- thing proposed , and consists of ( a ) the statement or enuncia- tion of the theorem , and ( b ) the ...
... proved , or it may be deduced from some previous course of reasoning . In the former case it is called a Proposition , that is , some- thing proposed , and consists of ( a ) the statement or enuncia- tion of the theorem , and ( b ) the ...
Page 3
Nathan Fellowes Dupuis. positive , and vice versa , and hence if either is proved the other is proved also . 6 ° . Two theorems are converse to one another when the hypothesis and conclusion of the one are respectively the conclusion and ...
Nathan Fellowes Dupuis. positive , and vice versa , and hence if either is proved the other is proved also . 6 ° . Two theorems are converse to one another when the hypothesis and conclusion of the one are respectively the conclusion and ...
Page 27
... prove the conclusion of the theorem to be true by showing that the acceptance of any other conclusion leads us to some relation which is absurd or untrue . 55 ° . Def . - The line - segment from a vertex of a triangle to the middle of ...
... prove the conclusion of the theorem to be true by showing that the acceptance of any other conclusion leads us to some relation which is absurd or untrue . 55 ° . Def . - The line - segment from a vertex of a triangle to the middle of ...
Page 32
... proved that PD = PB . Therefore two equal segments can be drawn from any point P to the line B ; and these lie upon opposite sides of PA . No other segment can be drawn equal to PD or PB . For it must lie upon the same side of the ...
... proved that PD = PB . Therefore two equal segments can be drawn from any point P to the line B ; and these lie upon opposite sides of PA . No other segment can be drawn equal to PD or PB . For it must lie upon the same side of the ...
Page 39
... Prove 58 ° from the axiom “ a straight line is the shortest distance between two given points . " 9. Show from 60 ° that a triangle cannot have two of its angles right angles . 10. If a triangle has a right angle , the side opposite ...
... Prove 58 ° from the axiom “ a straight line is the shortest distance between two given points . " 9. Show from 60 ° that a triangle cannot have two of its angles right angles . 10. If a triangle has a right angle , the side opposite ...
Other editions - View all
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