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 15
... describes the angle between OP and OP ' . Hence we have the following : - Def . 1. - The angle between two lines is the rotation neces- sary to bring one of the lines into the direction of the other . The word " rotation , " as employed ...
... describes the angle between OP and OP ' . Hence we have the following : - Def . 1. - The angle between two lines is the rotation neces- sary to bring one of the lines into the direction of the other . The word " rotation , " as employed ...
Page 16
... describes the LAOP . If it next rotates into direction OP ' it A describes the LPOP ' . But in its whole rotation it has described the AOP ' . Therefore , Similarly , LAOP ' LAOP + 4POP ' . LAOP LAOP ' - ¿ POP ' . Def . - When two ...
... describes the LAOP . If it next rotates into direction OP ' it A describes the LPOP ' . But in its whole rotation it has described the AOP ' . Therefore , Similarly , LAOP ' LAOP + 4POP ' . LAOP LAOP ' - ¿ POP ' . Def . - When two ...
Page 17
... describes in succession the angles AOB , BOC , ... , EOF , FOA . .. But in its complete rotation it describes a circumangle ( 36 ° ) . LAOB + 2BOC + ... + LFOA = a circumangle . Cor . The result may be thus stated : — q.e.d. The sum of ...
... describes in succession the angles AOB , BOC , ... , EOF , FOA . .. But in its complete rotation it describes a circumangle ( 36 ° ) . LAOB + 2BOC + ... + LFOA = a circumangle . Cor . The result may be thus stated : — q.e.d. The sum of ...
Page 18
... describes a straight angle . And conversely , if a radius vector describes a straight angle its original direction is reversed . Thus , if OA rotates through a straight angle it comes into the direction OB . And conversely , if it ...
... describes a straight angle . And conversely , if a radius vector describes a straight angle its original direction is reversed . Thus , if OA rotates through a straight angle it comes into the direction OB . And conversely , if it ...
Page 53
... unvarying distance B A A B from one another . Then , if one of the points A is fixed , while the other B moves over the paper or other plane surface , the moving point describes a physical circle . PARALLELS , ETC. 53.
... unvarying distance B A A B from one another . Then , if one of the points A is fixed , while the other B moves over the paper or other plane surface , the moving point describes a physical circle . PARALLELS , ETC. 53.
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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