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 4
... angle ) , and as X is ( corresponds to or is opposite ) Y , therefore Y is ( corresponds to or is opposite ) X. 8 ... right bisector of that segment . SECTION I. THE LINE AND POINT . 9. Space may be defined to be that which admits of ...
... angle ) , and as X is ( corresponds to or is opposite ) Y , therefore Y is ( corresponds to or is opposite ) X. 8 ... right bisector of that segment . SECTION I. THE LINE AND POINT . 9. Space may be defined to be that which admits of ...
Page 17
Nathan Fellowes Dupuis. One - half of a circumangle is a straight angle , and one- fourth of a circumangle is a right angle . 37 ° . Theorem . — If any number of lines meet in a point , the sum of all the adjacent angles formed is a ...
Nathan Fellowes Dupuis. One - half of a circumangle is a straight angle , and one- fourth of a circumangle is a right angle . 37 ° . Theorem . — If any number of lines meet in a point , the sum of all the adjacent angles formed is a ...
Page 18
... angle . And conversely , if a radius vector describes a straight angle its original direction is reversed . Thus ... right angle ( 36 ° ) . Therefore , if two adjacent angles formed by two intersect- ing lines are equal to each other ...
... angle . And conversely , if a radius vector describes a straight angle its original direction is reversed . Thus ... right angle ( 36 ° ) . Therefore , if two adjacent angles formed by two intersect- ing lines are equal to each other ...
Page 19
... right angle is denoted by the symbol The symbol also denotes two right angles or a straight angle . Def . 3. — When two angles together make up a right angle they are complementary to one another , and each is the complement of the other .
... right angle is denoted by the symbol The symbol also denotes two right angles or a straight angle . Def . 3. — When two angles together make up a right angle they are complementary to one another , and each is the complement of the other .
Page 20
... angles BOC and COA are each right angles ( 40 ° , Def . 2 ) . Therefore BOD is not a right angle , and OD is not 1 AB . But OD is any line other than OC . Therefore OC is the only perpendicular . q.ed. Def . The perpendicular to a line ...
... angles BOC and COA are each right angles ( 40 ° , Def . 2 ) . Therefore BOD is not a right angle , and OD is not 1 AB . But OD is any line other than OC . Therefore OC is the only perpendicular . q.ed. Def . The perpendicular to a line ...
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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