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 vi
... symbols , ( 1 ) by an elementary study of the modes of representing geometric ideas in the symbols of Algebra , and ( 2 ) by determining the consequent geometric interpretation which is to be given to each interpretable algebraic form ...
... symbols , ( 1 ) by an elementary study of the modes of representing geometric ideas in the symbols of Algebra , and ( 2 ) by determining the consequent geometric interpretation which is to be given to each interpretable algebraic form ...
Page 12
... AC- DE we can write AC = AB + DE . We thus see that in using these algebraic symbols , = , + , and - , a term , as DE , may be transferred from one side of the equation to another by changing its sign from + 12 SYNTHETIC GEOMETRY .
... AC- DE we can write AC = AB + DE . We thus see that in using these algebraic symbols , = , + , and - , a term , as DE , may be transferred from one side of the equation to another by changing its sign from + 12 SYNTHETIC GEOMETRY .
Page 15
... symbol is used for the word " angle . " 2. When two segments meet at a vertex the angle between them may be denoted by a single letter B placed at the vertex , as the 40 , or by a letter with or without an arch of dots , as 48 ; or by ...
... symbol is used for the word " angle . " 2. When two segments meet at a vertex the angle between them may be denoted by a single letter B placed at the vertex , as the 40 , or by a letter with or without an arch of dots , as 48 ; or by ...
Page 18
... lines form a right angle at their point of intersection , they are said to be perpendicular to one another , and each is perpendicular to the other . Perpendicularity is denoted by the symbol , to be read 18 SYNTHETIC GEOMETRY .
... lines form a right angle at their point of intersection , they are said to be perpendicular to one another , and each is perpendicular to the other . Perpendicularity is denoted by the symbol , to be read 18 SYNTHETIC GEOMETRY .
Page 19
... 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 . The right angle is 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 . The right angle is the ...
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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