Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 1
... sense in which some word or phrase is employed is a definition . A definition may select some one meaning out of several attached to a common word , or it may introduce some technical term to be used in a particular sense . Some terms ...
... sense in which some word or phrase is employed is a definition . A definition may select some one meaning out of several attached to a common word , or it may introduce some technical term to be used in a particular sense . Some terms ...
Page 10
... sense commonly attached to the word divide . But on account of the similar relations held by C and C ' to the end- points of the segment , it is convenient and advantageous to consider both points as dividing the segment AB . When thus ...
... sense commonly attached to the word divide . But on account of the similar relations held by C and C ' to the end- points of the segment , it is convenient and advantageous to consider both points as dividing the segment AB . When thus ...
Page 109
... Senses .-- A quantitative symbol , a , is in Algebra always affected with one of two signs , + or - , which , while leaving the absolute value of the symbol un- changed , impart to it certain properties exactly opposite in character ...
... Senses .-- A quantitative symbol , a , is in Algebra always affected with one of two signs , + or - , which , while leaving the absolute value of the symbol un- changed , impart to it certain properties exactly opposite in character ...
Page 110
... senses . Hence the algebraic distinction of positive and negative as applied to a single symbol of quantity is to be interpreted geometrically by the oppositeness of direction of the segment denoted by the symbol . Usually the ...
... senses . Hence the algebraic distinction of positive and negative as applied to a single symbol of quantity is to be interpreted geometrically by the oppositeness of direction of the segment denoted by the symbol . Usually the ...
Page 111
... sense of one of the sides . Similarly , if one of the sides of a crossed quadrangle be changed in sense the figure ceases to be a crossed quadrangle . Ex . 3. This is an example where segments which are par- allel but which are not in ...
... sense of one of the sides . Similarly , if one of the sides of a crossed quadrangle be changed in sense the figure ceases to be a crossed quadrangle . Ex . 3. This is an example where segments which are par- allel but which are not in ...
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Common terms and phrases
ABCD Algebra altitude becomes bisects c.p.-circles centre of similitude chord of contact circles touch circumcircle co-axal coincide collinear concurrent concurrent lines concyclic congruent cut the circle denote diagonals diameter divided double points 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