Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 4
... meet . 4. Every point equidistant from the end - points of a line- segment is on the right bisector of that segment . SECTION I. THE LINE AND POINT . 9 ° . Space may be defined to be that which admits of length or distance in every ...
... meet . 4. Every point equidistant from the end - points of a line- segment is on the right bisector of that segment . SECTION I. THE LINE AND POINT . 9 ° . Space may be defined to be that which admits of length or distance in every ...
Page 15
... meet is the vertex . Cor . From 31 ° , 2 , an angle does not in any way depend upon the lengths of its arms , but only upon their relative directions . 33 ° . Notation of Angles . - 1 . The symbol is used for the word " angle . " 2 ...
... meet is the vertex . Cor . From 31 ° , 2 , an angle does not in any way depend upon the lengths of its arms , but only upon their relative directions . 33 ° . Notation of Angles . - 1 . The symbol is used for the word " angle . " 2 ...
Page 17
... meet in a point , the sum of all the adjacent angles formed is a circumangle . OA , OB , OC , ... , OF are lines meeting in O. Then LAOB + 2BOC + 4COD + ... + LFOA = a circumangle . D E B F Proof - A radius vector which starts from ...
... meet in a point , the sum of all the adjacent angles formed is a circumangle . OA , OB , OC , ... , OF are lines meeting in O. Then LAOB + 2BOC + 4COD + ... + LFOA = a circumangle . D E B F Proof - A radius vector which starts from ...
Page 31
... passing through the point— I. The perpendicular to the line is the shortest . 2. Of any two segments the one which meets the line further from the perpendicular is the longer ; and con- THREE OR MORE POINTS AND LINES . 31.
... passing through the point— I. The perpendicular to the line is the shortest . 2. Of any two segments the one which meets the line further from the perpendicular is the longer ; and con- THREE OR MORE POINTS AND LINES . 31.
Page 32
... meets the line further from the perpendicular than the shorter does . 3. Two , and only two segments can be equal , and they lie upon opposite sides of the perpendicular . P P is any point and BC a line not pass- ing through it , and PA ...
... meets the line further from the perpendicular than the shorter does . 3. Two , and only two segments can be equal , and they lie upon opposite sides of the perpendicular . P P is any point and BC a line not pass- ing through it , and PA ...
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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