Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 1
... theorem , and ( b ) the argument or proof . The purpose of the argument is to show that the truth of the theorem depends upon that of some preceding theorem whose truth has already been established or admitted . Ex . " The sum of two ...
... theorem , and ( b ) the argument or proof . The purpose of the argument is to show that the truth of the theorem depends upon that of some preceding theorem whose truth has already been established or admitted . Ex . " The sum of two ...
Page 2
... theorem may be put into the hypothetical form , of which the type is-- If A is B then C is D. The first part " if A is B " is called the hypothesis , and the second part " then C is D " is the conclusion . Ex . The theorem " The product ...
... theorem may be put into the hypothetical form , of which the type is-- If A is B then C is D. The first part " if A is B " is called the hypothesis , and the second part " then C is D " is the conclusion . Ex . The theorem " The product ...
Page 3
... theorem which admits of a converse can be proved directly its converse can usually be proved indirectly . Examples will occur hereafter . 7 ° . Many geometric theorems are so connected with their converses that the truth of the theorems ...
... theorem which admits of a converse can be proved directly its converse can usually be proved indirectly . Examples will occur hereafter . 7 ° . Many geometric theorems are so connected with their converses that the truth of the theorems ...
Page 4
... theorem deduced from some other theorem , usually by some qualification or restriction , and occasionally by some amplification of the hypothesis . Or a corollary may be derived directly from an axiom or from a definition . As a matter ...
... theorem deduced from some other theorem , usually by some qualification or restriction , and occasionally by some amplification of the hypothesis . Or a corollary may be derived directly from an axiom or from a definition . As a matter ...
Page 17
... Theorem . — If any number of lines 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 ...
... Theorem . — If any number of lines 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 ...
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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