Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 3
... sides of a triangle only one can be the greater , and of the two angles opposite these sides only one can be the greater . Then , if it is proved that the greater side is opposite the greater angle it follows that the greater angle is ...
... sides of a triangle only one can be the greater , and of the two angles opposite these sides only one can be the greater . Then , if it is proved that the greater side is opposite the greater angle it follows that the greater angle is ...
Page 24
... sides are given , the triangle is com- X pletely given . This is not the case with a rectilinear figure having any ... opposite internal angles . 4. Any side of a triangle may be taken as its base , and then the angles at the extremities of ...
... sides are given , the triangle is com- X pletely given . This is not the case with a rectilinear figure having any ... opposite internal angles . 4. Any side of a triangle may be taken as its base , and then the angles at the extremities of ...
Page 25
... sides opposite by the cor- responding small letters a , b , c . 51 ° . Def . - When two figures compared by superposition coincide in all their parts and become virtually but one figure they are said to be congruent . Congruent figures ...
... sides opposite by the cor- responding small letters a , b , c . 51 ° . Def . - When two figures compared by superposition coincide in all their parts and become virtually but one figure they are said to be congruent . Congruent figures ...
Page 27
Nathan Fellowes Dupuis. Def . 2. -A triangle in which all the sides are equal to one another is an equilateral triangle . Cor . 3. Since an equilateral triangle is isosceles with re- spect to each side ... opposite side is a median of the ...
Nathan Fellowes Dupuis. Def . 2. -A triangle in which all the sides are equal to one another is an equilateral triangle . Cor . 3. Since an equilateral triangle is isosceles with re- spect to each side ... opposite side is a median of the ...
Page 28
... sides are opposite the equal angles . ( Converse of 53 ° , Cor . 1. ) :: Then But < PAB = 2PBA , then PA = PB ... sides are equal to one another . Or , an equiangular triangle is equilateral . 57 ° . From 53 ° and 56 ° it follows that ...
... sides are opposite the equal angles . ( Converse of 53 ° , Cor . 1. ) :: Then But < PAB = 2PBA , then PA = PB ... sides are equal to one another . Or , an equiangular triangle is equilateral . 57 ° . From 53 ° and 56 ° it follows that ...
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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