Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 49
... right angle , and the orthocentre is the right - angled vertex . Def . The side of a right - angled triangle opposite the right angle is called the hypothenuse . D 89 ° . The definition of 80 ° admits of PARALLELS , ETC. 49.
... right angle , and the orthocentre is the right - angled vertex . Def . The side of a right - angled triangle opposite the right angle is called the hypothenuse . D 89 ° . The definition of 80 ° admits of PARALLELS , ETC. 49.
Page 52
... hypothenuse of a right - angled triangle is equal to one - half the hypothenuse . 20. If one diagonal of a be equal to a side of the figure , the other diagonal is greater than any side . 21. If any point other than the point of ...
... hypothenuse of a right - angled triangle is equal to one - half the hypothenuse . 20. If one diagonal of a be equal to a side of the figure , the other diagonal is greater than any side . 21. If any point other than the point of ...
Page 65
... hypothenuse of a right - angled triangle is the diameter of its circumcircle . ( 88 ° , 3 , Def .; 97 ° , Def . ) Cor . 2. When P moves along the ○ the △ APC ( last figure ) has its base AC constant and its vertical angle APC constant ...
... hypothenuse of a right - angled triangle is the diameter of its circumcircle . ( 88 ° , 3 , Def .; 97 ° , Def . ) Cor . 2. When P moves along the ○ the △ APC ( last figure ) has its base AC constant and its vertical angle APC constant ...
Page 120
... hypothenuse , as distinguished from the remaining two sides . E 169 ° . Theorem . - In any right - angled triangle the square on one of the sides is equal to the rectangle G J Then ... Also , and B K F on the hypothenuse and the ...
... hypothenuse , as distinguished from the remaining two sides . E 169 ° . Theorem . - In any right - angled triangle the square on one of the sides is equal to the rectangle G J Then ... Also , and B K F on the hypothenuse and the ...
Page 121
... hypothenuse by b , and let a1 and c1 denote the projections of the sides a and cupon the hypothenuse . Then and .. a2 = a1b , c2 = c1b , a2 + c2 = b2 . Cor . 3. Denote the altitude to the hypothenuse by p . Then b = c1 + a1 , and ADB ...
... hypothenuse by b , and let a1 and c1 denote the projections of the sides a and cupon the hypothenuse . Then and .. a2 = a1b , c2 = c1b , a2 + c2 = b2 . Cor . 3. Denote the altitude to the hypothenuse by p . Then b = c1 + a1 , and ADB ...
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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