Elementary Synthetic Geometry of the Point, Line and Circle in the PlaneMacmillan, 1889 - 294 σελίδες Elementary Synthetic Geometry of the Point, Line and Circle in the Plane by Nathan Fellowes Dupuis, first published in 1889, is a rare manuscript, the original residing in one of the great libraries of the world. This book is a reproduction of that original, which has been scanned and cleaned by state-of-the-art publishing tools for better readability and enhanced appreciation. Restoration Editors' mission is to bring long out of print manuscripts back to life. Some smudges, annotations or unclear text may still exist, due to permanent damage to the original work. We believe the literary significance of the text justifies offering this reproduction, allowing a new generation to appreciate it. |
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... of a square , and A , E , F of an equilateral triangle inscribed in the same circle . What is the angle between the lines BE and DF ? between BF and ED ? SPECIAL SECANTS -- TANGENT . 109 ° . Let P 66 SYNTHETIC GEOMETRY .
... tangent . Def . 1. - A tangent to a circle is a secant in its limiting position when its points of intersection with the circle become coincident . is evident . That the tangent cannot cut or cross the For if it cuts the Oat P it must ...
... tangent to the same point on a circle are perpendicular to one another . D T PO S L ' is a centre - line and Ta tan ... tangent at the point of con- tact is a centre - line . ( Converse of the theorem . ) Cor . 3. The perpendicular to a ...
... tangent to S. Similarly BP is tangent to S. Cor . 1. Since PO is the right bisector of AB , PA = PB . ( 106 ° , Cor . 4 ) ( 110 ° , Cor . 3 ) ( 113 ° ) ( 53 ° ) Hence calling the segment PA the tangent from P to the circle , when length ...
... tangents at A and C are fixed , and the tangent at B is variable , we have the following theorem : — The segment of a variable tangent intercepted by two fixed tangents , all to the same circle , subtends a fixed angle at the centre ...
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