Elementary Synthetic Geometry of the Point, Line and Circle in the PlaneMacmillan, 1889 - 294 sider 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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... put into the form- If C is not D then A is not B , which is called the contrapositive of the former . The truth of a theorem establishes the truth of its contra- positive , and vice versa , and hence if either 2 SYNTHETIC GEOMETRY .
... hence a theorem and its converse have in general to be proved separately . But on account of the peculiar relation existing between the two , a relation exists also between the modes of proof for the two . These are known as the direct ...
... Hence we may consider the geometric line as being the limit towards which a physical line approaches as its breadth is continually diminished . We may consequently consider a geometric line as length abstracted from every other ...
... hence arguments in regard to geometric lines may be replaced by arguments in regard to physical lines , if from such arguments we exclude everything that would involve the idea of breadth . The diagrams employed to direct and assist us ...
... hence , in imagination , we may follow a line as far as we please without coming to any necessary termination . This property is conveniently expressed by saying that a line extends to infinity . 3. The hypothetical end - points of any ...
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Elementary Synthetic Geometry of the Point, Line and Circle in the Plane Nathan Fellowes Dupuis Uten tilgangsbegrensning - 1894 |
Elementary Synthetic Geometry of the Point, Line and Circle in the Plane Nathan Fellowes Dupuis Uten tilgangsbegrensning - 1894 |
Elementary Synthetic Geometry of the Point, Line and Circle in the Plane Nathan Fellowes Dupuis Uten tilgangsbegrensning - 1896 |
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