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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Side 18
... cut one another four angles are formed about the point of intersection , any one of which may be taken to be the angle between the lines . These four angles consist of two pairs of opposite or vertical angles , viz . , A , A ' , and B ...
... cut one another four angles are formed about the point of intersection , any one of which may be taken to be the angle between the lines . These four angles consist of two pairs of opposite or vertical angles , viz . , A , A ' , and B ...
Side 27
... cut AP ; and similarly it does not cut BP ; therefore it passes through P , or P is on the right bisector . q.e.d. This form of proof should be compared with that of Art . 53 ° , they being the kinds indicated in 6 ° . proof by reductio ...
... cut AP ; and similarly it does not cut BP ; therefore it passes through P , or P is on the right bisector . q.e.d. This form of proof should be compared with that of Art . 53 ° , they being the kinds indicated in 6 ° . proof by reductio ...
Side 28
... cut the right bisector in Q. QA = QB , and ¿ QAB = 4QBA . ( 53 ° and Cor . 1 ) LPBA = LQAB ; LPBA = LQBA , which is not true unless P and Q coincide . ( hyp . ) Therefore if P is not on the right bisector of AB , the ¿ PAB cannot be ...
... cut the right bisector in Q. QA = QB , and ¿ QAB = 4QBA . ( 53 ° and Cor . 1 ) LPBA = LQAB ; LPBA = LQBA , which is not true unless P and Q coincide . ( hyp . ) Therefore if P is not on the right bisector of AB , the ¿ PAB cannot be ...
Side 43
... All other triangles are called acute - angled triangles , and have three acute angles . 6. The acute angles in a right - angled triangle are comple- mentary to one another . 78 ° . Theorem . - If a line cuts PARALLELS , ETC. 43.
... All other triangles are called acute - angled triangles , and have three acute angles . 6. The acute angles in a right - angled triangle are comple- mentary to one another . 78 ° . Theorem . - If a line cuts PARALLELS , ETC. 43.
Side 44
... cuts every parallel to the given line . M L N Let L cut M , and let N be any parallel to M. Then L cuts N. But M is to N. Proof . - If L does not cut N it is || to N. Therefore through the same point P two lines L and M pass which are ...
... cuts every parallel to the given line . M L N Let L cut M , and let N be any parallel to M. Then L cuts N. But M is to N. Proof . - If L does not cut N it is || to N. Therefore through the same point P two lines L and M pass which are ...
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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 |
Vanlige uttrykk og setninger
A. W. VERRALL ABCD algebraic altitude Assistant Master bisects BOOK Cambridge centre of similitude centre-line circles touch circumcircle co-axal coincide collinear common concurrent concurrent lines concyclic congruent cuts denote diagonals diameter divided Edited ELEMENTARY end-points equal angles equianharmonic equilateral triangle excircles EXERCISES external bisector FASNACHT Fcap fixed point G. E. FASNACHT geometric given circles given line given point GREEK harmonic range Hence HISTORY homographic Illustrated inverse points ISAAC TODHUNTER isosceles LAOB line-segment LL.D Mathematical median middle point orthogonally Owens College pair parallel parallelogram passes pencil perpendicular plane point of contact point of intersection Prof Professor Proof quadrangle radical axis radius rectangle regular polygon respect revised right angle right bisector rotation School secant Similarly square straight angle symbol tangent theorem Theorem.-The three circles Translated Trinity College vertex vertices
Populære avsnitt
Side 176 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Side 9 - BLACKIE— GREEK AND ENGLISH DIALOGUES FOR USE IN SCHOOLS AND COLLEGES. By JOHN STUART BLACKIE, Professor of Greek in the University of Edinburgh.
Side 15 - Hales.— LONGER ENGLISH POEMS. With Notes, Philological and Explanatory, and an Introduction on the Teaching of English. Chiefly for use in Schools. Edited by JW HALES, MA, Professor of English Literature at King's College, London, &c. &c. Fifth Edition. Extra fcap. 8vo. 4*.
Side 50 - ANALYSIS OF ENGLISH HISTORY, based on Green's "Short History of the English People.
Side 14 - GRAMMAR : An Attempt to illustrate some of the Differences between Elizabethan and Modern English. By the Rev. EA ABBOTT, DD, Head Master of the City of London School.
Side 183 - The sides of a triangle are proportional to the sines of the opposite angles.
Side 49 - Lethbridge. — A SHORT MANUAL OF THE HISTORY OF INDIA. With an Account of INDIA AS IT is. The Soil, Climate, and Productions ; the People, their Races, Religions, Public Works, and Industries ; the Civil Services, and System of Administration. By ROPER...
Side 27 - ON THE ALGEBRAICAL AND NUMERICAL THEORY OF ERRORS OF OBSERVATIONS AND THE COMBINATION OF OBSERVATIONS.
Side 9 - HODGSON -MYTHOLOGY FOR LATIN VERSIFICATION. A brief Sketch of the Fables of the Ancients, prepared to be rendered into Latin Verse for Schools.
Side 54 - A GENERAL SURVEY OF THE HISTORY OF THE CANON OF THE NEW TESTAMENT DURING THE fIRST FOUR CENTURIES. Fourth Edition. With Preface on "Supernatural Religion.
Referanser til denne boken
The Classification of Quadrilaterals: A Study of Definition Zalman Usiskin,Jennifer Griffin,David Witonsky,Edwin Willmore Ingen forhåndsvisning tilgjengelig - 2008 |
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