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Sinopsis
Excerpt from Curiosa Mathematica, Vol. 1: A New Theory of Parallels
If only it could be proved, with equal ease, that "there is a Triangle whose angles are together not-less than two right angles"! But alas, that is an ignis fatuus that has never yet been caught! The man, who first proves that Theorem, without using Euclid's 12th Axiom or any substitute for it, will certainly deserve a place among the world's great discoverers.
I take this opportunity of replying to one or two criticisms, which have been published, on the Second Edition - earnestly assuring the writers of those criticisms that, in treating the questions at issue between us from a not-wholly-solemn point of view, I have been actuated by no feeling of disrespect towards them, but simply from the wish to lighten a subject, naturally somewhat too heavy and sombre, and thus to make it a little more palatable to the general Reader.
At p. 12 of the and Edition, the enunciation of Prop. VI (which re-appears, in a modified form, at p. 34 of the 3rd Edition) stood thus: -
"If the vertical angle of a Sector of a Circle be divided by radii into 2n equal angles, thus forming 2n equal Sectors; and if the chord of each such Sector be not less than the radius of the Circle: the original Sector is not less than a times the Triangle cut off from it by its chords." My controversy with Nature on this enunciation, will be best given in the form of a dialogue. (Of course I quote verbatim.)
Nature. (Dec.6, 1888.) "How are the figures to be constructed, if n be greater than 2?"
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Excerpt from Curiosa Mathematica, Vol. 1: A New Theory of Parallels
Well, suppose u were equal to 4: i. E. We have to divide the vertical angle into 24 equal parts. Bisect it: that gives halves. Bisect the halves: that gives quarters. Bisect again: that gives eighths. Bisect once more that give sixteenths. Voila tout!
Nature. (june 13, Shade of Euclid! Who knows not such things? We admitted the same, but stated that our difficulty in the construction was the con dition imposed in the enunciation: viz., the chord of each such sector not less than the radius of the circle.' Take Mr. Dodgson's illustration of a sixteenth: this would necessitate that the original angle should be at least 960 we have further noted that no one of the chords in Mr. Dodgson's figures is even equal to the radius.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Reseña del editor
Excerpt from Curiosa Mathematica, Vol. 1: A New Theory of Parallels
If only it could be proved, with equal ease, that "there is a Triangle whose angles are together not-less than two right angles"! But alas, that is an ignis fatuus that has never yet been caught! The man, who first proves that Theorem, without using Euclid's 12th Axiom or any substitute for it, will certainly deserve a place among the world's great discoverers.
I take this opportunity of replying to one or two criticisms, which have been published, on the Second Edition - earnestly assuring the writers of those criticisms that, in treating the questions at issue between us from a not-wholly-solemn point of view, I have been actuated by no feeling of disrespect towards them, but simply from the wish to lighten a subject, naturally somewhat too heavy and sombre, and thus to make it a little more palatable to the general Reader.
At p. 12 of the and Edition, the enunciation of Prop. VI (which re-appears, in a modified form, at p. 34 of the 3rd Edition) stood thus: -
"If the vertical angle of a Sector of a Circle be divided by radii into 2n equal angles, thus forming 2n equal Sectors; and if the chord of each such Sector be not less than the radius of the Circle: the original Sector is not less than a times the Triangle cut off from it by its chords." My controversy with Nature on this enunciation, will be best given in the form of a dialogue. (Of course I quote verbatim.)
Nature. (Dec.6, 1888.) "How are the figures to be constructed, if n be greater than 2?"
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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Paperback. Condición: New. Print on Demand. This book delves into the fascinating and challenging world of pure mathematics, specifically focusing on the age-old quest to prove Euclid's 12th Axiom, a cornerstone of geometry. The author takes the reader on a journey through the history of this problem, highlighting the many attempts ââ â some successful, others tragically misguided ââ â to find a more solid foundation for this crucial mathematical principle. Through engaging dialogues and clear explanations, the author explores the complexities of infinity and infinitesimals, contrasting them with the absolute certainty offered by finite magnitudes. This fresh perspective allows for a novel approach to proving key geometric theorems, including the famous proposition that the angles of any triangle sum to two right angles. This book offers a unique and thought-provoking exploration of a fundamental mathematical concept, inviting the reader to appreciate the beauty and depth of geometric reasoning while contemplating the very nature of mathematical certainty. Ultimately, it leaves us with a renewed sense of wonder at the power and potential of the human intellect to unravel the mysteries of the universe through the lens of mathematics. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Nº de ref. del artículo: 9781332008186_0
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Condición: New. KlappentextrnrnExcerpt from Curiosa Mathematica, Vol. 1: A New Theory of ParallelsWell, suppose u were equal to 4: i. E. We have to divide the vertical angle into 24 equal parts. Bisect it: that gives halves. Bisect the halves: that give. Nº de ref. del artículo: 2147915308
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Curiosa Mathematica, Vol. 1 : A New Theory of Parallels (Classic Reprint)
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