By Thomas Taylor
Subtitle: In 3 Books : Containing the Substance of All That Has Been Written in this topic through Theo of Smyrna, Nicomachus, Iamblichus, and Boetius... basic Books e-book date: 2009 unique ebook date: 1816 unique writer: pr. for the writer, via A.J. Valpy Notes: it is a black and white OCR reprint of the unique. It has no illustrations and there's typos or lacking textual content. if you purchase the final Books version of this ebook you get unfastened trial entry to Million-Books.com the place you could choose between greater than one million books at no cost. Excerpt: bankruptcy V. 'Lhe department of the even quantity. -- And at the lightly. even quantity, and its homes. Of the even quantity besides the fact that there are 3 species. For one species is that generally known as the evenly-even, yet one other is denominated the evenly-odd, and the 3rd is the oddly-odd. And the species certainly that are opposite, and acquire where of extremes are the evenly-even, and the frivolously extraordinary. however the species that's a definite medium, and participates of every of the extremes, is the quantity often called oddly-odd. back, the evenly-even quantity is that that could be divided into equivalent components, and every of those components into different equivalent elements, and every of those will be divided in an analogous demeanour, and the department of the components should be endured until eventually it's evidently terminated by way of indivisible solidarity. therefore the quantity sixty four has for its part 32, however the half this can be sixteen, the 1/2 sixteen is eight, the 1/2 eight is four, of four, , and the 1/2 2 is 1, which certainly doesn't admit of department. To this quantity it occurs that no matter what could be its half is located to be calmly. even either in denomination and volume. And apparently this quantity was once referred to as evenly-even, simply because all its components are stumbled on to be evenly-even either in identify and volume. we will despite the fact that hereafter express how this quantity has even components either in volume and appellation. however the iteration of those numbers is as follows : All numbers i...
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We must necessarily take cum grano the apparently circumstantial accounts of Euclid given by Arabian authors; and indeed the origin of their stories can be explained as the result (1) of the Arabian tendency to romance, and (2) of misunderstandings. We read4 that “Euclid, son of Naucrates, grandson of Zenarchus5, called the author of geometry, a philosopher of somewhat ancient date, a Greek by nationality domiciled at Damascus, born at Tyre, most learned in the science of geometry, published a most excellent and most useful work entitled the foundation or elements of geometry, a subject in which no more general treatise existed before among the Greeks: nay, there was no one even of later date who did not walk in his footsteps and frankly profess his doctrine.
I. INTRODUCTION. CHAPTERI. EUCLID AND THE TRADITIONS ABOUT HIM. As in the case of the other great mathematicians of Greece, so in Euclid’s case, we have only the most meagre particulars of the life and personality of the man. Most of what we have is contained in the passage of Proclus’ summary relating to him, which is as follows1: “Not much younger than these (sc. Hermotimus of Colophon and Philippus of Medma) is Euclid, who put together the Elements, collecting many of Eudoxus’ theorems, perfecting many of Theaetetus’, and also bringing to irrefragable demonstration the things which were only somewhat loosely proved by his predecessors.
Equally remarkable are the Arabian accounts of the relation of Euclid and Apollonius1. According to them the Elements were originally written, not by Euclid, but by a man whose name was Apollonius, a carpenter, who wrote the work in 15 books or sections2. In the course of time some of the work was lost and the rest became disarranged, so that one of the kings at Alexandria who desired to study geometry and to master this treatise in particular first questioned about it certain learned men who visited him and then sent for Euclid who was at that time famous as a geometer, and asked him to revise and complete the work and reduce it to order.