Subtitle: In Three Books : Containing the Substance of All That Has Been Written on This Subject by Theo of Smyrna, Nicomachus, Iamblichus, and Boetius... General Books publication date: 2009 Original publication date: 1816 Original Publisher: pr. for the author, by A.J. Valpy Notes: This is a black and white OCR reprint of the original. It has no illustrations and there may be typos or missing text. When you buy the General Books edition of this book you get free trial access to Million-Books.com where you can select from more than a million books for free. Excerpt: CHAPTER V. 'Lhe division of the even number. -- And on the evenly. even number, and its properties. Of the even number however there are three species. For one species is that which is called the evenly-even, but another is denominated the evenly-odd, and the third is the oddly-odd. And the species indeed which are contrary, and obtain the place of extremes are the evenly-even, and the evenly odd. But the species which is a certain medium, and participates of each of the extremes, is the number which is called oddly-odd. Again, the evenly-even number is that which may be divided into two equal parts, and each of these parts into two other equal parts, and each of these may be divided in a similar manner, and the division of the parts may be continued till it is naturally terminated by indivisible unity. Thus the number 64 has for its half 32, but the half of this is 16, the half of 16 is 8, the half of 8 is 4, of 4, two, and the half of 2 is 1, which naturally does not admit of division. To this number it happens that whatever may be its part is found to be evenly. even both in denomination and quantity. And it seems that this number was called evenly-even, because all its parts are found to be evenly-even both in name and quantity. We shall however hereafter show how this number has even parts both in quantity and appellation. But the generation of these numbers is as follows : All numbers i...