17th-century Mathematician Quotes
Sneezing absorbs all the functions of the soul just as much as the [sexual] act, but we do not draw from it the same conclusions against the greatness of man, because it is involuntary; although we bring it about, we do so involuntarily. It is not for the sake of the thing in itself but for another end, and is therefore not a sign of man's weakness, or his subjection to this act.
We have found a beautiful and most general proposition, namely, that every integer is either a square, or the sum of two, three or at most four squares. This theorem depends on some of the most recondite mysteries of number, and is not possible to present its proof on the margin of this page.
Mathematicks therefore is a Science which teaches or contemplates whatever is capable of Measure or Number as such. When it relates to Number, it is called Arithmetick; but when to measure, as Length, Breadth, Depth, Degrees of Velocity in Motion, Intenseness or Remissness of Sounds, Augmentation or Diminution of Quality, 6tc. it is called Geometry.
It hath been my Lot to live in a time, wherein have been many and great Changes and Alterations. It hath been my endeavour all along, to act by moderate Principles, between the Extremities on either hand, in a moderate compliance with the Powers in being, in those places, where it hath been my Lot to live, without the fierce and violent animosities usual in such Cases, against all, that did not act just as I did, knowing that there were many worthy Persons engaged on either side. And willing whatever side was upmost, to promote (as I was able) any good design for the true Interest of Religion, of Learning, and the publick good; and ready so to do good Offices, as there was Opportunity; And, if things could not be just, as I could wish, to make the best of what is: And hereby, (thro' God's gracious Providence) have been able to live easy, and useful, though not Great.
I have endeavour'd to make every thing so plain, that a very little Skill in Geometry may be sufficient to enable one to read this Book by himself. And upon this occasion I would advise all my Readers, who desire to make themselves Masters of this Subject, not to be contented with the Schemes they find here; but upon every Occasion to draw new ones of their own, in all the Variety of Circumstances they can think of. This will take up a little more Time at first; but in a little while they will find the vast Benefit of it, by the extensive Notions it will give them of the Nature of these Principles.
In the machine for a new use of gunpowder, which is described in the 'Acta Eruditorum' for the month of September, 1688, the first desideratum was, that the gunpowder fired in the bottom of the tube AA should fill the whole cavity with flame, so that the air might be entirely expelled from it, and the tube remain a perfect vacuum beneath the piston BB. But there it was mentioned, that the desired effect could not be sufficiently attained... But hitherto such attempts have been in vain; and always, after the flame of the gunpowder is extinguished, about a fifth part of the air remains in the tube AA.
We behold indeed, in the motions of the celestial bodies, some effects of [the attraction] that may be call'd more august or pompous. But methinks these little hyperbolas, form'd by a fluid between two glass planes, are not a-whit less fine and curious than the spacious ellipses describ'd by the planets, in the bright expanse of Heaven.