Top 15 John Napier Quotes

Any desired geometrical mean between two sines has for its Logarithm the corresponding arithmetical mean between the Logarithms of the sines.

And if any number of equals to a first sine be multiplied together producing a second, just so many equals to the Logarithm of the first added together produce the Logarithm of the second.

If a first sine be multiplied into a second producing a third, the Logarithm of the first added to the Logarithm of the second produces the Logarithm of the third. So in division, the Logarithm of the divisor subtracted from the Logarithm of the dividend leaves the Logarithm of the quotient.

From the Radical table completed in this way, you will find with great exactness the logarithms of all sines between radius and the sine 45 degrees; from the arc of 45 degrees doubled, you will find the logarithm of half radius; having obtained all these, you will find the other logarithms. Arrange all these results as described, and you will produce a Table, certainly the most excellent of all Mathematical tables, and prepared for the most important uses.

Whence a geometrically moving point approaching a fixed one has its velocities proportionate to its distances from the fixed one.

To decrease geometrically is this, that in equal times, first the whole quantity then each of its successive remainders is diminished, always by a like proportional part.

It is picked out from numbers progressing in continuous proportion. Of continuous progressions, an arithmetical is one which proceeds by equal intervals; a geometrical one which advances by unequal and proportionally increasing or decreasing intervals. Arithmetical progressions: 1, 2, 3, 4, 5, 6, 7, &c.; or 2, 4, 6, 8, 10, 12, 14, 16, &c, Geometrical progressions: 1, 2, 4, 8, 16, 32, 64, &c.; or 243, 81, 27, 9, 3, 1.

A Logarithmic Table is a small table by the use of which we can obtain a knowledge of all geometrical dimensions and motions in space, by a very easy calculation. It is deservedly called very small, because it does not exceed in size a table of sines; very easy, because by it all multiplications, divisions, and the more difficult extractions of roots are avoided; for by only a very few most easy additions, subtractions, and divisions by two, it measures quite generally all figures and motions.

But now, some of our countrymen in this island, well affected to these studies, and the more public good, procured a most learned mathematician to translate the same into our vulgar English tongue, who after he had finished it, sent a copy of it to me, to be seen and considered on by myself. I having most willingly and gladly done the same, find it to be most exact and precisely conformable to my mind and the original. Therefore it may please you who are inclined to these studies, to receive it from me and the translator, with as much good will as we recommend it unto you.—Fare thee well.

Seeing there is nothing, (right well beloved students of mathematics,) that is so troublesome to mathematical practice, nor that doth more molest and hinder calculations, that the multiplications, divisions, square and cubical extractions of great numbers, which besides the tedious expence of time, are for the most part subject to many slippery errors, I began, therefore, to consider in my mind, by what certain and ready art I might remove these hindrances. And having thought upon many things to this purpose, I found at length some excellent brief rules to be treated of perhaps hereafter: But amongst all, none more profitable than this, which together with the hard and tedious multiplications, divisions, and extractions of roots, doth also cast away even the very numbers themselves that are to be multiplied, divided, and resolved into roots, and putteth other numbers in their place which perform as much as they can do, only by addition and substraction, division by two, or division by three. Which secret invention being, (as all other good things are,) so much the better as it shall be the more common, I thought good heretofore, to set forth in Latin for the public use of mathematicians.

Conclusion. Then for conclusion, by these interpretative propositions, followeth foure thinges marvelous and notable. First, that the interpretation of every parte of the Revelation, is accessorie or consectarie to other: that is to say, it is so chained and linked together, that every mysterie opens other to the discoverie of the whole. Secondly, that the first halfe of the book is orderly, that is to say, it containeth in order of time the most notable accidents that concerneth Gods Church, from the time of Christs Baptisme successively to the latter day. Thirdly, that every historie prophecied, is limited or dated with his own nŭber of years. Fourthly and last of all, that whatsoever historie is more orderlie and summarlie, than plainly set downe in the first orderlie parte of the booke, the same is repeated, interpreted, or amplified in the last part of the booke: deviding the whole Revelation according to the table following, before we proceed to the principall matter.

So ends this demonstratiue resolution of all difficulties of the Revelation, first of all dates and times, and last of the principall termes and matters, as to the meaner termes and smaller matters, they are interpreted in the notes of the principall treatise.

36 Proposition. The 1260 years of the Antichrists universal raign over Christians, begins about the year of Christ 300. or 316. at the farthest.

35 Proposition. The Devils bondage a thousand yeares (cap. 20) is no waies els, but from stirring up of universall warres among nations.

34 Proposition. The thousand yeares that Sathan was bound (Revel. 20.) began in Anno Christi 300. or thereabout.