John Napier

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 …

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 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.

for the public use of mathematicians.

so much the better as it shall be the more common, I thought good heretofore, to set forth

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

doth also cast away even the very numbers themselves

which together with the hard and tedious

I found at length some excellent brief rules

to consider in my mind, by what certain and ready art I might remove these hindrances. And

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

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 …

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.

33 Proposition. The armies of Gog and Magog (cap. 20) are all one with the armies of the sixt Trumpet and sixt Viall.

32 Proposition. Gog is the Pope, and Magog is the Turkes and Mahometanes.

31 Proposition. The visible marks of the Beast, are the abused characters, of λρς and crosses of all kindes, taken out of the number of the first beasts name.

30 Proposition. The marke of the Romane beast, is that invisible profession of servitude and obedience, that his subjects hath professed to his Empire, since the first beginning thereof, noted afterward by the Pope, with divers visible …

28 Proposition. The image of the Beast, is these degenerate Princes, that in name onely were called Roman Emporours, and were neither Romans of blood, nor Emperours of Magnanimitie.