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 togeth… - John Napier

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.

10 Proposition. The last Trumpet and Viall beginneth anno Christe 1541 and should end in anno Christi 1786.

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.