John Napier

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

"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."

"In my tender years and bairn-age, at schools, having on the one part contracted a loving familiaritie with a certain gentleman a papist, and on the other part being attentive to the sermons of that worthy man of God, Maister Christopher Goodman, teaching upon the Apocalyps, I was moved in admiration against the blindness of papists that could not most evidentlie see their seven hilled Citie of Rome, painted out there so lively by Saint John, as the Mother of all Spiritual Whoredome: that not onlie bursted I oute in continuall reasoning against my said familiar, but also from thence forth I determined with myself by the assistance of God's spirit to employ my study and diligence to search out the remanent mysteries of that holy booke (as to this houre praised be the Lord I have bin doing at all such times as convenientlie I might have occasion) &c."

"Here then (belove reader) thou hast this work devided into two treatises, the first is the said introduction and reasoning, for investigation of the true sense of every cheife Theological tearme and date contained in the Revelation, whereby, not onely is it opened, explained and interpreted, but also that same explanation and interpretation is proved, confirmed and demonstrated, by evidente proofe and coherence of scriptures, agreeable with the event of histories. The seconde is, the principall treatise, in which the whole Apocalyps, Chapter by chapter, Verse by verse, and Sentence by sentence, is both Paraphrastically expounded and Historically applyed. ...And because this whole work of Revelation concerneth most the discoverie of the Antichristian and Papisticall kingdome, I have therefore (for removing of all suspition) in al histories and prophane matters, taken my authorities and cited my places either out of Ethnick auctors, or then papistical writers, whose testimonies by no reason can be refuted against themselves. But in matters of divinitie, doctrine & interpretation of mysteries (leaving all opinions of men) I take me onely to the interpretation and discoverie thereof, by coherence of scripture, and godly reasons following thereupon; which also not only no Papist, but even no Christian may justly refuse. And forasmuch as our scripturs herein are of two fortes, the one our ordinary text, the other extraordinary citations; In our ordinary text, I follow not altogether the vulgar English translation, but the best learned in the Greek tong, so that (for satisfying the Papists) I differ nothing from their vulgar text of S. Jerome, as they cal it, except is such places, where I prove by good reasons, that hee differeth from the Original Greek. In the extraordinary texts of other scriptures cited by me, I followe ever Jeromes latine translation, where any controverse stands betwixt us and the Papists, and that moveth me in divers places to insert his very latine text, for their cause, with the just English thereof, for supply of the unlearned."

"The First Proposition. In propheticall dates of daies, weekes, moneths, and yeares, everie common propheticall day is taken for a yeare."

"2. Proposition. The Seven Trumpets of the 8. and 9. chapters, and the Seven Vials of the 16. Chapter, are all one."

"3. Proposition. The Star and locusts of the fift trumpet, are not the greate Antichrist and his Cleargie, but the Dominator of the Turkes and his armie, who began their dominion in anno Christi 1051."

"4 Proposition. The kinges of the East, or four Angels, specified in the sixt trumpet, or sixt vial. Cap. 9. & 16. are the four nations, Mahometanes beyond and about Euphrates, who began their empire by Ottoman, in the yeare of Christ, 1296. or thereabout."

"5 Proposition. The space of the fift trumpet or vial containeth 245. years, and so much also, every one of the rest of the trumpets or vials doe containe."

"6 Proposition. The first Trumpet or Viall began at the Jubelee, in anno Christi 71."

"7 Proposition. The last of the Seven Seales, and first of the Seven Trumpets or Vials, begin both at once, in An. 71."

"8 Proposition. The first Seal beginneth to be opened in Anno Christi 29. compleat."

"9 Proposition. Everie Seale must containe the Space of Seven yeares."

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

"11 Proposition. The Seven Thunders, whose voices are commanded to bee sealed, and not written (cap.10.4.) are the Seven Angels, specified cap.14. vers. 6.8.9.14.15.17.18."

"12 Proposition. The first of the Seven thunders, and the seventh and last Trumpet or Viall, begin both at once in An.1541."

"13 Proposition. Every one of the first three thundering Angels containeth a Jubelee, and then the last foure al at once compleateth the day of judgement."

"14 Proposition. The day of Gods judgement appears to fall betwixt the yeares of Christ, 1688. and 1700."

"15 Proposition. The 42. moneths, a thousand two hundred and three score propheticall daies, three greate daies and a halfe, and a time, times, and a halfe a time mentioned in Daniel, & in the Revelation, are all one date."

"16 Proposition. The 42. moneths, 1260 propheticall daies, three great daies and a halfe: And a time, times and halfe a time, signifieth everie one of them, 1260 Julliane yeares."

"17 Proposition. The description of the throne of God in the fourth chapter, is not the description of the majestie of God in heaven, but of his true religion, wherein he is authorised and sits in the throne among his holy elect on earth."

"18 Proposition. The 24. Elders, are the 24 books of the old Testament, and (metonymicè) all the true professors thereof."

"19 Proposition. The foure beasts are the foure Evangelles with all the true writers and professors thereof."

"20 Proposition. Gods Temple, although in heaven, is also taken for his holy Church among his heavenly Elect upon the earth, and metonymicè for the whole contents thereof."

"21 Proposition. The two witnesses mentioned (Reve.11) are the two Testamĕts, and (metonymicè) the whole true professors thereof."

"22 Proposition. The Woman clad with the Sunne (chap. 12) is the true Church of God."

"23 Proposition. The Whoore, who in the Revelation is Stiled Spirituall Babylon, is not reallie Babylon, but the verie present Citie of Rome."

"24 Proposition. The great ten-horned beast, is the whole bodie of the Latine Empire, whereof the Antichrist is a part."

"25 Proposition. The two horned Beast, is the Antichrist and his kingdome, it alone."

"26 Proposition. The Pope is that only Antichrist, prophecied of, in particular."

"27 Proposition. The image, marke, name, and number of the beast: are of the first great Romane beast, and whole Latine impyre universallie, and not of the second beaste, or Antichrist alone in particular."

"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."

"29 Proposition. The name of the beast expressed by the number 666. (cap. 13.) is the name λαγεινος onely."

"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 markes."

"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."

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

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

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

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

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

"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."

"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."

"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."

"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."

"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."

"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."

"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."