[n] Although the Quadrature of the Circle, hath in former Ages exercis’d some of the greatest mathematical Wits; yet nothing has been done in that Way so considerable, as in, and since the Middle of the last Century; when in the Year 1657, those very ingenious and great Men, Mr William Neile, and my Lord Brounker, and Sir Christopher Wren afterwards, in the same Year, geometrically demonstrated the Equality of some Curves to a strait Line. Soon after which, others at Home, and Abroad, did the like in other Curves. And not long afterwards, this was brought under an analytical Calculus: The first Specimen whereof, that was ever publish’d. Mr. Mercator gave in 1688, in a Demonstration of my Lord Brounker’s Quadrature of the Hyperbola, by Dr Wallis’s Reduction of a Fraction, into an infinite Series by Division. But the penetrating Genius of Sir Isaac Newton, had discover’d a Way of attaining the Quantity of all quadrible Curves analytically, by his Method of Fluxions, some Time before the Year 1668, as I find very probable from an historical Account, in a long Letter of Mr. Collins, written in his own Hand, and sent to Richard Townley, Esq; of Lancashire, whose Papers are in my Hands. In that Letter, Mr. Collins saith, That in September 1668, Mr. Mercator publish’d his Logarithmotechnia, one of which he soon sent to Dr. Barrow, who thereupon sent him up some Papers of Mr. Newton’s, [now Sir Isaac;] by which, and former Communications made thereof by the Author, to the Doctor; it appears that the said Method was invented some Years before, by the said Mr. Newton, and generally apply’d. And then he goes on to give some Account of the Method; what it performs in the Circle, &c. what Mr. Gregory had done in that kind, who intended to publish somewhat in Latin about it, but would not anticipate Mr. Newton, the first Inventor thereof; with much more of this Nature. The Design, I find, of that indefatigable Promoter of Mathematicks, Mr. Collins, was to acquaint Mr. Townley, in his Letter, with what had been done; and to get the Assistance of that ingenious Gentleman, towards the compleating a Body of Algebra.
[o] I do not mention here the perpetual Motion, which hath exercis’d the mechanical Wits for many Ages; because it is a Thing impossible, if not a Contradiction: As the before-commended Dr. Clarke asserts in Rohaul. Phys. p. 133.
[p] Grew’s Cosmol. Sacr. l. 1. c. 5. §. 25.
[q] Nemo igitur vir magnus sine aliquo afflatu divino unquam fuit. Cic. de Nat. Deor. l. 2. c. 66.
[r] Ægypt, and some of the eastern Nations, are celebrated for their Skill in polite Literature: both in Scripture and profane story: Job was of those Parts; so were the Σοφοὶ and Μάγοι, the Brachmans and Gymnosophists. Moses and Daniel had their Education in these Parts: And Pythagoras, Democritus, and others, travell’d into these Parts for the Sake of their Learning.
[] As we are not to accuse any falsly; so far be it from me to detract from so great a Man as Monsieur Cartes was: Whose Principles, although many have perverted to atheistical Purposes, and whose Notions have, some of them, but an ill Aspect; yet I am unwilling to believe he was an Atheist; since in his Principia Philosiphiæ, and other of his Works, he vindicates himself from this Charge; and frequently shews seemingly a great Respect for Religion: Besides, That many of his suspicious Opinions are capable of a favourable Interpretation, which will make them appear in a better Form: Thus when he discardeth final Causes from his Philosophy, it is not a Denial of them; but only excluding the Consideration of them, for the Sake of free philosophising; it being the Business of a Divine, rather than a Philosopher, to treat of them.
[t] For Ages of Learning and Ignorance, we may compare the present, and some of the Ages before the Reformation. The last Century, and the few Years of this, have had the Happiness to be able to vie with any Age for the Number of learned Men of all Professions, and the Improvement made in all Arts and Sciences; too many, and too well known to need a Specification.
But for Ignorance, we may take the ninth Age, and so down to the Reformation; even as low as Queen Elizabeth, although Learning began to flourish; yet we may guess how Matters stood, even among the Clergy, by her 53 Injunct. Nᵒ. 1559, Such as are but mean Readers, shall peruse over before, once or twice, the Chapters and Homilies, to the Intent they may read to the better Understanding of the People, the more Encouragement of Godliness. Spar. Collect. p. 82. But this is nothing, in comparison to the Ages before, when the Monk said, Græcum non est legi; or as Espencæus more elegantly hath it, Gracè nôsse suspectum, Hebraicè prope Hæreticum. Which Suspicion, (said the learned Hakewill,) Rhemigius surely was not guilty of, in commenting upon diffamatus, 1 Thes. i. 8. who saith, that St. Paul somewhat improperly put that for divulgatus, not being aware that St. Paul wrote in Greek, and not in Latin. Nay, so great was their Ignorance, not only of Greek, but of Latin too, that a Priest baptiz’d in nomine Patria, & Filia, & Spiritua sancta. Another suing his Parishioners for not paving his Church, prov’d it from Jer. xvii. 18. Paveant illi, non paveam ego. Some Divines in Erasmus’s Time, undertook to prove Hereticks ought to be burnt, because the Apostle said, Hæreticum devita. Two Fryars disputing about a Plurality of Worlds, one prov’d it from Annon decem sunt facti mundi? The other reply’d, Sed ubi sunt novem? And notwithstanding their Service was read in Latin, yet so little was that understood, that an old Priest in Hen. VIII. read Mumpsimus Domine, for Sumpsimus: And being admonish’d of it, he said, he had done so for thirty Years, and would not leave his old Mumpsimus for their new Sumpsimus. Vid. Hakew. Apol. L. 3. c. 7. Sect. 2.
[] There is (it seems) in Wits and Arts, as in all Things beside, a kind of circular Progress: They have their Birth, their Growth, their Flourishing, their Failing, their Fading; and within a while after, their Resurrection, and Reflourishing again. The Arts flourished for a long Time among the Persians, the Chaldæans, the Ægyptians.——But afterwards the Grecians got the start of them, and are now become as barbarous themselves, as formerly they esteemed all besides themselves to be. About the Birth of Christ, Learning began to flourish in Italy, and spread all over Christendom; till the Goths, Huns, and Vandals ransacked the Libraries, and defaced almost all the Monuments of Antiquity: so that the Lamp of Learning seemed to be put out for near the Space of 1000 Years, till the first Mansor, king of Africa and Spain, raised up, and spurred forward the Arabian Wits, by great Rewards and Encouragement. Afterwards Petrarch opened such Libraries as were undemolished. He was seconded by Boccace, and John of Ravenna, and soon after by Aretine, Philelphus, Valla, &c. And those were followed by Æneas Sylvius, Angelus Politianus, Hermolaus Barbarus, Marsilius Ficinus, and Joh. Picus, of Mirandula. These were backed by Rud. Agricola, Reucline, Melancthon, Joach. Camerarius, Wolphlazius, Beat. Rhenanus, Almaines; By Erasmus of Rotterdam; Vives a Spaniard; Bembus, Sadoletus, Eugubinus, Italians: Turnebus, Muretus, Ramus, Pithæus, Budæus, Amiot, Scaliger, Frenchmen; Sir Tho. More and Linaker, Englishmen. And about this Time, even those Northern Nations yielded their great Men; Denmark yielded Olaus Magnus, Holster, Tycho Brahe, and Hemingius; and Poland, Hosius, Frixius, and Crumerus. But to name the Worthies that followed these, down to the present Time, would be endless, and next to impossible. See therefore Hakewill’s Apolog. L. 3. c. 6. §. 2.
[w] Dr. Gilbert, the most learned and accurate Writer on the Magnet, shews, that its Attractive Virtue was known as early as Plato and Aristotle: but its Direction was a Discovery of later Ages. He saith, Superiori ævo 300 aut 400 labentibus annis, Motus Magneticus in Boream & Austrum repertus, aut ab hominibus rursus recognitus fuit. De Mag. L. 1. c. 1. But who the happy Inventer of this lucky Discovery was, is not known. There is some, not inconsiderable, Reason, to think our famous Country-man, Rog. Bacon, either discovered, or at least knew of it. But for its Use in Navigation, Dr. Gilbert saith, in regno Neapolitano Melphitani omnium primi (utì ferunt) pyxidem instruebant nauticam.——edocti à cive quodam Jol. Goia A. D. 1300. ibid. If the Reader hath a mind to see the Arguments for the Invention, being as old as Solomon’s or Plautus’s Time, or of much younger Date, he may consult Hakewill. ib. c. 10. §. 4. or Purchas Pilgr. L. 1. c. 1. §. 1.