BLTC Press Titles

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Through the Looking Glass

Lewis Carroll

Novalis Including Hymns to the Night

Novalis, George MacDonald, Thomas Carlyle

Knowledge of Higher Worlds and its Attainment

Rudolf Steiner

Paradoxes of the Highest Science

Eliphas Levi

Geometrical lectures

by Isaac Barrow


ralibus, or as they were produced as firsts than be at the Trouble of reducing them into any other Form> which perhaps might have displeased. For when I resolved to publish, I could not bear the Pains of readding over again a great Part of these Things j either from my being tired with them, or not caring to undergo the Pains and Study in new modelling them : But I have done in this as weakly Mothers, who give up their Offspring to the Care of their Friends, either to Nurse and bring up, or abandon to the wide World. One of which (for I think my self bound to Name them) is Mr. Isaac Newton, my Collegue, a Man of great Learning and Sagacity, who revised my Copy and noted such Th'mgs as wanted CorreBion, and even gave me some of his own, which you will fee here and there interspersed with mine, not


•without their due Commendations,. The other is Mr. John Collins (who may be deservedly called theMerscnnas of our Nation, Born to promote this Science> both with his own Labours, and those os others. Who mth much Trouble took care of the Edition. I could also put several other Obstacles to your Expectations,or offer many other Excuses (tfiz. the Narrowness of my own Genius, the Want of Experiments, and Business interfering) did not I fear Cato the Seniors Jest, should be now thrown at me, Recte si Amphictyonum decreto constrictus hæc evulgas. Justice partly required a Preface of this Kind from me, and I was partly induced to it by the natural Love of a Parent for his own Offspring, that this Production might the more readily be excused, and in some Measure preserved from Censure. But if you


are too severe and will not admit of these Excuses, you may (for me) blame on.

AM now entring into a new Field, whether more pleafant or jpj fruitful, I cannot truly fay, buc " yielding a most copious Variety which consequently is agreeablejand as it comprehends,for the most Part, the Original of Mathematical Hypotheses, from whence Defin it ions are formed, and Properties flow, it must Neceflarily be very useful too. What I mean, is the Generation of Magnitudes, or the several Ways whereby the various Species of Magnitudes may be conceiv'dio be generated or p-oduced. Nor indeed is there any Magr:tude given, but what may be conceiv'd to be prce ced, and really is produced innumerable Ways; yet these may be brought under souas general Heads, at least such as have hitherto been used, of which the following occur to me at this Time; by local Motion; by the Intersections of Magnitudes; by determinate Distances from assigned Places in Quantity and Position ; by the drawing of Magnitudes into Magnitudes; and by the Applications of Magnitudes to Magnitudes; by the joining together of Magnitudes peculiarly disposed; by the Appofition or adding of Magnitudes to other Magnitudes, or by their Subdues ion from others; or lastly by organical Effeclion (deduced or contrived from any one of these.) Among these Ways, or any other whatever, of generating Magnitudes, the Primary and Chief is, that perform'd by local Motion, which all of them must in some Sort suppose, because without Motion, nothing can be generated or produced, and therefore this must first be considered. The following Axiom of Ari/Iotle concerning Motion is famous, dyvoxfAivift i ""?'• eujTtjg (juvj;ffe&j) dyvoeii&cu K. Tiw cputriv .. He that is ignorant of Motion, must necessarily know nothing of Nature ; and consequently \y nothing can be done without it in Physicks. Nor is this asserted without Rcafen, because that in Nature, (so far at least as our Understandings can trace, or Experience shew) every Thing created is produe'd by Motion, or certainly not without Motion. Accordingly Philosophers argue with great Subtilty on the Nature of Motion, its true Definition; the Causes thereof, and the several Differences, all which are of very little Concern to Mathematicians. 'Tis enough that these take for granted what is allow'd by common Sense, and proved by obvious Experience; and first, this general Principle, viz. That any Magnitude (among which I esteem even a Point, as the least of all Magnitudes, and likewise an Infinite or greatest Magnitude, between which two, all intermediate finite Magnitudes are plac'd) is moveable; that is, in what Manner soever we behold it, the fame may be made to change its Place continually, according to prescribed Differences, viz. with a strait or circular Motion; equally Swift, or in any manner more accelerated, or retarded : I fay, Mathematicians assume at Pleasure any Motions of this Kind as evidently possible, in order to find out and demonstrate what follows from thence. We therefore shall treat of these Differences of Motion, their Number and Qualities. What Mathematicians Chiefly consider in Motion, is, the

B 2 Mode Made of Lation or Manner of bearing, and the Quantity os the motive Force: And first, the Mode of Lation, according to which, some Motions are Progressive, others Circumrotatory, and others made up of both these •, then, the Quantity of the motive Force, according to which, One is declar'd swifter, flower, or equally swift in Respect of another ; or faid to be equal in itself, accelerated or retarded. From these Springs the Differences of Motions flow, the latter whereof we shall treat first, because it contains some foreign Things which I would first remove, in order that those remaining may afterwards be more perspicuous. But because the Quantity of motive Force cannot be known withoutTime, we must fay something concerning its Nature. Now pray tell me what Time is? You know the very trite Saying of St. Austin, If no one ajks me, I know ; but if any Person fiould require me to tell him, I cannot. But because Mathematicians frequently make use of Time, they ought to have a distinct Idea of the meaning of that Word, otherwise they are Quacks. My Auditors may therefore, on this Occasion, very justly require an Answer from me, which I shall now give, and that in the plainest and least ambiguous Expressions, avoiding as much as possible all trifling and empty Words. Time, (to speak abstractedly) is the continuance of any Thing in its

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