System of

V.

The Copernican System easily accounts for all the Celestial Phenomena, Ticho Brahe and tho' Observation and Argument are equally favourable to it, yet TichoBrabe an eminent Philofopher of that Age refused his assent to the Evidence of these Discoveries, whether deluded by an ill-formed Experiment, (b) or carried away by the Vanity of making a new System, he composed one which steers a middle Course between those of Ptolomy and Copernicus; he supposed the Earth to be at rest and the other Planets which move round the Sun, to revolve with him round the Earth, in the Space of 24 Hours; thus retaining the most exceptionable Part of Ptolomy's Syftem, viz. the inconceivable Rapidity with which the primum Mobile is supposed to revolve, from whence we may learn into what dangerous Errors the mifapplication of Genius may lead us.

tive to the

The Disco- Tho' Tycho erred in the Manner he made the Celestial Bodies move, veries rela- yet he contributed very much to the Progress of the Discoveries relative to System of the System of the World, by the Accuracy and long Series of his Observathe World, tions. He determined the Position of a vast Number of Stars to a Degree of improved exactness unknown before; he discovered the Refraction of the Atmosphere, by Tycho.

by which the Celestial Phenomena are so much influenced; he was the first who proved from the Parallax of the Comets, that they afcend above the Moon; he was the first who observed what is called the Moon's variation; and in fine, it is from his Obfervations on the Motions of the Planets, that Kepler who resided with him, near Prague, during the last Years of his Life, deduced his admirable Theory of the Motions of the Heavenly Bodies.

VI.

Copernicus undoubtedly rendered important Services to Human Reason remained to by re-establishing the true System of the World: It was already a great ed after Co- point gained that Human Vanity condescended to place the Earthin the Numpernicus. ber of the simple Planets; but much still remained to be discovered: neither the Forms of the Planetary Orbits, nor the Laws by which their Motions. are regulated, were known; for these important Discoveries we are in debted to Kepler.

of Kepler.

This eminent Philosopher found out, that the Notion which generally prevailed before his time, that the Planets revolved in circular Orbits, was er- Discoveries roneous; and he discovered, by the means of Ticho's Observations, that the el pticity the Planets move in Ellipses, the Sun residing in one of the Foci: and that of the orbits. they move over the different Parts of their Orbit, with different Velocities, so the proportionality of that the Area described by a Planet, that is, the Space included between the the areas and straight lines drawn from the Sun to any two Places of the Planet, is always the times. proportional to the time which the Planet employs to pass from one to the

other.

Relation

Some years afterwards, comparing the Times of the Revolutions of the different Planets about the Sun, with their different Distances from him, he which fubfound that the Planets which are placed the farthest from the Sun to move sists between flowest, and examining whether this Proportion was that of their Distances, the periodic he discovered after many Trials, in the Year 1618, that the Times of the distantheir Revolutions were as the Square Roots of the Cubes of their mean ces. Distances from the Sun.

VII.

Kepler not only discovered these two Laws, which retain his Name, and which regulate the Motions of all the Planets, and the Curve they describe, but had also some Notion of the Force which makes them describe this Curve; in the Preface to his Commentaries on the Planet Mars, we discover the first Hints of the attractive Power; he even goes so far as to say, that the Flux and Reflux of the Sea, arifes from the gravity of the Waters towards the Moon: but he did not deduce from this Principle what might be expected from his Genius and indefatigable Industry. For in his Epitome of Astronomy(c) he proposes a physical Account of the planetary Motions from quite different Principles; and in this fame Book of the Planet Mars, he supposes in the Planets a friendly and a hoftile Hemisphere, that the Sun attracts the one and repels the other, the friendly Hemisphere being turned to the Sun in the Planets descent to its Perhihelium, and the Hostile in its Recess.

VIII..

The Attraction of the Celestial Bodies was suggested much more clearly by M. Hook, in his Treatise on the Motion of the Earth, printed in the Year 1674, twelve Years before the Principia appeared. These are his Words, Page 27, "I shall explain hereafter a System of the World, different in ma" ny Particulars from any yet known, answering in all Things to the com" mon Rules of Mechanical Motions. This depends on the three following "Suppositions.

times and

Singular a" ift That all celestial Bodies, whatever, have an Attraction, or gravitating necdote con- ،، Power towards their own Centers, whereby they attract, not only their

cerning at

traction.

own Parts and keep them from flying from them, as we may observe the "Earth to do, but that they do also attract all the other celestial Bodies that are within the Sphere of their Activity; and confequently not only the "Sun and the Moon have an Influence upon the Body and Motion of the Earth, and the Earth on the Sun and Moon, but also, that Mercury, Venus, Mars, Jupiter aud Saturn, by their attractive Powers, have a confi"derable Influence upon the Motion of the Earth, as in the same Manner "the corresponding attractive Power of the Earth hath a confiderable influ "ence upon the Motion of the Planets."

"2d That all Bodies whatever that are put into a direct and simple Motion, " will fo continue to move forward in a streight Line, till they are by fome " other effectual Power deflected and turned into a Motion, defcribing a Cir"cle, an Ellipse, or fome other more compounded Curve Line."

66

3d That these attractive Powers are so much the more powerful in operating, by how much the nearer the Body wrought upon is to their own: " Center."

"These several Degrees I have not yet experimentally verified, but it is "a Notion which if fully profecuted as it ought to be, will mightily affift the "Aftronomer to reduce all the celestial Motions to a certain Rule, which I "doubt will never be done true without it. He that understands the Na-. "ture of the circular Pendulum and circular Motion, will easily understand "the whole Ground of this Principle, and know where to find Directions "in Nature for the true stating thereof. This I only hint at present to fuch " as have a Capacity and Opportunity of profecuting this Enquiry, &c."

IX.

We are not to imagine, that this Hint thrown out casually by Hook; detracts from the Glory of Newton, who even took Care to make Mention of it in his Book de Systemate mundi (d). the Example of Hook and Kepler makes us perceive the wide Difference between having a Notion of the Truth, and being able to establish it by irrefragable Demonftration; it also shews us how little the greatest Sagacity can penetrate into the Laws and Conftitution of Nature, without the Aid and Direction of Geometry..

X.

Kepler, who made such important Discoveries, whilst he followed this untions of Keperring Guide, affords us a convincing Proof of the Errors into which the brightest Genius may be seduced, by indulging the pleasing Vanity of inventing Systems; who could believe, for Instance, that fuch a Man could

adopt the wild Fancies and whimsical Reveries of the Pythagoreans, concerning Numbers: yet he thought that the Number and Interval of the primary Planets bore some Relation to the five regular Solids of Elementary Geómetry (e), imagining that a Cube inscribed in the Sphere of Saturn would touch the Orb of Jupiter with its fix Planes, and that the other four regular Solids, in like Manner, fitted the Intervals that are betwixt the Spheres of the other Planets: afterwards on discovering that this Hypothesis did not square with the Distances of the Planets, he fancied that the celestial Motions are performed in Proportions corresponding with those, according to which a Cord is divided in order to produce the Tones which compose the Octave in Music (f);

Kepler having fent to Ticho a Copy of the Work, in which he attempted to establish those Reveries. Ticho recommended to him, in his An- Wife coun fwer(g), to relinquish all Speculations deduced from first Principles, all rea- fel of Ticho soning a Priori, and rather study to establish his Researches on the fure and firm Ground of Observation.

to Kepler.

notion of

The great Hugbens himself (h) believed that the fourth Satellite of Saturn, Whimsical which retains his Name, making up with our Moon and the four Satellites of Hughens. Jupiter fix fecundary Planets, the Number of the Planets was complete, and it was labour loft to attempt to discover any more, because the principle Planets are alfo fix in Number, and the Number Six is a perfect Number, as being equal to the Sum of its aliquot Parts, 1, 2 and 3.

XL

It was by never deviating from the most profound Geometry, that Newton discovered the Proportion in which Gravity acts, and that in his Hands the Principle of which Kepler and Hook had only fome faint Notion, became the Source of the most admirable and unhoped for Discoveries.

Advantages

over Kepler

One of the Causes which prevented Kepler from applying the Principles of Newton of Attraction to explain the Phænomena of Nature with Success, was his in his time, Ignorance of the true Laws of Motion. Newton had the Advantage over the theory of Kepler of profiting of the Laws of Motion, established by Hughens, which motion was he has carried to so great a Height in his Mathematical Principles of Natu-derstood. ral Philofophy.

XII.

better un

The Mathematical Principles of Natural Philosophy consist of three Analysis of Books, besides the Definitions, the Laws of Motion and their Corollaries; the first Book is compofed of fourteen Sections, the second contains nine,

and the third, the Application of the two first to the Explication of the Phænomena of the System of the World.

XIII.

The Principia commence with eight Definitions; Newton shews in the Definitions. two first how the Quantity of Matter and the Quantity of Motion should be measured; he defines in the third, the Vis intertiæ, or refifting Force, which all Matter is endued with; he explains in the fourth what is to be understood by active Force; he defines in the fifth the centripetal Force, and lays down in the fixth, seventh and eighth the Manner of measuring its abfolute Quantity,. its motrix Quantity, and its accelarative Quantity; afterwards he establishes the three following Laws of Motion.

XIV.

Laws of mo ist. That a Body always perseveres of itself, in its State of Rest, or of

tion.

First book, the ist secti

uniform Motion in a straight Line.

2d. That the change of Motion, is proportional to the Force impressed, and is produced in the straight Line in which that Force acts.

3d. That Action and Reaction are always equal with opposite Direaions.

XV.

Newton having explained those Laws, and deduced from them several on contains Corollaries, commences his first Book with eleven Lemmas, which comthe princi- pose the first Section, he unfolds in those eleven Lemmas his Method of ples of infiPrime and ultimate Ratios; this Method is the Foundation of infinitessimal nitessimal Geometry, and by its Assistance, this Geometry is rendered as certain as that of the Ancients.

geometry

the other 13

The thirteen other Sections of the first Book of the Principia, are employgeneral pro-ed in demonstrating general Propositions on the Motion of Bodies, Abstracpositions on the motion ting from the Species of these Bodies and of the Medium in which they

of bodies. move.

It is in this first Book that Newton unfolds all his Theory of the gravitation of the celestial Bodies, but does not confine himself to examine the Questions relative to it; he has rendered his Solutions general, and has given a great Number of Applications of those Solutions.

XVI.

In the second Book, Newton treats of the Motion of Bodies in resisting

Second book
it treats of
the motionof Mediums.

bodies in re- This second Book which contains a very profound Theory of Fluids, and fifting me of the Motion of Bodies which are immersed in them, seems to have been intended to destined to over throw the System of Vortices, though it is only in the Scholioverthrow um of the last Propofition, that Newton openly attacks Descartes, and proves of Defcartes that the celestial Motions are not produced by Vortices.