Progress of the Discoveries relative to the Syftem of the World.

I.

First views

TH HE first Views which Philofophers had of the Syftem of the World, of Philofowere no better than thofe of the Vulgar, being the immediate Suggestions phers of the Syftem of Sense; but they corrected them; thus the first System supposed the of the World Earth to be an extended Plane, and the Center round which the Heavenly Bodies revolved.

II.

Discoveries

The Babylonians from examining the Appearances of Sence were the of the Babyfirst who discovered the Earth to be round, and the Sun to be the Cen- lonians, and ter of the Universe (a) in these Points they were followed by Pythagoras and of Pythage

his School.

III.

ras.

The true Syftem of the World being difcovered, it may appear furprizing that the Notion of the Earth's being the Center of the Celestial Motions fhould generally prevail: for tho' on a fuperficial Survey it feems to be recommended by its Simplicity, and to fquare exactly with the Ap-Efforts that pearances of Sence, yet on Examination it is found entirely infufficient to have been explain the Phenomena, and to account for the Heavenly Motions: This made to constrained Ptolemy and his followers to incumber and embarrass the Hea- the Earth vens with a Number of Circles and Epicycles equally arduous to be con- to be at rest. ceived and employed, for nothing fo difficult as to fubftitute Error in the Syftem of room of Truth.

Probably the Influence of Ariftotle's Authority, whofe Writings in Ptolomy's Time were held in the highest Esteem, and confidered as the Standard of Truth, lead this Philofopher into Error: But why did not Ariftotle declare in favour of the true Syftem, which he knew, fince he endeavoured to overthrow it: this Reflection is fufficiently mortifying to the Pride of the Human Understanding, whatever was the Caufe, thus much is certain, that the Ptolomaic Syftem generally prevailed to the Time of Copernicus.

IV.

maintain

Ptolomy.

tem of Py

This great Man revived the ancient Syftem of the Babylonians, and of Copernicus] Pythagoras which he confirmed by fo many Arguments and Discoveries revives the that Error could no longer maintain its Ground against the Fvidence of ancient SyfDemonftration; thus the Sun was reinftated by Copernicus in the Center of thagoras. the World, or to speak more exactly, in the Center of our Planetary System.

(a) NEWTON in his Book DE SYSTEMATE MUNDI attributes this Opinion to Numa Pompilius, and lays, (Page 1.) it was to represent the Sun in the Center of the Celestial Orbits that Numa caufed a round Temple to be built in honour of Vesta, the Goddess of Fire in the Middle of which a perpetual Fire was preserved.

V.

The Copernican System easily accounts for all the Celestial Phenomena, Syftem of Ticho Brahe and tho' Obfervation and Argument are equally favourable to it, yet TichoBrabe an eminent Philofopher of that Age refufed his affent to the Evidence of these Discoveries, whether deluded by an ill-formed Experiment, (b) or carried away by the Vanity of making a new Syftem, he compofed one which steers a middle Course between thofe of Ptolomy and Copernicus; he fuppofed the Earth to be at reft 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 fuppofed to revolve, from whence we may learn into what dangerous Errors the mifapplication of Genius may lead us.

The Difco

tive to the

Tho' Tycho erred in the Manner he made the Celestial Bodies move, veries rela- yet he contributed very much to the Progrefs of the Discoveries relative to Syftem of the Syftem of the World, by the Accuracy and long Series of his Obfervathe World, tions. He determined the Pofition of a vaft Number of Stars to a Degree of improved exactnefs unknown before; he discovered the Refraction of the Atmosphere, by Tycho. by which the Celestial Phenomena are fo much influenced; he was the firit 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 refided with him, near Prague, during the last Years of his Life, deduced his admirable Theory of the Motions of the Heavenly Bodies.

be discover

VI.

How much Copernicus undoubtedly rendered important Services to Human Reafon remained to by re-establishing the true Syftem of the World: It was already a great ed after Co-point gained that Human Vanity condefcended to place the Earth in the Number of the fimple Planets; but much still remained to be difcovered: neither the Forms of the Planetary Orbits, nor the Laws by which their Motions. are regulated, were known; for these important Discoveries we are indebted to Kepler.

pernicus.

(b) It was objected to Copernicus, that the Motion of the Earth would produce Effects which did not take Place; that, for Example, if the Earth moved, a Stone dropp'd from the Top of a Tower, ought not to fall at the Foot of it, because the Earth moved during the Time of the Stone's defcent, that notwithstanding it falls at the Foot of the Tower. COPERNICUS replied, that the Situation of the Earth with refpect to Bodies that fall on its Surface was the fame as that of a Ship in Motion, with respect to Bodies that are made to fall in it; he afferted, that a Stone let fall from the Top of the Maft of a Vessel in Motion, would fall at the Foot of it. This Experiment which is now inconteftible was then ill-made, and was the Cante or the Pretext which made Ticho refufe his affent to the Discoveries of Copernicus.

the proper

This eminent Philofopher found out, that the Notion which generally pre- Discoveries vailed before his time, that the Planets revolved in circular Orbits, was er- of Kepler Toneous; and he discovered, by the means of Ticho's Obfervations, that the el pticity the Planets move in Ellipfes, the Sun refiding in one of the Foci: and that of the orbits. they move over the different Parts of their Orbit, with different Velocities, fo tionality of that the Area defcribed by a Planet, that is, the Space included between the the areas and ftraight 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 pafs from one to the other.

Some years afterwards, comparing the Times of the Revolutions of the Relation different Planets about the Sun, with their different Distances from him, he which fubfound that the Planets which are placed the fartheft from the Sun to move fifts between the periodic flowest, and examining whether this Proportion was that of their Distances, and he discovered after many Trials, in the Year 1618, that the Times of the diftantheir 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 defcribe, but had alfo fome Notion of the Force which makes them defcribe this Curve; in the Preface to his Commentaries on the Planet Mars, we discover the first Hints of the attractive Power; he even goes fo far as to fay, 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 Aftronomy(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 Hoftile in its Recefs.

VIII..

The Attraction of the Celestial Bodies was fuggefted much more clearly by M. Hook, in his Treatife on the Motion of the Earth, printed in the Year 1674, twelve Years before the Principia appeared. These are bis Words, Page 27, "I fhall explain hereafter a Syftem of the World, different in many Particulars from any yet known, answering in all Things to the common Rules of Mechanical Motions. This depends on the three following Suppofitions."

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(c) See Gregory, Book 1, Page 69.

cerning attraction.

Singular a-6 ft That all celeftial Bodies, whatever, have an Attraction, or gravitating necdote con- Power towards their own Centers, whereby they attract, not only their "own Parts and keep them from flying from them, as we may observe the "Earth to do, but that they do alfo 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 fame Manner "the correfponding attractive Power of the Earth hath a confiderable influ66 ence upon the Motion of the Planets."

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

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3d That these attractive Powers are so much the more powerful in ope" rating, 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 afsist 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 eafily understand: "the whole Ground of this Principle, and know where to find Directions "in Nature for the true ftating 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 cafually by Hook, detracts from the Glory of Newton, who even took Care to make Mention of it in his Book de Syftemate 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 Demonstration; it alfo fhews 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 fuch important Discoveries, whilft he followed this unStrange notions of Keperring Guide, affords us a convincing Proof of the Errors into which the brightest Genius may be feduced, by indulging the pleasing Vanity of inventing Systems; who could believe, for Inftance, that fuch a Man could

ler.

page. 3 Édition of 1738

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 fome Relation to the five regular Solids of Elementary Geometry (e), imagining that a Cube infcribed 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 difcovering that this Hypothefis did not fquare with the Distances of the Planets, he fancied that the celestial Motions are performed in Proportions correfponding with thofe, according to which a Cord is divided in order to produce the Tones which compofe the Octave in Mufic (f);

to Kepler.

Kepler having fent to Ticho a Copy of the Work, in which he attempted to establish thofe Reveries. Ticho recommended to him, in his An- Wife counfwer(g), to relinquifh all Speculations deduced from first Principles, all rea- fel of Tiche foning a Priori, and rather study to establish his Refearches on the fure and firm Ground of Obfervation. The great Hugbens himself (h) believed that the fourth Satellite of Saturn, Whimfical which retains his Name, making up with our Moon and the four Satellites of 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 also fix in Number, and the Number Six is a perfect Ñumber, as being equal to the Sum of its aliquot Parts, 1, 2 and 3.

XI.

It was by never deviating from the most profound Geometry, that Newten 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 Difcoveries..

notion of

Hughens.

One of the Caufes which prevented Kepler from applying the Principles over Kepler Advantages of Newton of Attraction to explain the Phænomena of Nature with Succefs, 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 fo great a Height in his Mathematical Principles of Natu- derstood. ral Philosophy.

XII.

better 12

The Mathematical Principles of Natural Philofophy confift of three Analysis of Books, befides the Definitions, the Laws of Motion and their Corollaries; the principia the first Book is compofed of fourteen Sections, the fecond contains nine,

(e) Myfterium Cofmographicum.

(f). Myfterium Cofmographicum.

(g) Uti fufpenfis speculationibus a priori defcendentibus animum potius ad obfervationes quas fimul offerebat confiderandas adjicerem (it is Kepler who speaks) notæ in fecundam: editionem myfterii cosmographici