



PRINCIPIA. 



riilNTINO. 



perceives and <indrrrtnd all things. Ha ia altogether without body 

 or figure, and thence can neither be aeen, heard, touched, nor 

 worshipped under the likeness of any corporeal thing. We have idea* 

 of hw attribute*, but we know nothing of the substance of any thing. 

 We see only the figures and colour* of bodies, we hear only Hound*, 

 we touch only external surface, we smell only odours, and taste tastea : 

 we can perceive the inmost substance by no sense, by no reflected 

 action ; much less can we have an idea of the substance of Ood. Him 

 WP know only by hi* properties and attributes, and by the most wise 

 and excellent structure and final causes of things ; and we wonder at 

 him for his perfections, but we venerate and worship him for his 

 dominion. We worship him as servants, and a Ood without dominion, 

 providence, and final causes is nothing else but fate and nature. From 

 a blind metaphysical necessity, which is certainly the same always and 

 everywhere, no variation of things can arise. Every diversity of created 

 things in space and in time can only arise from the ideas and the will 

 of a necessarily existing being. But Ood is said allegorically to see, 

 hear, speak, laugh, love, hate, desire, give, receive, rejoice, be made 

 angry, fight, work, build, and construct. For every expression con- 

 cerning Ood is drawn from human affairs by a certain 6gure of 

 similitude, not perfect indeed, but something like. And this much of 

 Ood, of whom it certainly belongs to natural philosophy to treat from 

 pi BsBi 



' So far I have explained the phenomena of our heavens and the sea 

 by the force of gravity : but I have not yet assigned the cause of 

 gravity. Certainly this force arises from some cause, which penetrates 

 even to the centre of the sun and planets, without diminution of ito 

 virtue ; and which acts not accenting to the superficial magnitude of 

 particles (as do many mechanical causes), but according to the quantity 

 of solid matter ; and of which the action is extended in every direction 

 to ji^pi*""*" distances, diminishing always in the duplicate ratio of the 

 distances. Gravity towards the sun ia compounded of the gravity 

 towards all the several particles of the gun, and in receding from the 

 sun diminishes accurately in the duplicate ratio of the distances, as 

 far as the orbit of Saturn, as is made manifest by the quiescence of the 

 nphi-li.1 of the planets, and even as far as the aphelia of the comets, if 

 thry also do not move. But I have not yet been able to deduce the 

 reason of these properties of gravity from phenomena, and I do not 

 frame hypotheses. For whatever is not deduced from phenomena, is 

 to be called hypothaii: and hypotheses, whether metaphysical or 

 physical, or of occult qualities, or mechanical, have no place in 

 <.ri,frimetal philatojihy. In this philosophy propositions are deduced 

 from phenomena, and are rendered general by induction. So impene- 

 trability, mobility, the impetus of bodies, and the laws of motion and 

 gravity have become known. And it is enough that gravity really 

 exists and acts according to laws explained by me, and suffices for all 

 the motions of the heavenly bodies and of our sea. 



" I might add something on that most subtile spirit which pervades 

 solid bodies and lies hidden in them, by the force and action of which 

 the particles of bodies attract each other at the smallest distances, anc 

 adhere when contiguous : and by which electric bodies act at greater 

 distances, both by attracting and repelling neighbouring particles ; auc 

 by which light is emitted, reflected, refracted, inflected, and gives hea' 

 to bodies ; and by which all sensation is excited, and the limbs of 

 niml are moved at pleasure, namely, by its vibrations through the 

 solid capillaments of the nerves, propagated from the external organs 

 of sense to the brain, and from the brain to the muscles. But this 

 could not be explained in few words ; nor is there a sufficient quantity 

 of experiments to show and determine the laws according to whicl 

 this ipiritiu acts." 



There is Dot a sentence of the preceding scholium which has not a 

 direct reference to some common opinion, at home or abroad, of the 

 physios, metaphysics, or theology of Newton's system. He ha< 

 probably seen and heard enough, in the interval between the editions 

 to teach him on what points explanation was desirable ; certain it is 

 that there is hardly an objector since his time who might not have 

 found himself already answered, if he had read this scholium witl 

 candour and attention. 



The commentators of Newton have one and all, as might be 

 opposed, treated their author as a source of elementary instruction 

 to be explained and cleared from the effects of that brevity am 

 obscurity (the latter more than due to the former) which the Principi 

 almost everywhere presents. But the time has arrived when this 

 work hardly in the beginner's course, though it may be recommended 

 to him, when lit- lion studied the modern analysis, to make himsel 

 acquainted with Ita methods until lie has caught their spirit. Wha 

 we now want i* rather an historical commentary, which shall put th 

 student in possession of the modes of reasoning peculiar to Newton' 

 predecessors, shall point out how the I'rincipia came to have its form 

 and shall place him, so far as is possible, in the midst of that atiuo 

 sphere of remnant* of the old philosophy and aspirations after the new 

 in which the mind of Newton gained it* growth. 



In 17:", I'r. .luliii Clarke published 'A Demonstration of some o 

 the principal sections of Sir I. Newton's Principles,' Ac. This wor 

 contains the greater part of the first book somewhat expanded, an 

 with the applications of the third book intermixed. But it omits th 

 most important part of the eleventh m-.->i . in-viTtlii-lon, a studen 

 wlm Mi'iuld join with Dr. Clarke's work the article OKAVITATIOM i 



le present one, would have the most important parts of the Prim-ipi.i . 

 so far as is necessary to gain an insight into Newton's methods. 



In the same year, 1780, Oeorge Peter Domck published his ' Philos. 



lath. Newt. Illustrate Tomi Duo, Londini' (This work is son 

 wrongly called an edition of the I'rincipia, and it* author's name is 

 sometimes spelled Douick.) The first volume of it is only a prepa- 

 ratory course of mathematics ; the second gives a large part of the first 



wok in Newton's manner, and gives more of the results of the eleventh 

 section. It also enters upon some of the numerical applications of the 

 third book. 



The Commentary of the Minims (Jesuits they are usually l.ut 

 wrongly called) Le Sueur and Jacquier (1739) is an excellent perform- 

 ance for ita time, considered as attempting to smooth the detail 

 mathematical difficulties. It uses algebra freely, but is totally 



nsufficient to show the use of the differential calculus as now known , 

 >ut it very frequently developes satisfactorily a point at which Newton 

 only hinted. 



Emerson's ' Short Comment on Newton's I'rincipia,' 1770, is a brief 

 explanation of some of the mathematical difficulties and obscurities, 

 oUowed by defence* of the Principia, the Optics, and the Cliron 

 Smerson defended everything of Newton's. 



The popular explanations of Maclaurin, Pemberton, and Voltaire are 



widely known to need description ; they do not much help the 



mathematical student. Many so-called explanations of Newtonian 



philosophy (such as Benjamin Martin's, 1761) are literally nothing but 



treatises on general physics. 



The additions to Madame du Chastellet's translation consist of a 

 popular rfmmt and the mathematical treatment of various questions 

 >f the Principia. The latter must be considered as emanating from 

 Jlairaut, since they were his lessons to his pupil. Some have supposed 

 that Voltaire's work belongs in the same sense to Madame du 

 Chastellet 



In the 'Mecanique Celeste,' book 18, cap. 2, Laplace has exhibited 

 the results of Newton's lunar theory, and connected them with tin' 

 modern analysis of the subject to a certain extent. The preciseness 

 of the manner of compressing Newton's results renders this chapter 

 valuable, and likely to assist the student of the Principia. 



Mr. Airy's development and extension of the results of the eleventh 

 section (which forms the article GRAVITATION in this work) places one 

 of the methods of the Principia, and one which ought to last, within 

 the reach of every student. It is unique, the difficulties of the 

 eleventh section having left it almost without a commentator, ami 

 altogether without on explainer ; and it takes in several of the dis- 

 coveries of the present time. 



Many commentaries on the Principia have been written at Cam 

 by private tutors for the use of their pupils, of which some have been 

 printed. Of the following we have never seen more than the title : 

 I ita quadam e Princ. Phil. Nat., cum notis variorum,' Cambridge, 

 1765. There is Carr's three sections of Newton, a modern woi !. 

 on exposition of various parts of the Principia contained in the second 

 edition of Professor Whewell's ' Dynamics." We believe that several 

 recent Cambridge works contain some help on the subject. 



To give a view of the foreign objections to Newton's system, at the 

 time of its first introduction, the following works may sen 

 'Collection of Papers which passed between Mr. Leibnitz and I'r. 

 Clarke, in 1715 and 1716,' by Dr. Samuel Clarke; London, 1717. -', 

 ' Trait<5 de Paix entre Des Cartes et Newton,' by the Jesuit I 

 Henri-Paulian ; Avignon, 1763. 3, ' Le vrai Systome de 1'liyciquf 

 gdne'rale de M. Isaac Newton, expose 1 ot analyst! en parallele avec celui 

 de Des Cartes,' by the Jesuit Louis Castcl ; Paris, 1743 (a defence of 

 Descartes). 4, ' Anti-Newtonianismus,' by Celestial Cominale, M.D. ; 

 Naples, 1754. 5, ' Discours sur les difKrentes Figures des Astros,' by 

 Maupertuis, the first assertor of Newton's doctrines in France ; Paris, 

 1732, and in the collection of his works. 6, 'Letters to a German 

 Princess,' by Euler (first published in 1770, translated into Englinh 

 by Dr. H. Hunter, 1795). 



The most celebrated comments in the way of objection are those of 

 LEIBNITZ, JOHN BERNOULLI, and HUYOHENS [see Bioo. I Hv.] ; 1 1 

 and third real admirers of the genius of Newton, the second also an 

 admirer after his fashion. Many of their remarks may be found in 

 the published correspondence of the first two, but the history of the 

 effect produced by the Principia in the years following its publication 

 is scattered in too many places for us to attempt to give the particular 

 publications which should be consulted. 



PRINCIPLE, D'ALEMBEUT'S. [FORCES, IMPRESSED AND EF- 

 FECTIVE; VIRTUAL VELOCITIES.] 



I'lilXTINO, in the widest sense of the word, may be defined to be 

 the art of producing copies of any writing or other marks by pressure, 

 cither upon a substance so soft as (like wax or clay) to take the Hli.-i|.r. 

 whether in relief or by indentation, of the stamp applied to it, and \< ' 

 not so perfectly fluid (like water) as to refuse to retain the f<> 

 L-iven (.. it; or upon a substance sufficiently bibulous or oth< 

 attractive as to receive colour from some pigment with whieh tli. 

 stamp is daubed. The essence of printing is the production of a <..,,.. 

 by pressure. Correctly speaking, however, it is not an exact copy or 

 fac-simile which printing produces in any case; so far from that, 

 <T the surface is raised in the stamp, it is sunk in the imjinv- 

 sion, and rice renA, and even a merely coloured mark is always reversed 



