TRANSCRIBER’S NOTES:
—Obvious print and punctuation errors were corrected.
—The transcriber of this project created the book cover image using the title page of the original book. The image is placed in the public domain.
A
VIEW
OF
Sir ISAAC NEWTON’s
PHILOSOPHY.
LONDON:
Printed by S. Palmer, 1728.
To the Noble and Right Honourable
Sir ROBERT WALPOLE.
SIR,
I Take the liberty to send you this view of Sir Isaac Newton’s philosophy, which, if it were performed suitable to the dignity of the subject, might not be a present unworthy the acceptance of the greatest person. For his philosophy operations of nature, which for so many ages had imployed the curiosity of mankind; though no one before him was furnished with the strength of mind necessary to go any depth in this difficult search. However, I am encouraged to hope, that this attempt, imperfect as it is, to give our countrymen in general some conception of the labours of a person, who shall always be the boast of this nation, may be received with indulgence by one, under whose influence these kingdoms enjoy so much happiness. Indeed my admiration at the surprizing inventions of this great man, carries me to conceive of him as a person, who not only must raise the glory of the country, which gave him birth; but that he has even done honour to human nature, by having extended the greatest and most noble of our faculties, reason, to subjects, which, till he attempted them, appeared to be wholly beyond the reach of our limited capacities. And what can give us a more pleasing prospect of our own condition, than to see so exalted a proof of the strength of that faculty, whereon the conduct of our lives, and our happiness depends; our passions and all our motives to action being in such manner guided by our opinions, that where these are just, our whole behaviour will be praise-worthy? But why do I presume to detain you, Sir, with such reflections as these, who must have the fullest experience within your own mind, of the effects of right reason? For to what other source can be ascribed that amiable frankness and unreserved condescension among your friends, or that masculine perspicuity and strength of argument, whereby you draw the admiration of the publick, while you are engaged in the most important of all causes, the liberties of mankind?
I humbly crave leave to make the only acknowledgement within my power, for the benefits, which I receive in common with the rest of my countrymen from these high talents, by subscribing my self
SIR,
Your most faithful,
and
Most humble Servant,
Henry Pemberton.
PREFACE.
I Drew up the following papers many years ago at the desire of some friends, who, upon my taking care of the late edition of Sir Isaac Newton’s Principia, perswaded me to make them publick. I laid hold of that opportunity, when my thoughts were afresh employed on this subject, to revise what I had formerly written. And I now send it abroad not without some hopes of answering these two ends. My first intention was to convey to such, as are not used to mathematical reasoning, some idea of the philosophy of a person, who has acquired an universal reputation, and rendered our nation famous for these speculations in the learned world. To which purpose I have avoided using terms of art as much as possible, and taken care to define such as I was obliged to use. Though this caution was the less necessary at present, since many of them are become familiar words to our language, from the great number of books wrote in it upon philosophical subjects, and the courses of experiments, that have of late years been given by several ingenious men. The other view I had, was to encourage such young gentlemen as have a turn for the mathematical sciences, to pursue those studies the more chearfully, in order to understand in our author himself the demonstrations of the things I here declare. And to facilitate their progress herein, I intend to proceed still farther in the explanation of Sir Isaac Newton’s philosophy. For as I have received very much pleasure from perusing his writings, I hope it is no illaudable ambition to endeavour the rendering them more easily understood, that greater numbers may enjoy the same satisfaction.
It will perhaps be expected, that I should say something particular of a person, to whom I must always acknowledge my self to be much obliged. What I have to declare on this head will be but short; for it was in the very last years of Sir Isaac’s life, that I had the honour of his acquaintance. This happened on the following occasion. Mr. Polenus, a Professor in the University of Padua, from a new experiment of his, thought the common opinion about the force of moving bodies was overturned, and the truth of Mr. Libnitz’s notion in that matter fully proved. The contrary of what Polenus had asserted I demonstrated in a paper, which Dr. Mead, who takes all opportunities of obliging his friends, was pleased to shew Sir Isaac Newton This was so well approved of by him, that he did me the honour to become a fellow-writer with me, by annexing to what I had written, a demonstration of his own drawn from another consideration. When I printed my discourse in the philosophical transactions, I put what Sir Isaac had written in a scholium by it self, that I might not seem to usurp what did not belong to me. But I concealed his name, not being then sufficiently acquainted with him to ask whether he was willing I might make use of it or not. In a little time after he engaged me to take care of the new edition he was about making if his Principia. This obliged me to be very frequently with him, and as he lived at some distance from me, a great number of letters passed between us on this account. When I had the honour of his conversation, I endeavoured to learn his thoughts upon mathematical subjects, and something historical concerning his inventions, that I had not been before acquainted with. I found, he had read fewer of the modern mathematicians, than one could have expected; but his own prodigious invention readily supplied him with what he might have an occasion for in the pursuit of any subject he undertook. I have often heard him censure the handling geometrical subjects by algebraic calculations; and his book of Algebra he called by the name of Universal Arithmetic, in opposition to the injudicious title of Geometry, which Des Cartes had given to the treatise, wherein he shews, how the geometer may assist his invention by such kind of computations. He frequently praised Slusius, Barrow and Huygens for not being influenced by the false taste, which then began to prevail. He used to commend the laudable attempt of Hugo de Omerique to restore the ancient analysis, and very much esteemed Apollonius’s book De sectione rationis for giving us a clearer notion of that analysis than we had before. Dr. Barrow may be esteemed as having shewn a compass of invention equal, if not superior to any of the moderns, our author only excepted; but Sir Isaac Newton has several times particularly recommended to me Huygens’s stile and manner. He thought him the most elegant of any mathematical writer of modern times, and the most just imitator of the antients. Of their taste, and form of demonstration Sir Isaac always professed himself a great admirer: I have heard him even censure himself for not following them yet more closely than he did; and speak with regret of his mistake at the beginning of his mathematical studies, in applying himself to the works of Des Cartes and other algebraic writers, before he had considered the elements of Euclide with that attention, which so excellent a writer deserves. As to the history of his inventions, what relates to his discoveries of the methods of series and fluxions, and of his theory of light and colours, the world has been sufficiently informed of already. The first thoughts, which gave rise to his Principia, he had, when he retired from Cambridge in 1666 on account of the plague. As he sat alone in a garden, he fell into a speculation on the power of gravity: that as this power is not found sensibly diminished at the remotest distance from the center of the earth, to which we can rise, neither at the tops of the loftiest buildings, nor even on the summits of the highest mountains; it appeared to him reasonable to conclude, that this power must extend much farther than was usually thought; why not as high as the moon, said he to himself? and if so, her motion must be influenced by it; perhaps she is retained in her orbit thereby. However, though the power of gravity is not sensibly weakened in the little change of distance, at which we can place our selves from the center of the earth; yet it is very possible, that so high as the moon this power may differ much in strength from what it is here. To make an estimate, what might be the degree of this diminution, he considered with himself, that if the moon be retained in her orbit by the force of gravity, no doubt the primary planets are carried round the sun by the like power. And by comparing the periods of the several planets with their distances from the sun, he found, that if any power like gravity held them in their courses, its strength must decrease in the duplicate proportion of the increase of distance. This be concluded by supposing them to move in perfect circles concentrical to the sun, from which the orbits of the greatest part of them do not much differ. Supposing therefore the power of gravity, when extended to the moon, to decrease in the same manner, he computed whether that force would be sufficient to keep the moon in her orbit. In this computation, being absent from books, he took the common estimate in use among geographers and our seamen, before Norwood had measured the earth, that 60 English miles were contained in one degree of latitude on the surface of the earth. But as this is a very faulty supposition, each degree containing about 69½ of our miles, his computation did not answer expectation; whence he concluded, that some other cause must at least join with the action of the power of gravity on the moon. On this account he laid aside for that time any farther thoughts upon this matter. But some years after, a letter which he received from Dr. Hook, put him on inquiring what was the real figure, in which a body let fall from any high place descends, taking the motion of the earth round its axis into consideration. Such a body, having the same motion, which by the revolution of the earth the place has whence it falls, is to be considered as projected forward and at the same time drawn down to the center of the earth. This gave occasion to his resuming his former thoughts concerning the moon; and Picart in France having lately measured the earth, by using his measures the moon appeared to be kept in her orbit purely by the power of gravity; and consequently, that this power decreases as you recede from the center of the earth in the manner our author had formerly conjectured. Upon this principle he found the line described by a falling body to be an ellipsis, the center of the earth being one focus. And the primary planets moving in such orbits round the sun, he had the satisfaction to see, that this inquiry, which he had undertaken merely out of curiosity, could be applied to the greatest purposes. Hereupon he composed near a dozen propositions relating to the motion of the primary planets about the sun. Several years after this, some discourse he had with Dr. Halley, who at Cambridge made him a visit, engaged Sir Isaac Newton to resume again the consideration of this subject; and gave occasion to his writing the treatise which he published under the title of mathematical principles of natural philosophy. This treatise, full of such a variety of profound inventions, was composed by him from scarce any other materials than the few propositions before mentioned, in the space of one year and an half.
Though his memory was much decayed, I found he perfectly understood his own writings, contrary to what I had frequently heard in discourse from many persons. This opinion of theirs might arise perhaps from his not being always ready at speaking on these subjects, when it might be expected he should. But as to this, it may be observed, that great genius’s are frequently liable to be absent, not only in relation to common life, but with regard to some of the parts of science they are the best informed of. Inventors seem to treasure up in their minds, what they have found out, after another manner than those do the same things, who have not this inventive faculty. The former, when they have occasion to produce their knowledge, are in some measure obliged immediately to investigate part of what they want. For this they are not equally fit at all times: so it has often happened, that such as retain things chiefly by means of a very strong memory, have appeared off hand more expert than the discoverers themselves.
As to the moral endowments of his mind, they were as much to be admired as his other talents. But this is a field I leave others to exspatiate in. I only touch upon what I experienced myself during the few years I was happy in his friendship. But this I immediately discovered in him, which at once both surprized and charmed me: Neither his extreme great age, nor his universal reputation had rendred him stiff in opinion, or in any degree elated. Of this I had occasion to have almost daily experience. The Remarks I continually sent him by letters on his Principia were received with the utmost goodness. These were so far from being any ways displeasing to him, that on the contrary it occasioned him to speak many kind things of me to my friends, and to honour me with a publick testimony of his good opinion. He also approved of the following treatise, a great part of which we read together. As many alterations were made in the late edition of his Principia, so there would have been many more if there had been a sufficient time. But whatever of this kind may be thought wanting, I shall endeavour to supply in my comment on that book. I had reason to believe he expected such a thing from me, and I intended to have published it in his life time, after I had printed the following discourse, and a mathematical treatise Sir Isaac Newton had written a long while ago, containing the first principles of fluxions, for I had prevailed on him to let that piece go abroad. I had examined all the calculations, and prepared part of the figures; but as the latter part of the treatise had never been finished, he was about letting me have other papers, in order to supply what was wanting. But his death put a stop to that design. As to my comment on the Principia, I intend there to demonstrate whatever Sir Isaac Newton has set down without express proof, and to explain all such expressions in his book, as I shall judge necessary. This comment I shall forthwith put to the press, joined to an english translation of his Principia, which I have had some time by me. A more particular account of my whole design has already been published in the new memoirs of literature for the month of march 1727.
I have presented my readers with a copy of verses on Sir Isaac Newton, which I have just received from a young Gentleman, whom I am proud to reckon among the number of my dearest friends. If I had any apprehension that this piece of poetry stood in need of an apology, I should be desirous the reader might know, that the author is but sixteen years old, and was obliged to finish his composition in a very short space of time. But I shall only take the liberty to observe, that the boldness of the digressions will be best judged of by those who are acquainted with Pindar.
A
POEM
ON
Sir ISAAC NEWTON.
To Newton’s genius, and immortal fame
Th’ advent’rous muse with trembling pinion soars.
Thou, heav’nly truth, from thy seraphick throne
Look favourable down, do thou assist
My lab’ring thought, do thou inspire my song.
Newton, who first th’ almighty’s works display’d,
And smooth’d that mirror, in whose polish’d face
The great creator now conspicuous shines;
Who open’d nature’s adamantine gates,
And to our minds her secret powers expos’d;
Newton demands the muse; his sacred hand
Shall guide her infant steps; his sacred hand
Shall raise her to the Heliconian height,
Where, on its lofty top inthron’d, her head
Shall mingle with the Stars. Hail nature, hail,
O Goddess, handmaid of th’ ethereal power,
Now lift thy head, and to th’ admiring world
Shew thy long hidden beauty. Thee the wise
Of ancient fame, immortal Plato’s self,
The Stagyrite, and Syracusian sage,
From black obscurity’s abyss to raise,
(Drooping and mourning o’er thy wondrous works)
With vain inquiry sought. Like meteors these
In their dark age bright sons of wisdom shone:
But at thy Newton all their laurels fade,
They shrink from all the honours of their names.
So glimm’ring stars contract their feeble rays,
When the swift lustre of Aurora’s face
Flows o’er the skies, and wraps the heav’ns in light.
The Deity’s omnipotence, the cause,
Th’ original of things long lay unknown.
Alone the beauties prominent to sight
(Of the celestial power the outward form)
Drew praise and wonder from the gazing world.
As when the deluge overspread the earth,
Whilst yet the mountains only rear’d their heads
Above the surface of the wild expanse,
Whelm’d deep below the great foundations lay,
Till some kind angel at heav’n’s high command
Roul’d back the rising tides, and haughty floods,
And to the ocean thunder’d out his voice:
Quick all the swelling and imperious waves,
The foaming billows and obscuring surge,
Back to their channels and their ancient seats
Recoil affrighted: from the darksome main
Earth raises smiling, as new-born, her head,
And with fresh charms her lovely face arrays.
So his extensive thought accomplish’d first
The mighty task to drive th’ obstructing mists
Of ignorance away, beneath whose gloom
Th’ inshrouded majesty of Nature lay.
He drew the veil and swell’d the spreading scene.
How had the moon around th’ ethereal void
Rang’d, and eluded lab’ring mortals care,
Till his invention trac’d her secret steps,
While she inconstant with unsteady rein
Through endless mazes and meanders guides
In its unequal course her changing carr:
Whether behind the sun’s superior light
She hides the beauties of her radiant face,
Or, when conspicuous, smiles upon mankind,
Unveiling all her night-rejoicing charms.
When thus the silver-tressed moon dispels
The frowning horrors from the brow of night,
And with her splendors chears the sullen gloom,
While sable-mantled darkness with his veil
The visage of the fair horizon shades,
And over nature spreads his raven wings;
Let me upon some unfrequented green
While sleep sits heavy on the drowsy world,
Seek out some solitary peaceful cell,
Where darksome woods around their gloomy brows
Bow low, and ev’ry hill’s protended shade
Obscures the dusky vale, there silent dwell,
Where contemplation holds its still abode,
There trace the wide and pathless void of heav’n,
And count the stars that sparkle on its robe.
Or else in fancy’s wild’ring mazes lost
Upon the verdure see the fairy elves
Dance o’er their magick circles, or behold,
In thought enraptur’d with the ancient bards,
Medea’s baleful incantations draw
Down from her orb the paly queen of night.
But chiefly Newton let me soar with thee,
And while surveying all yon starry vault
With admiration I attentive gaze,
Thou shalt descend from thy celestial seat,
And waft aloft my high-aspiring mind,
Shalt shew me there how nature has ordain’d
Her fundamental laws, shalt lead my thought
Through all the wand’rings of th’ uncertain moon,
And teach me all her operating powers.
She and the sun with influence conjoint
Wield the huge axle of the whirling earth,
And from their just direction turn the poles,
Slow urging on the progress of the years.
The constellations seem to leave their seats,
And o’er the skies with solemn pace to move.
You, splendid rulers of the day and night,
The seas obey, at your resistless sway
Now they contract their waters, and expose
The dreary desart of old ocean’s reign.
The craggy rocks their horrid sides disclose;
Trembling the sailor views the dreadful scene,
And cautiously the threat’ning ruin shuns.
But where the shallow waters hide the sands,
There ravenous destruction lurks conceal’d,
There the ill-guided vessel falls a prey,
And all her numbers gorge his greedy jaws.
But quick returning see th’ impetuous tides
Back to th’ abandon’d shores impell the main.
Again the foaming seas extend their waves,
Again the rouling floods embrace the shoars,
And veil the horrours of the empty deep.
Thus the obsequious seas your power confess,
While from the surface healthful vapours rise
Plenteous throughout the atmosphere diffus’d,
Or to supply the mountain’s heads with springs,
Or fill the hanging clouds with needful rains,
That friendly streams, and kind refreshing show’rs
May gently lave the sun-burnt thirsty plains,
Or to replenish all the empty air
With wholsome moisture to increase the fruits
Of earth, and bless the labours of mankind.
O Newton, whether flies thy mighty soul,
How shall the feeble muse pursue through all
The vast extent of thy unbounded thought,
That even seeks th’ unseen recesses dark
To penetrate of providence immense.
And thou the great dispenser of the world
Propitious, who with inspiration taught’st
Our greatest bard to send thy praises forth;
Thou, who gav’st Newton thought; who smil’dst serene,
When to its bounds he stretch’d his swelling soul;
Who still benignant ever blest his toil,
And deign’d to his enlight’ned mind t’ appear
Confess’d around th’ interminated world:
To me O thy divine infusion grant
(O thou in all so infinitely good)
That I may sing thy everlasting works,
Thy inexhausted store of providence,
In thought effulgent and resounding verse.
O could I spread the wond’rous theme around,
Where the wind cools the oriental world,
To the calm breezes of the Zephir’s breath,
To where the frozen hyperborean blasts.
To where the boist’rous tempest-leading south
From their deep hollow caves send forth their storms.
Thou still indulgent parent of mankind,
Left humid emanations should no more
Flow from the ocean, but dissolve away
Through the long series of revolving time;
And left the vital principle decay,
By which the air supplies the springs of life;
Thou hast the fiery visag’d comets form’d
With vivifying spirits all replete,
Which they abundant breathe about the void,
Renewing the prolifick soul of things.
No longer now on thee amaz’d we call,
No longer tremble at imagin’d ills,
When comets blaze tremendous from on high,
Or when extending wide their flaming trains
With hideous grasp the skies engirdle round,
And spread the terrors of their burning locks.
For these through orbits in the length’ning space
Of many tedious rouling years compleat
Around the sun move regularly on;
And with the planets in harmonious orbs,
And mystick periods their obeysance pay
To him majestick ruler of the skies
Upon his throne of circled glory fixt.
He or some god conspicuous to the view,
Or else the substitute of nature seems,
Guiding the courses of revolving worlds.
He taught great Newton the all-potent laws
Of gravitation, by whose simple power
The universe exists. Nor here the sage
Big with invention still renewing staid.
But O bright angel of the lamp of day,
How shall the muse display his greatest toil?
Let her plunge deep in Aganippe’s waves,
Or in Castalia’s ever-flowing stream,
That re-inspired she may sing to thee,
How Newton dar’d advent’rous to unbraid
The yellow tresses of thy shining hair.
Or didst thou gracious leave thy radiant sphere,
And to his hand thy lucid splendours give,
T’ unweave the light-diffusing wreath, and part
The blended glories of thy golden plumes?
He with laborious, and unerring care,
How different and imbodied colours form
Thy piercing light, with just distinction found.
He with quick sight pursu’d thy darting rays,
When penetrating to th’ obscure recess
Of solid matter, there perspicuous saw,
How in the texture of each body lay
The power that separates the different beams.
Hence over nature’s unadorned face
Thy bright diversifying rays dilate
Their various hues: and hence when vernal rains
Descending swift have burst the low’ring clouds,
Thy splendors through the dissipating mists
In its fair vesture of unnumber’d hues
Array the show’ry bow. At thy approach
The morning risen from her pearly couch
With rosy blushes decks her virgin cheek;
The ev’ning on the frontispiece of heav’n
His mantle spreads with many colours gay;
The mid-day skies in radiant azure clad,
The shining clouds, and silver vapours rob’d
In white transparent intermixt with gold,
With bright variety of splendor cloath
All the illuminated face above.
When hoary-headed winter back retires
To the chill’d pole, there solitary sits
Encompass’d round with winds and tempests bleak
In caverns of impenetrable ice,
And from behind the dissipated gloom
Like a new Venus from the parting surge
The gay-apparell’d spring advances on;
When thou in thy meridian brightness sitt’st,
And from thy throne pure emanations flow
Of glory bursting o’er the radiant skies:
Then let the muse Olympus’ top ascend,
And o’er Thessalia’s plain extend her view,
And count, O Tempe, all thy beauties o’er.
Mountains, whose summits grasp the pendant clouds,
Between their wood-invelop’d slopes embrace
The green-attired vallies. Every flow’r
Here in the pride of bounteous nature clad
Smiles on the bosom of th’ enamell’d meads.
Over the smiling lawn the silver floods
Of fair Peneus gently roul along,
While the reflected colours from the flow’rs,
And verdant borders pierce the lympid waves,
And paint with all their variegated hue
The yellow sands beneath. Smooth gliding on
The waters hasten to the neighbouring sea.
Still the pleas’d eye the floating plain pursues;
At length, in Neptune’s wide dominion lost,
Surveys the shining billows, that arise
Apparell’d each in Phœbus’ bright attire:
Or from a far some tall majestick ship,
Or the long hostile lines of threat’ning fleets,
Which o’er the bright uneven mirror sweep,
In dazling gold and waving purple deckt;
Such as of old, when haughty Athens power
Their hideous front, and terrible array
Against Pallene’s coast extended wide,
And with tremendous war and battel stern
The trembling walls of Potidæa shook.
Crested with pendants curling with the breeze
The upright masts high bristle in the air,
Aloft exalting proud their gilded heads.
The silver waves against the painted prows
Raise their resplendent bosoms, and impearl
The fair vermillion with their glist’ring drops:
And from on board the iron-cloathed host
Around the main a gleaming horrour casts;
Each flaming buckler like the mid-day sun,
Each plumed helmet like the silver moon,
Each moving gauntlet like the light’ning’s blaze,
And like a star each brazen pointed spear.
But lo the sacred high-erected fanes,
Fair citadels, and marble-crowned towers,
And sumptuous palaces of stately towns
Magnificent arise, upon their heads
Bearing on high a wreath of silver light.
But see my muse the high Pierian hill,
Behold its shaggy locks and airy top,
Up to the skies th’ imperious mountain heaves
The shining verdure of the nodding woods.
See where the silver Hippocrene flows,
Behold each glitt’ring rivulet, and rill
Through mazes wander down the green descent,
And sparkle through the interwoven trees.
Here rest a while and humble homage pay,
Here, where the sacred genius, that inspir’d
Sublime Mæonides and Pindar’s breast,
His habitation once was fam’d to hold.
Here thou, O Homer, offer’dst up thy vows,
Thee, the kind muse Calliopæa heard,
And led thee to the empyrean feats,
There manifested to thy hallow’d eyes
The deeds of gods; thee wise Minerva taught
The wondrous art of knowing human kind;
Harmonious Phœbus tun’d thy heav’nly mind,
And swell’d to rapture each exalted sense;
Even Mars the dreadful battle-ruling god,
Mars taught thee war, and with his bloody hand
Instructed thine, when in thy sounding lines
We hear the rattling of Bellona’s carr,
The yell of discord, and the din of arms.
Pindar, when mounted on his fiery steed,
Soars to the sun, opposing eagle like
His eyes undazled to the fiercest rays.
He firmly seated, not like Glaucus’ son,
Strides his swift-winged and fire-breathing horse,
And born aloft strikes with his ringing hoofs
The brazen vault of heav’n, superior there
Looks down upon the stars, whose radiant light
Illuminates innumerable worlds,
That through eternal orbits roul beneath.
But thou all hail immortalized son
Of harmony, all hail thou Thracian bard,
To whom Apollo gave his tuneful lyre.
O might’st thou, Orpheus, now again revive,
And Newton should inform thy list’ning ear
How the soft notes, and soul-inchanting strains
Of thy own lyre were on the wind convey’d.
He taught the muse, how sound progressive floats
Upon the waving particles of air,
When harmony in ever-pleasing strains,
Melodious melting at each lulling fall,
With soft alluring penetration steals
Through the enraptur’d ear to inmost thought,
And folds the senses in its silken bands.
So the sweet musick, which from Orpheus’ touch
And fam’d Amphion’s, on the sounding string
Arose harmonious, gliding on the air,
Pierc’d the tough-bark’d and knotty-ribbed woods,
Into their saps soft inspiration breath’d
And taught attention to the stubborn oak.
Thus when great Henry, and brave Marlb’rough led
Th’ imbattled numbers of Britannia’s sons,
The trump, that swells th’ expanded cheek of fame,
That adds new vigour to the gen’rous youth,
And rouzes sluggish cowardize it self,
The trumpet with its Mars-inciting voice,
The winds broad breast impetuous sweeping o’er
Fill’d the big note of war. Th’ inspired host
With new-born ardor press the trembling Gaul;
Nor greater throngs had reach’d eternal night,
Not if the fields of Agencourt had yawn’d
Exposing horrible the gulf of fate;
Or roaring Danube spread his arms abroad,
And overwhelm’d their legions with his floods.
But let the wand’ring muse at length return;
Nor yet, angelick genius of the sun,
In worthy lays her high-attempting song
Has blazon’d forth thy venerated name.
Then let her sweep the loud-resounding lyre
Again, again o’er each melodious string
Teach harmony to tremble with thy praise.
And still thine ear O favourable grant,
And she shall tell thee, that whatever charms,
Whatever beauties bloom on nature’s face,
Proceed from thy all-influencing light.
That when arising with tempestuous rage,
The North impetuous rides upon the clouds
Dispersing round the heav’ns obstructive gloom,
And with his dreaded prohibition stays
The kind effusion of thy genial beams;
Pale are the rubies on Aurora’s lips,
No more the roses blush upon her cheeks,
Black are Peneus’ streams and golden sands
In Tempe’s vale dull melancholy sits,
And every flower reclines its languid head.
By what high name shall I invoke thee, say,
Thou life-infusing deity, on thee
I call, and look propitious from on high,
While now to thee I offer up my prayer.
O had great Newton, as he found the cause,
By which sound rouls thro’ th’ undulating air,
O had he, baffling times resistless power,
Discover’d what that subtle spirit is,
Or whatsoe’er diffusive else is spread
Over the wide-extended universe,
Which causes bodies to reflect the light,
And from their straight direction to divert
The rapid beams, that through their surface pierce.
But since embrac’d by th’ icy arms of age,
And his quick thought by times cold hand congeal’d,
Ev’n Newton left unknown this hidden power;
Thou from the race of human kind select
Some other worthy of an angel’s care,
With inspiration animate his breast,
And him instruct in these thy secret laws.
O let not Newton, to whose spacious view,
Now unobstructed, all th’ extensive scenes
Of the ethereal ruler’s works arise;
When he beholds this earth he late adorn’d,
Let him not see philosophy in tears,
Like a fond mother solitary sit,
Lamenting him her dear, and only child.
But as the wise Pythagoras, and he,
Whose birth with pride the fam’d Abdera boasts,
With expectation having long survey’d
This spot their ancient seat, with joy beheld
Divine philosophy at length appear
In all her charms majestically fair,
Conducted by immortal Newton’s hand.
So may he see another sage arise,
That shall maintain her empire: then no more
Imperious ignorance with haughty sway
Shall stalk rapacious o’er the ravag’d globe:
Then thou, O Newton, shalt protect these lines.
The humble tribute of the grateful muse;
Ne’er shall the sacrilegious hand despoil
Her laurel’d temples, whom his name preserves:
And were she equal to the mighty theme,
Futurity should wonder at her song;
Time should receive her with extended arms,
Seat her conspicuous in his rouling carr,
And bear her down to his extreamest bound.
Fables with wonder tell how Terra’s sons
With iron force unloos’d the stubborn nerves
Of hills, and on the cloud-inshrouded top
Of Pelion Ossa pil’d. But if the vast
Gigantick deeds of savage strength demand
Astonishment from men, what then shalt thou,
O what expressive rapture of the soul,
When thou before us, Newton, dost display
The labours of thy great excelling mind;
When thou unveilest all the wondrous scene,
The vast idea of th’ eternal king,
Not dreadful bearing in his angry arm
The thunder hanging o’er our trembling heads;
But with th’ effulgency of love replete,
And clad with power, which form’d th’ extensive heavens.
O happy he, whose enterprizing hand
Unbars the golden and relucid gates
Of th’ empyrean dome, where thou enthron’d
Philosophy art seated. Thou sustain’d
By the firm hand of everlasting truth
Despisest all the injuries of time;
Thou never know’st decay when all around,
Antiquity obscures her head. Behold
Th’ Egyptian towers, the Babylonian walls,
And Thebes with all her hundred gates of brass,
Behold them scatter’d like the dust abroad.
Whatever now is flourishing and proud,
Whatever shall, must know devouring age.
Euphrates’ stream, and seven-mouthed Nile,
And Danube, thou that from Germania’s soil
To the black Euxine’s far remoted shore,
O’er the wide bounds of mighty nations sweep’st
In thunder loud thy rapid floods along.
Ev’n you shall feel inexorable time;
To you the fatal day shall come; no more
Your torrents then shall shake the trembling ground,
No longer then to inundations swol’n
Th’ imperious waves the fertile pastures drench,
But shrunk within a narrow channel glide;
Or through the year’s reiterated course
When time himself grows old, your wond’rous streams
Lost ev’n to memory shall lie unknown
Beneath obscurity, and Chaos whelm’d,
But still thou sun illuminatest all
The azure regions round, thou guidest still
The orbits of the planetary spheres;
The moon still wanders o’er her changing course,
And still, O Newton, shall thy name survive:
As long as nature’s hand directs the world,
When ev’ry dark obstruction shall retire,
And ev’ry secret yield its hidden store,
Which thee dim-sighted age forbad to see
Age that alone could stay thy rising soul.
And could mankind among the fixed stars,
E’en to th’ extremest bounds of knowledge reach,
To those unknown innumerable suns,
Whose light but glimmers from those distant worlds,
Ev’n to those utmost boundaries, those bars
That shut the entrance of th’ illumin’d space
Where angels only tread the vast unknown,
Thou ever should’st be seen immortal there:
In each new sphere, each new-appearing sun,
In farthest regions at the very verge
Of the wide universe should’st thou be seen.
And lo, th’ all-potent goddess Nature takes
With her own hand thy great, thy just reward
Of immortality; aloft in air
See she displays, and with eternal grasp
Uprears the trophies of great Newton’s fame.
R. Glover.
THE
CONTENTS.
INTRODUCTION concerning Sir Isaac Newton’s
method of reasoning in philosophy————————pag. 1
Book I.
| [Chap. 1.] Of the laws of motion | |
| The first law of motion proved | [p. 29] |
| The second law of motion proved | [p. 29] |
| The third law of motion proved | [p. 31] |
| [Chap. 2.] Further proofs of the laws of motion | |
| The effects of percussion | [p. 49] |
| The perpendicular descent of bodies | [p. 55] |
| The oblique descent of bodies in a straight line | [p. 57] |
| The curvilinear descent of bodies | [p. 58] |
| The perpendicular ascent of bodies | [ibid.] |
| The oblique ascent of bodies | [p. 59] |
| The power of gravity proportional to the quantity of matter in each body | [p. 60] |
| The centre of gravity of bodies | [p. 62] |
| The mechanical powers | [p. 69] |
| The lever | [p. 71] |
| The wheel and axis | [p. 77] |
| The pulley | [p. 80] |
| The wedge | [p. 83] |
| The screw | [ibid.] |
| The inclined plain | [p. 84] |
| The pendulum | [p. 86] |
| Vibrating in a circle | [ibid.] |
| Vibrating in a cycloid | [p. 91] |
| The line of swiftest descent | [p. 93] |
| The centre of oscillation | [p. 94] |
| Experiments upon the percussion of bodies made by pendulums | [p. 98] |
| The centre of percussion | [p. 100] |
| The motion of projectiles | [p. 102] |
| The description of the conic sections | [p. 106] |
| The difference between absolute and relative motion,as also between absolute and relative time | [p. 112] |
| [Chap. 3.] Of centripetal forces | [p. 117] |
| [Chap. 4.] Of the resistance of fluids | [p. 143] |
| Bodies are resisted in the duplicate proportion of their velocities | [p. 147] |
| Of elastic fluids and their resistance | [p. 149] |
| How fluids may be rendered elastic | [p. 150] |
| The degree of resistance in regard to the proportionbetween the density of the body and of the fluid | |
| In rare and uncompressed fluids | [p. 153] |
| In compressed fluids | [p. 155] |
| The degree of resistance as it depends upon the figure of bodies | |
| In rare and uncompressed fluids | [p. 155] |
| In compressed fluids | [p. 158] |
Book II.
| [Chap. 1.]That the planets move in a space empty of sensible matter | [p. 161] |
| The system of the world described | [p. 162] |
| The planets suffer no sensible resistance in their motion | [p. 166] |
| They are not kept in motion by a fluid | [p. 168] |
| That all space is not full of matter without vacancies | [p. 169] |
| [Chap. 2.]Concerning the cause that keeps in motion the primary planets | [p. 171] |
| They are influenced by a centripetal power directed to the sun | [p. 171] |
| The strength of this power is reciprocally in theduplicate proportion of the distance | [ibid.] |
| The cause of the irregularities in the motions of the planets | [p. 175] |
| A correction of their motions | [p. 178] |
| That the frame of the world is not eternal | [p. 180] |
| [Chap. 3.] Of the motion of the moon and the othersecondary planets | |
| That they are influenced by a centripetal force directedtoward their primary, as the primary are influenced by the sun | [p. 182] |
| That the power usually called gravity extends to the moon | [p. 189] |
| That the sun acts on the secondary planets | [p. 190] |
| The variation of the moon | [p. 193] |
| That the circuit of the moons orbit is increased by thesun in the quarters, and diminished in the conjunction and opposition | [p. 198] |
| The distance of the moon from the earth in the quartersand in the conjunction and opposition is altered by the sun | [p. 200] |
| These irregularities in the moon’s motion varied by thechange of distance between the earth and sun | [p. 201] |
| The period of the moon round the earth and her distancevaried by the same means | [ibid.] |
| The motion of the nodes and the inclination of themoons orbit | [p. 202] |
| The motion of the apogeon and change of theeccentricity | [p. 218] |
| The inequalities of the other secondary planets deduciblefrom these of the moon | [p. 229] |
| [Chap. 4.] Of comets | |
| They are not meteors, nor placed totally without theplanetary system | [p. 230] |
| The sun acts on them in the same manner as on theplanets | [p. 231] |
| Their orbits are near to parabola’s | [p. 233] |
| The comet that appeared at the end of the year 1680,probably performs its period in 575 years, and anothercomet in 75 years | [p. 234] |
| Why the comets move in planes more different fromone another than the planets | [p. 235] |
| The tails of comets | [p. 238] |
| The use of them | [p. 243 244] |
| The possible use of the comet it self | [p. 245 246] |
| [Chap. 5.] Of the bodies of the sun and planets | |
| That each of the heavenly bodies is endued with anattractive power, and that the force of the samebody on others is proportional to the quantity ofmatter in the body attracted | [p. 247] |
| This proved in the earth | [p. 248] |
| In the sun | [p. 250] |
| In the rest of the planets | [p. 251] |
| That the attractive power is of the same nature inthe sun and in all the planets, and therefore isthe same with gravity | [p. 252] |
| That the attractive power in each of these bodies isproportional to the quantity of matter in the body attracting | [ibid.] |
| That each particle of which the sun and planets arecomposed is endued with an attracting power, thestrength of which is reciprocally in the duplicateproportion of the distance | [p. 257] |
| The power of gravity universally belongs to all matter | [p. 259] |
| The different weight of the same body upon the surfaceof the sun, the earth, Jupiter and Saturn; the respectivedensities of these bodies, and the proportionbetween their diameters | [p. 261] |
| [Chap. 6.] Of the fluid parts of the planets | |
| The manner in which fluids press | [p. 264] |
| The motion of waves on the surface of water | [p. 269] |
| The motion of sound through the air | [p. 270] |
| The velocity of sound | [p. 282] |
| Concerning the tides | [p. 283] |
| The figure of the earth | [p. 296] |
| The effect of this figure upon the power of gravity | [p. 300] |
| The effect it has upon pendulums | [p. 302] |
| Bodies descend perpendicularly to the surface of the earth | [p. 304] |
| The axis of the earth changes its direction twice a year,and twice a month | [p. 313] |
| The figure of the secondary planets | [ibid.] |
Book III.
| [Chap. 1.] Concerning the cause of colours inherent in the light | |
| The sun’s light is composed of rays of different colours | [p. 318] |
| The refraction of light | [p. 319 320] |
| Bodies appear of different colour by day-light, becausesome reflect one kind of light more copiously than therest, and other bodies other kinds of light | [p. 329] |
| The effect of mixing rays of different colours | [p. 334] |
| [Chap. 2.] Of the properties of bodies whereon theircolours depend. | |
| Light is not reflected by impinging against the solidparts of bodies | [p. 339] |
| The particles which compose bodies are transparent | [p. 341] |
| Cause of opacity | [p. 342] |
| Why bodies in the open day-light have different colours | [p. 344] |
| The great porosity of bodies considered | [p. 355] |
| [Chap. 3.] Of the refraction, reflection, andinflection of light. | |
| Rays of different colours are differently refracted | [p. 357] |
| The sine of the angle of incidence in each kind of raysbears a given proportion to the sine of refraction | [p. 361] |
| The proportion between the refractive powers in differentbodies | [p. 366] |
| Unctuous bodies refract most in proportion to theirdensity | [p. 368] |
| The action between light and bodies is mutual | [p. 369] |
| Light has alternate fits of easy transmission andreflection | [p. 371] |
| The fits found to return alternately many thousandtimes | [p. 375] |
| Why bodies reflect part of the light incident upon themand transmit another part | [ibid.] |
| Sir Isaac Newton’s conjectureconcerning the cause of this alternate reflection andtransmission of light | [p. 376] |
| The inflection of light | [p. 377] |
| [Chap. 4.] Of optic glasses. | |
| How the rays of light are refracted by a sphericalsurface of glass | [p. 378] |
| How they are refracted by two such surfaces | [p. 380] |
| How the image of objects is formed by a convex glass | [p. 381] |
| Why convex glasses help the sight in old age, and concaveglasses assist short-sighted people | [p. 383] |
| The manner in which vision is performed by the eye | [p. 385] |
| Of telescopes with two convex glasses | [p. 386] |
| Of telescopes with four convex glasses | [p. 388] |
| Of telescopes with one convex and one concave glass | [ibid.] |
| Of microscopes | [p. 389] |
| Of the imperfection of telescopes arising from thedifferent refrangibility of the light | [p. 390] |
| Of the reflecting telescope | [p. 393] |
| [Chap. 5.] Of the rainbow | |
| Of the inner rainbow | [p. 394 395 398 399] |
| Of the outter bow | [p. 396 397 400] |
| Of a particular appearance in the inner rainbow | [p. 401] |
| Conclusion | [p. 405] |
ERRATA.
PAGE 25. line 4. read In these Precepts. p. 40. l. 24. for I read K. p. 53. l. penult. f. Æ. r. F. p. 82. l. ult. f. 40. r. 41. p. 83 l. ult. f. 43. r. 45. p. 91. l. 3. f. 48. r. 50. ibid. l. 25. for 49. r. 51. p. 92. l. 18. f. A G F E. r. H G F C. p. 96. l. 23. dele the comma after {⅓}. p. 140. l. 12. dele and. p. 144. l. 15. f. threefold. r. two-fold. p. 162. l. 25. f. {⅓}. r. {⅞}. p. 193. 1. 2. r. always. p. 199. l. penult. and p. 200. l. 3. 5. f. F. r. C. p. 201. l. 8. f. ascends. r. must ascend. ibid. l. 10. f. it descends. r. descend. p. 208. l. 14. f. W T O. r. N T O. In fig. 110. draw a line from I through T, till it meets the circle A D C B, where place W. p. 216. l. penult. f. action. r. motion. p. 221. l. 23. f. A F. r. A H. p. 232. l. 23. after invention put a full point. p. 253. l. penult. delete the comma after remarkable. p. 255. l. ult. f. D E. r. B E. p. 278. l. 17. f. ξ τ. r. ξ π. p. 299. l. 19 r. the. p. 361. l. 12. f. I. r. t. p. 369. l. 2, 3. r. Pseudo-topaz. p. 378. l. 12. f. that. r. than. p. 379. l. 15. f. converge. r. diverge. p. 384. l. 7. f. optic-glass. r. optic-nerve. p. 391. l. 18. r. as 50 to 78. p. 392. l. 18. after telescope add be about 100 feet long and the. in fig. 161. f. δ put ε. p. 399. l. 8. r. A n, A x. &c. p. 400. 1. 19. r. A π, A ρ. A σ, A τ. A φ. p. 401. l. 14. r. fig. 163. The pages 374, 375, 376 are erroneously numbered 375, 376, 377; and the pages 382, 383 are numbered 381, 382.
A LIST of such of the
SUBSCRIBERS NAMES
As are come to the Hand of the
AUTHOR.
A
MOnseigneur d’Aguesseau, Chancelier de France
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Capt. George Abell
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Thomas Abney, Esq;
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B
His Grace the Duke of Bedford
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Rt. Rev. Lord Bishop of Bristol
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Mr David Barclay
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Y
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