Fall 1999: Week 12

IN VIRI PRAESTANTISSIMI
ISAACI NEWTONI
OPUS HOCCE MATHEMATICO-PHYSICUM
SECULI GENTISQUE NOSTRAE
DECUS EGREGIUM

TO THE ILLUSTRIOUS MAN
ISAAC NEWTON
AND THIS HIS WORK DONE IN FIELDS OF THE MATHEMATICS AND PHYSICS A SINGLE DISTINCTION OF OUR TIME AND RACE

En tibi norma poli, et divae libramina molis,
Computus en Jovis; et quas, dum primordia rerum
Pangeret, omniparens leges violare Creator
Noluit, atque operum quae fundamenta locarit.
Intima panduntur victi penetralia coeli,
Nec latet extremos quae vis circumrotat orbes.
Sol solio residens ad se jubet omnia prono
Tendere descensu, nec recto tramite currus
Sidereos patitur vastum per inane moveri;
Sed rapit immotis, se centro, singula gyris.
Jam patet horrificis quae sit via flexa cometis;
Jam non miramur barbati phaenomena astri.
Discimus hinc tandem qua causa argentea Phoebe
Passibus haud aequis graditur; cur subdita nulli
Hactenus astronomo numerorum fraena recuset:
Cur remeant nodi, curque auges progrediuntur.
Discimus et quantis refluum vaga Cynthia pontum
Viribus impellit, fessis dum fluctibus ulvam
Deserit, ac nautis suspectas nudat arenas;
Alternis vicibus suprema ad littora pulsans.
Quae toties animos veterum torsere sophorum,
Quaeque scholas frustra rauco certamine vexant,
Obvia conspicimus, nubem pellente mathesi.
Jam dubios nulla caligine praegravat error,
Queis superum penetrare domos atque ardua coeli
Scandere sublimis genii concessit acumen.
Surgite, mortales, terrenas mittite curas;
Atque hinc coeligenae vires dignoscite mentis,
A pecudum vita longe lateque remotae.
Qui scriptis jussit tabulis compescere caedes,
Furta et adulteria, et perjurae crimina fraudis;
Quive vagis populis circundare moenibus urbes
Auctor erat; Cererisve beavit munere gentes;
Vel qui curarum lenimen pressit ab uva;
Vel qui Niliaca monstravit arundine pictos
Consociare sonos, oculisque exponere voces;
Humanam sortem minus extulit: utpote pauca
Respiciens miserae tantum solamina vitae.
Jam vero superis convivae admittimur, alti
Jura poli tractare licet, jamque abdita caecae
Claustra patent Terrae, rerumque immobilis ordo,
Et quae praeteriti latuerunt secula mundi.
Talia monstrantem mecum celebrate camoenis,
Vos O coelicolum gaudentes nectare vesci,
Newtonum clausi reserantem scrinia veri,
Newtonum Musis charum, cui pectore puro
Phoebus adest, totoque incessit numine mentem:
Nec fas est propius mortali attingere divos.

EDM. HALLEY

Lo, for your gaze, the pattern of the skies!
What balance of the mass, what reckonings
Divine! Here ponder too the Laws which God,
Framing the universe, set not aside
But made the fixed foundations of his work.
The inmost places of the heavens, now gained,
Break into view, nor longer hidden is
The force that turns the farthest orb. The sun
Exalted on his throne bids all things tend
Toward him by inclination and descent,
Nor suffers that the courses of the stars
Be straight, as through the boundless void they move,
But with himself as centre speeds them on
In motionless eclipses. Now we know
The sharply veering ways of comets, once
A source of dread, nor longer do we quail
Beneath appearances of bearded stars.
At last we learn wherefore the silver moon
Once seemed to travel with unequal steps,
As if she scorned to suit her pace to numbers–
Till now made clear to no astronomer;
Why, though the Seasons go and then return,
The Hours move ever forward on their way;
Explained too are the forces of the deep,
How roaming Cynthia bestirs the tides,
Whereby the surf, deserting now the kelp
Along the shore, exposes shoals of sand
Suspected by the sailors, now in turn
Driving its billows high upon the beach.
Matters that vexed the minds of ancient seers,
And for our learned doctors often led
To loud and vain contention, now are seen
In reason’s light, the clouds of ignorance
Dispelled at last by science. Those on whom
Delusion cast its gloomy pall of doubt,
Upborne now on the wings that genius lends,
May penetrate the mansions of the gods
And scale the heights of heaven. O mortal men,
Arise! And, casting off your earthly cares,
Learn ye the potency of heaven-born mind,
Its thought and life far from the herd withdrawn!
The man who through the tables of the laws
Once banished theft and murder, who suppressed
Adultery and crimes of broken faith,
And put the roving peoples into cities
Girt round with walls, was founder of the state,
While he who blessed the race with Ceres’ gift,
Who pressed from grapes an anodyne to care,
Or showed how on the tissue made from reeds
Growing beside the Nile one may inscribe
Symbols of sound and so present the voice
For sight to grasp, did lighten human lot,
Offsetting thus the miseries of life
With some felicity. But now, behold,
Admitted to the banquets of the gods,
We contemplate the polities of heaven;
and spelling out the secrets of the earth,
Discern the changeless order of the world
And all the aeons of its history.
Then ye who now on heavenly nectar fare,
Come celebrate with me in song the name
Of Newton, to the Muses dear; for he
Unlocked the hidden treasuries of Truth:
So richly through his mind had Phoebus cast
The radiance of his own divinity.
Nearer the gods no mortal may approach.

AXIOMATA, sive
LEGES MOTUS

AXIOMS, or
LAWS OF MOTION

LEX I.

Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impresssis cogitar statum illum mutare.

Projectilia perseverant in motibus suis, nisi quatenus a resistentia aeris retardantur, et vi gravitatis impelluntur deorsum. Trochus, cujus partes cohaerendo perpetuo retrahunt sese a motibus rectilineis, non cessat rotari, nisi quatenus ab aere retardatur. Majora autem Planetarum et Cometarum corpora motus suos et progressivos et circulares in spatiis minus resistentibus factos conservant diutius

LAW I.

Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it.

Projectiles continue in their motions, so far as they are not retarded by the resistance of the air, or impelled downwards by the force of gravity. A top, whose parts by their cohesion are continually drawn aside from rectilinear motions, does not cease its rotation, otherwise than as it is retarded by the air. The greater bodies of the planets and comets, meeting with less resistance in freer spaces, preserve their motions both progressive and circular for a much longer time.

LEX II.

Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur.

Si vis aliqua motum quemvis generet; dupla duplum, tripla triplum generabit, sive simul et semel, sive gradatim et successive impressa fuerit. Et hic motus (quoniam in eandem semper plagam cum vi generatrice determinatur) si corpus antea movebatur, motui ejus vel comspiranti additur, vel contrario subducitur, vel obliquo oblique adjicitur, et cum eo secundum utriusque determinationem componitur.

LAW II.

The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.

If any force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively. And this motion (being always directed the same way with the generating force), if the body moved before, is added to or subtracted from the former motion, according as they directly conspire with or are directly contrary to each other; or oblique joined, when they are oblique, so as to produce a new motion compounded from the determination of both.

LEX III.

Actioni contrariam semper et aequalem esse reactionem: sive corporum duorum actiones in se mutuo semper esse aequales et in partes contrarias dirigi.

Quicquid premit vel trahit alterum, tantundem ab eo premitur vel trahitur. Si quis lapidem digito premit, premitur et huius digitus a lapide. Si equus lapidem funi alligatum trahit, retrahetur etiam et equus (ut ita dicam) aequaliter in lapidem: nam funis utrinque distentus eodem relaxandi se conatu urgebit equum versus lapidem, ac lapidem versus equum; tantumque impediet progressum unius quantum promovet progressum alterius. Si corpus aliquod in corpus aliud impingens, motum ejus vi sua quomodocunque mutaverit, idem quoque vicissim in motu proprio eandem mutationem in partem contrariam vi alterius (ob aequalitatem pressionis mutuae) subibit. His actionibus aequales fiunt mutationes, non velocitatum, sed motuum; scilicet in corporibus non aliunde impeditis. Mutationes enim velocitatum, in contrarias itidem partes factae, quia motus aequlaiter mutantur, sunt corporibus reciproce proportionales. Obtinet etiam haec Lex in Attractionibus, ut in Scholio proximo probabitur.

LAW III.

To every action there is always opposed an equal reaction: or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

Whatever draws or presses another is as much drawn or pressed by that other. If you press a stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied to a rope, the horse (if I may so say) will be equally drawn back to the stone; for the distended rope, by the same endeavor to relax or unbend itself, will draw the horse as much towards the stone as it does the stone towards the horse, and will obstruct the progress of the one as much as it advances that of the other. If a body impinge upon another, and by its force change the motion of the other, that body also (because of the equality of the mutual pressure) will undergo an equal change, in its own motion, towards the contrary part. The changes made by these actions are equal, not in the velocities but in the motions of bodies; that is to say, if the bodies are not hindered by any other impediments. For, because the motions are equally changed, the changes of the velocities made towards contrary parts are inversely proportional to the bodies. This law takes place also in attractions, as will be proved in the next Scholium.