Did Archimedes Discover the Law of Buoyancy?

Most venerated Supreme Court Justice Bryer in his Prometheus decision (a patent case issued recently by the US Supreme Court) wrote a long aside on the fact that Archimedes discovered the law of nature of buoyancy, and that such a discovery would not be patentable under modern US Patent Laws.

But did Aristotle discover the laws of buoyancy?  Was Prometheus chained to a rock for daring to defy the Gods and bring fire to humans?  Well, some things are myth, and others are mystery, and others are merely the stuff of legend.  We shall see which is which here.

This claim to fame for our Archimedes rests primarily on two treastises attributed to our Syracusan Scholar, On Floating Bodies I, and On Floating Bodies II, and primarily to On Floating Bodies I (see Heath, The Works of Aristotle, 1953).

However, Heath, the pre-eminent historian of Greek Mathematics, points out that the only extent Greek original manuscript of Archimedes of Syracuse was, in fact, lost, and that there is and was no original Greek manuscript for the treatises "On Floating Bodies I" or "On Floating Bodies II".  Moreoever, when the noted Renaissance humanist, attorney and mathematician Tartaglia first published his Latin translation of the Works of Archimedes, he entirely omitted both these works entirely--they only appear in a later edition re-compiled from another Latin translation.

It is known that there was an anonymous Latin poem circa 500 AD which credits Archimedes with the discovery of the principle of buoyancy, but that is not, as lawyers say, the best evidence.  Moreover, Archimedes was such a legendary figure that by hundreds of years later, and in the Dark Ages, scholars were crediting him with all sorts of discoveries.

 SYRACUSE - THE GREATEST AND RICHEST OF GREEK CITIES

LAY ON THE SOUTHEAST CORNER OF SIKILIA OR SICILY IN 

MAGNA GRAECIA.  IT WAS THE HOME OF ARCHMEDES.

 THE SCREW OF ARCHIMEDES WOULD

OBVIOUSLY HAVE BEEN PATENTABLE

HERE'S ONE ARTIST'S EMBODIMENT DRAWING

THEY DIDN'T HAVE PATENTS IN 250 BC THEY

KEPT ROYAL SECRETS AND PAID THE ROYAL INVENTOR

HANDSOMELY OR KEPT HIM LOCKED UP

Heath, the Works of Archimedes, Introduction, p. xxvii.

explaining that the manuscript of Tartaglia did not contain a greek original 

of de insidentibus aquae "on floating objects" which is the alleged source

of the claim that Archimedes discovered the principle of buoyancy

Heath, the Works of Archimedes, Introduction, p. xxvii, footnote, explaining that the extant

Greek fragments of de insidentibus aquae "on floating objects" which is the alleged source

of the claim that Archimedes discovered the principle of buoyancy are of doubtful authenticity

Critical to understanding this argument, according to Heath, is the fact that thru the Middle Ages, and even under the watchful eye of the libraries of the Eastern Roman Empire of Constantinople, only three actual works of Archimedes survived, and none of them dealt with buoyancy or on floating objects; when a greek manuscript did surface and made its way to Italy in the Renaissance, it was copied twice, but the original was lost.  It is thought that Cardinal Bessarion, the great Greek Byzantine Scholar, had a copy, but we no longer possess his copy either, and both the original and the copy have been lost, and there are currently only two copies of greek texts extant, neither of which contain the treatises "on floating objects".

Next, Archimedes wrote in a Dorian dialect.  For those unfamiliar with Ancient Greek, it was written in three main dialects--Ionian, prevalent in Asia Minor (which was mainly Greek until 1923), Attic, which was spoken most prevalently in Athens @450 BC (the so-called "Golden Age") and Dorian, which was popular in Magna Graecia (Southern Italy was mainly Greek well into Siculo-Norman and Angevin rule in the 1300s, and still retains many distinct characteristics which separate it from the Northern Italians) as well as the Pelopponese.  

Archimedes wrote in the Dorian dialect, and thus, without an original Greek manuscript, the genuineness of the two books on buoyancy can neither be admitted nor denied.  

This is the taxonomy of all the original manuscripts written during the Renaissance humanist period according to Heath:

Heath, The Works of Aristotle, Introduction, p. xxx.  

For more information on all of these, one should consult Heath.  What is critical is that the two treatises on buoyancy do not actually appear until the edition of Commandinus in 1558, according to Heath, and then only in Latin.  That does certain seem odd, considering taht there are several prior editions of Archimides as well as several greek texts extent during the 1400s in uncial manuscripts.

It seems to imply, though one cannot conclude, that these two manuscripts may or might be spurious, and that Archimedes may not, in fact, be the author of these two treatises at all.

Of course, there are many stories about Archimedes having a brilliant revelation in his bathtub about the weighing of the two crowns, and rushing down the street yelling "eureka eureka" which means in greeek, "i have discovered or found it".  It is certainly possible he solved the problem of the crowns but was not the author of the treatises.

The primary source for this is located in VITRUVIUS, a roman architect, who wrote about 300 years later, around 50 AD, the following story:

 9. Archimedis vero cum multa miranda inventa et varia fuerint, ex omnibus etiam infinita sollertia id quod exponam videtur esse expressum. nimirum Hiero Syracusis auctus regia potestate, rebus bene gestis cum auream coronam votivam diis inmortalibus in quodam fano constituisset ponendam, manupretio locavit faciendam et aurum ad sacoma adpendit redemptori. is ad tempus opus manu factum subtiliter regi adprobavit et ad sacoma pondus coronae visus est praestitisse.

 10. posteaquam indicium est factum dempto auro tantundem argenti in id coronarium opus admixtum esse, indignatus Hiero se contemptum esse neque inveniens qua ratione id furtum deprehenderet, rogavit Archimeden uti insumeret sibi de eo cogitationem. tunc is cum haberet eius rei curam, casu venit in balineum ibique cum in solium descenderet, animadvertit quantum corporis sui in eo insideret tantum aquae extra solium effluere. idque cum eius rei rationem explicationis ostendisset, non est moratus sed exsiluit gaudio motus de solio et nudus vadens domum versus significabat clara voce invenisse quod quaereret. nam currens identidem graece clamabat ευρηκα ευρηκα.

 11. tum vero ex eo inventionis ingressu duas fecisse dicitur massas aequo pondere quo etiam fuerat corona, unam ex auro et alteram ex argento. cum ita fecisset, vas amplum ad summa labra implevit aqua, in quo demisit argenteam massam. cuius quanta magnitudo in vase depressa est, tantum aquae effluxit. ita exempta massa quanto minus factum fuerat refudit sextario mensus, ut eodem modo quo prius fuerat ad labra aequaretur. ita ex eo invenit quantum pondus argenti ad certam aquae mensuram responderet.

 12. cum id expertus esset, tum auream massam similiter pleno vase demisit et ea exempta eadem ratione mensura addita invenit deesse aquae non tantum sed minus, quanto minus magno corpore eodem pondere auri massa esset quam argenti. postea vero repleto vase in eadem aqua ipsa corona demissa invenit plus aquae defluxisse in coronam quam in auream eodem pondere massam, et ita ex eo quod defuerit plus aquae in corona quam in massa, ratiocinatus deprehendit argenti in auro mixtionem et manifestum furtum redemptoris.

9. Though Archimedes discovered many curious matters which evince great intelligence, that which I am about to mention is the most extraordinary. Hiero, when he obtained the regal power in Syracuse, having, on the fortunate turn of his affairs, decreed a votive crown of gold to be placed in a certain temple to the immortal gods, commanded it to be made of great value, and assigned an appropriate weight of gold to the manufacturer. He, in due time, presented the work to the king, beautifully wrought, and the weight appeared to correspond with that of the gold which had been assigned for it.

10. But a report having been circulated, that some of the gold had been abstracted, and that the deficiency thus caused had been supplied with silver, Hiero was indignant at the fraud, and, unacquainted with the method by which the theft might be detected, requested Archimedes would undertake to give it his attention. Charged with this commission, he by chance went to a bath, and being in the vessel, perceived that, as his body became immersed, the water ran out of the vessel. Whence, catching at the method to be adopted for the solution of the proposition, he immediately followed it up, leapt out of the vessel in joy, and, returning home naked,º cried out with a loud voice that he had found that of which he was in search, for he continued exclaiming, in Greek, εὑρηκα, (I have found it out).

11. After this, he is said to have taken two masses, each of a weight equal to that of the crown, one of them of gold and the other of silver. Having prepared them, he filled a large vase with water up to the brim, wherein he placed the mass of silver, which caused as much water to run out as was equal to the bulk thereof. The mass being then taken out, he poured in by measure as much water as was required to fill the vase once more to the brim. By these means he found out what quantity of water was equal to a certain weight of silver.

12. He then placed the mass of gold in the vessel, and, on taking it out, found that the water which ran over was lessened, because, as the magnitude of the gold mass was smaller than that containing the same weight of silver. After again filling the vase by measure, he put the crown itself in, and discovered that more water ran over then than with the mass of gold that was equal to it in weight; and thus, from the superfluous quantity of water carried over the brim by the immersion of the crown, more than that displaced by the mass, he found, by calculation, the quantity of silver mixed with the gold, and made manifest the fraud of the manufacturer.b

Marcus Vitruvius Pollio:
de Architectura, Book IX

http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Vitruvius/9*.html 

Now Vitruvius is one of the most important writers of the Renaissance, but in fact, he himself was not rediscovered until the Renaissance either--around the mid-1400s or so.

So consequently, no one really knew this story about Archimedes for a very long time, or perhaps it was known, or perhaps Vitruvius embellished it.  

What we don't have is the original papers of Archimedes published by Vitruvius.

The mere discovery or story by Vitruvius would not make Archimedes the discoverer of buyoancy, since whatever Archimedes actually knew, he told no one, and took his secrets to his grave.  

Sci Fi writer (and Greek Harvard grad Thania Papas St. John, Mather House Class of 1983) has certainly put this Eureka story to good use on her syfy show Eureka, and recently also recycled a Greek theme on Grimm with "the three coins of Zakynthos".  

http://en.wikipedia.org/wiki/Eureka_(TV_series) 

The executive producers of the current season are Paglia, Charles Grant Craig, and Thania St. John. Id.

http://www.hulu.com/watch/335787/grimm-the-coins-of-zakynthos 

http://en.wikipedia.org/wiki/Thania_St._John 

But is this all mythology, or is this empirically verifiable?  Today, scholars publish, inventors patent or keep trade secrets in a vault, and we can verify empirically.  But how can we separate myth, legend, fact and mystery with the ancients? 

Without an actual greek original text, it's really hard to say.  Heath, who is the foremost Greek scholar on Archimedes, does include the two texts on buoyancy, but his comments in the foreword also cast doubts in part on their authenticity if one reads them closely.

So this remains an open questions.

Did Aristotle discover the principle of buoyancy?  Not settled in this scholar's humble opinion, and more importantly, not really settled in Prof. Heath's text.  

If you read Wikipedia, this is one case where you really have to study the books to get it right.  Fortunately Prof. Heath's able text is available for PDF download on Google books and can be studied by anyone, though I do recommend some knowledge of geometry and ancient greek as the proofs are rigourous.

T.L.Heath, The Works of Archimedes (Cambridge, 1953) google books (scanned from U Michigan Libraries). (available for free download)

http://books.google.com/books?id=M93q1XYZU0UC&printsec=frontcover&dq=Heath+archimedes&hl=en&sa=X&ei=u1VrT_q2Cc6Etgeku8TBBg&ved=0CEIQ6AEwAA#v=onepage&q=Heath%20archimedes&f=false 

Also, one can download Tartaglia's original books in the original Italian if one is so disposed, as well.

And, if he did discover it, it was not merely a law of nature he discovered, he also disclosed a method and apparatus of weighing comparable weights of crowns to determine whether one or the other was adulterated with baser metals than gold.

So that would clearly be patentable.  Useful, nonobvious and novel and clearly an embodiment going well beyond a mere law of nature.  Since they didn't have patents in 250 BC, Archimedes and his king Hieron of Syracuse merely kept state secrets, and Archimedes just became wealthy.  

Which is why at the siege of Syracuse during the Second Punic Wars, the Romans tried to capture Archimdes--because in 250 BC, capturing the enemy's scientist was tantamount to capturing their intangible assets portfolio.  It was as valuable as looting the gold of their treasury.  

No one remotely familiar with ancient scientific or greek scientific history can possibly believe that the ancient world actually shared valuable secrets freely.  Rather, they were kept secret for the benefit of the inventor's city state, and the inventors were handsomely rewarded.  Aristotle tutored Alexander the Great, and Alexander conquered the World.  Plato was of service to many well-known tyrants, and was a known advocate of the aristocratic party.  And Archimedes was loyal to Syracuse, and constructed many novel weapons used to crash Roman ships against the rocks, and delay and nearly defeat the Roman siege of Syracuse.  He was a true hero of Greek freedom.  

Moreover, we do know that the Lord spoke to Noah in Genesis and told Noah to build an Ark, and that the flood legend is prevalent in all cultures.  And that Noah built the Ark and knew it would float when the Great Flood came.  So perhaps the principle of buoyancy, like so many other principles, was perhaps divinely revealed.  

It is commendable of Justice Breyer to look to the Ancient Greeks for inspiration in resolving a scientific question and especially Archimedes, that greatest of all Greek mathematicians.

"Except for the forces of nature herself, there is nothing in our world that is not Greek in its origin"

--Sir Henry Sumner Maine

--Art Kyriazis