Department of Mathematics, Statistics
and Computer Science
Wim Ruitenburg's Fall 2009 MATH 1300-101
The Method of Mechanical Theorems
Athina Stanitsa made the presentation material re The Method by
Archimedes of Syracuse.
Archimedes
Archimedes of Syracuse died in 212 BC, when his home town fell to the Roman
Republic after a siege of two years.
His city happened to have chosen the losing side in the Second Punic War
between Carthage and Rome.
His death is often associated with the beginning of the decline of intellectual
inquiry.
The Romans failed to capture him alive; Archimedes was highly admired for his
impressive engineering skills.
Our interest is in his mathematical work.
Archimedes determined areas and volumes of figures and solids with a skill
which apparently surpassed the abilities of all his contemporaries.
The Method
Archimedes calculated areas and volumes by procedures that fall within the
constraints of Euclidean geometry as it was understood at the time.
However, that was not the way by which he originally discovered such answers.
Archimedes used other methods, some related to modern Newtonian infinitesimal
calculus, to establish the true answers, before proving them correct by
Euclidean means.
In his document The Method of Mechanical Theorems, or The Method,
Archimedes describes the process of discovery of these truths, which precede
his later Euclidean proofs.
- Printing presses did not yet exist, so The Method was widely
copied by hand.
- As the copies deteriorated over time, new manual copies were made, and
so on.
All may have disappeared, except one.
The copy that we are interested in, is a book written shortly before 1000 AD.
This book also contains some other works by Archimedes.
- A few centuries later the book is taken apart, the pages scraped so that
the text becomes almost invisible to the human eye, cut in two, rotated 90
degrees, and rebound in a book half the former size.
On the scraped surface, a scribe writes healing prayers.
Such a book of re-used parchment is called a palimpsest.
- Scholars and others notice the book in the 19th century, in the library
of the Church of the Holy Sepulchre in Constantinople.
In 1906, Johan Heiberg photographs the pages, and tries to read the barely
visible underlying text.
- After the end of the first world war in 1918, the book is gone.
- In 1971, one leaf of the book is found in the Nachlass of a
person in Oxford.
It seems that this person had ripped it out of the book in the library in
Constantinople, some time in the 19th century.
- In 1991, a family in Paris asks experts of Christie's auction house to
appraise an ancient book with healing prayers, under which there apparently is
some mathematical text.
A family member had bought the text from a dealer in Istanbul some time in the
1930s.
The palimpsest is found.
- In 1998, the book is sold for 2 million dollars to an unknown bidder.
- With strong support of the owner, the book is held for restoration and
study at the Walters Art Museum in Baltimore.
A broad international team of researchers is actively restoring the original
mathematical text, using the latest technologies.
Experts hope that The Method will be completely recovered.
Last updated: November 2009
Comments and suggestions to wimr@mscs.mu.edu