# Mathematician:Archimedes of Syracuse/Writings

## Mathematician

These works of Archimedes have survived in some form:

*On Plane Equilibriums*(2 books)*On the Quadrature of the Parabola**The Method*(which includes the calculation of the volume of a sphere)*On the Sphere and Cylinder*(2 books)*On Conoids and Spheroids**On Spirals**On Floating Bodies*(2 books)*Measurement of a Circle**The Sand-Reckoner*

The following works appear no longer to exist:

*On Sphere-making*, believed to have dealt with the techniques for building his solar system model- A work on semiregular polyhedra, mentioned by Pappus of Alexandria
- A work on the number system proposed in
*The Sand-Reckoner*, mentioned by Archimedes himself *On balances and levers*mentioned by Pappus of Alexandria- A treatise about mirrors, mentioned by Theon of Alexandria

## Historical Note

Heron of Alexandria, Pappus of Alexandria and Theon of Alexandria all reference works of Archimedes which no longer exist.

It is therefore clear that such works were still in existence in Alexandria as late as the $3$rd or $4$th century CE.

Eutocius of Ascalon wrote commentaries of *On Plane Equilibriums*, *On the Sphere and Cylinder* and *Measurement of a Circle*.

However, he makes no mention of *On the Quadrature of the Parabola* or *On Spirals*, so it is supposed he did not have access to them.

Isidorus of Miletus revised the commentaries of Eutocius on *Measurement of a Circle* and *On the Sphere and Cylinder*.

It also appears that Isidorus also translated, updated and added interpretations for ease of comprehension.

But at that time there appears to be no collected edition of Archimedes' works.

Leon the Mathematician gathered many of Archimedes' works during his restoration of the library of the University of Constantinople in the $9$th Century.

This passed:

- $12$th century: to the Norman court at Palermo, thence to House of Hohenstaufen
- $1266$: to the Pope by Charles of Anjou after the Battle of Benevento
- $1269$ to $1311$: in the Papal Library
- Some time after $1368$: passed into private hands
- $1491$: Belonged to Giorgius Valla, who translated part of it into his (posthumous) $1501$ work
*De Expetendis et Fugiendis Rebus* - $1500$: Bought by Albertus Pius
- $1530$: Passed to his nephew Rodolphus Pius
- $1544$ to $1564$: vanished without trace

In $1529$ William of Moerbeke translated the greater part of Archimedes' works into Latin.

The translation was hasty and occasionally misunderstood, but it was an attempt at a word-for-word translation and not an interpretation and commentary.

Included in these were *On Floating Bodies*, *On Plane Equilibriums* and *On the Quadrature of the Parabola*.

Several other translations can also be traced down through the ages.

Much of the later task of collating the various editions fell to Johan Ludvig Heiberg.

Most importantly, in $1906$ he discovered a hitherto unknown palimpsest containing *The Method*, practically intact.

## Sources

- 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.5$: Archimedes (ca. $\text {287}$ – $\text {212}$ B.C.) - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $2$: The Logic of Shape: Archimedes