Roy Lotz’s Reviews > The Works of Archimedes > Status Update

If thou art able, O stranger, to find out all these things and gather them together in your mind, giving all the relations, thou shall depart crowned with glory and knowing that thou hast been adjudged perfect in this species of wisdom.

The surface of any fluid at rest is the surface of a sphere whose centre is the same as that of the earth.

I conceive that these things, King Gelon, will appear incredible to the great majority of people who have not studied mathematics, but that to those who are conversant therewith and have given thought to the question of the distances and sizes of the earth, the sun, the moon, and the whole universe, the proof will carry conviction.

There are some, King Gelon, who think that the number of the sand is infinite in multitude; and I mean by the sand not only that which exists about Syracuse and the rest of Sicily but also that which is found in every region, whether inhabited or uninhabited. Again there are some who, without regarding it as infinite, yet think no number has been named which is great enough to exceed the multitude.

I postulate the following: 1. Equal weights at equal distances are in equilibrium, and equal weights at unequal distances are not in equilibrium but incline toward the weight which is at the greater distance. 2. If, when weights at certain distances are in equilibrium, something be added to one of the weights, they are not in equilibrium but incline towards that weight to which the addition was made.

My adventure in Greek mathematics continues. I fear, however, that there is a very low ratio of enlightenment to effort in my case.