Any solid lighter than a fluid will, if placed in the fluid, be so far immersed that the weight of the solid will be equal to the weight of the fluid displaced.
On floating bodies I, prop 5.
Archimedes to Eratosthenes greeting. ... certain things first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards because their investigation by the said method did not furnish an actual demonstration. But it is of course easier, when we have previously acquired by the method, some knowledge of the questions, to supply the proof than it is to find it without any previous knowledge.
The Method in The Works of Archimedes translated by T L Heath (Cambridge 1912)
I have found [it].
Vitruvius, De Architectura ix, 215
Give me a place to stand and I will move the earth.
On the lever in Pappus Synagoge
Noli turbare circulos meos.
Do not disturb my circles!
Last words. Sometimes reported as:
Soldier, stand away from my diagram.
There are things which seem incredible to most men who have not studied mathematics.
Quoted in D MacHale, Comic Sections (Dublin 1993)
Having been the discoverer of many splendid things, he is said to have asked his friends and relations that, after his death, they should place on his tomb a cylinder enclosing a sphere, writing on it the proportion of the containing solid to that which is contained.
Plutarch, Life of Marcellus
If thou art able, O stranger, to find out all these things and gather them together in your mind, giving all the relations, thou shalt depart crowned with glory and knowing that thou hast been adjudged perfect in this species of wisdom.
Preamble to the Cattle problem