# Archimedes Quotes

130 Archimedes Quotes

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Give me a fulcrum on which to rest, and I will move the earth.

Archimedes

Those who claim to discover everything but produce no proofs of the same may be confuted as having actually pretended to discover the impossible.

Archimedes

Stand away, fellow, from my diagram.

Archimedes

Give me a place to stand on, and I can move the earth.

(Also):

Give me a place to stand, and I will move the earth.

Give me a place to stand, and I can move the earth.

Archimedes

If I was given another earth, I would cross over to it and move this one.

Archimedes

There are some, King Gelon, who think that the number of the sand is infinite in multitude…

Archimedes

[On King Hiero and Archimedes talking and Archimedes saying that it was quite easy to apply mathematics to real things] In fact, I have figured it out carefully, and there is no weight, anywhere, that could not be not be moved if enough force were applied. Had I but another earth on which to stand, my friend, I could move this earth itself.

Archimedes

Now it is easy to see that this is impossible; for, since the centre of the sphere has no magnitude, we cannot conceive it to bear any ratio whatever to the surface of the sphere.

Archimedes

With a given force it is possible to move any given weight. And by the strength of the proof, if there was another world and I could go to it, I would move this one.

Archimedes

Compute the number of the oxen of the sun, giving thy mind thereto, if thou hast a share of wisdom.

Archimedes

I have decided to write down and make known the method partly because we have already talked about it heretofore and so no one would think that we were spreading abroad idle talk…

Archimedes

Eureka! Eureka! (I have found, I have found it!)

Archimedes

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 the proof without any previous knowledge.

Archimedes

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.

Archimedes

Give me some other great weight and I will move it myself with no help from any man.

Archimedes

[King Hiero said ‘I have in my fleet a new ship with three masts, so big and heavy that so far the combined strength of all my slaves who work on the docks has not been enough to move it from the slip. Move that weight singlehanded, Archimedes, and I will believe your story.] I accept your challenge. [He achieved this and King Hiero said that from that point on Archimedes word was to be accepted on every subject.]

Archimedes

[On the theorm that circles are to one another as the squares on their diameters] Of unequal lines, unequal surfaces, or unequal solids, the greater exceeds the less by such a magnitude as is capable, if added [continually] to itself of exceeding any given magnitude of those which are comparable with one another.

Archimedes

[On supervising the construction of a great ship for [King] Hieron II it contained a] Chamber dedicated to Aphrodite [Goddess of love], with three couches.

Archimedes

[On being approached by a Roman Solider and ordered to follow him to Marcellus] Disturb not my circle. Hold off for a moment, till I have finished my problem.

Archimedes

Fellow, stand away from my diagram.

Archimedes

Don’t disturb my circles (Noli turbare circulos meos.)

Archimedes

Please don’t disturb this. (Noli obsecro istum disturbare.)

Archimedes

[To his friends and kinsmen he besought them to place on his grave] …A cylinder enclosing a sphere, with an inscription giving the proportion by which the volume of the cylinder exceeds that of the sphere.

Archimedes

Though I had often tried to investigate them previously, I had failed to arrive at because I found their discovery attended with some difficulty. And this is why even the propositions themselves were not published with the rest. But afterwards, when I had studied them with greater care, I discovered what I had failed in before.

Archimedes

Let straight lines be conceived to be drawn.

Archimedes

The proposition is therefore obvious, or is proved.

Archimedes

The lever arm times the area of one equals a constant times the area of the other.

Archimedes

Any object completely or partially submerged in a fluid is buoyed up by a force with magnitude equal to the weight of the fluid displaced by the object.

Archimedes

I have found it!

Archimedes

After I had thus perceived that the surface of a sphere is four times as great as its largest circle, in which I proceeded from the idea that just as a circle is equal to a triangle whose base is the periphery of the circle, and whose altitude is equal to its radius, so a sphere is equal to a cone whose base is the same as the surface of the sphere and whose altitude is equal to the radius of the sphere.

Archimedes

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 that no number has been named which is great enough to exceed its multitude.

Archimedes

If they imagined a mass made up of sand in other respects as large as the mass of the earth, including in it all the seas and the hollows of the earth filled up to a height equal to that of the highest of the mountains, would be many times further still from recognising that any number could be expressed which exceeded the multitude of the sand so taken.

Archimedes

I will try to show you, by means of geometrical proofs, which you will be able to follow, that, of the numbers named by me and given in the work which I sent to Zeuxippus, some exceed not only the number of the mass of sand equal in magnitude to the earth filled up in the way described, but also that of a mass equal in magnitude to the universe.

Archimedes

You are aware that ‘universe’ is the name given by most astronomers to the sphere the centre of which is the centre of the earth and whose radius is equal to the straight line between the centre of the sun and the centre of the earth. This is the common account, as you have heard from astronomers. But Aristarchus of Samos brought out a book consisting of some hypotheses, in which the premisses lead to the result that the universe is many times greater than that now so called.

Archimedes

His [Aristarchus of Samos] hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun in the circumference of a circle, the sun lying in the middle of the orbit, and that the sphere of the fixed stars, situated about the same centre as the sun, is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed stars as the centre of the sphere bears to its surface. Now it is easy to see that this is impossible; for, since the centre of the sphere has no magnitude, we cannot conceive it to bear any ratio whatever to the surface of the sphere.

Archimedes

We must however take Aristarchus to mean this: since we conceive the earth to be, as it were, the centre of the universe, the ratio which the earth bears to what we describe as the ‘universe’ is the same as the ratio which the sphere containing the circle in which he supposes the earth to revolve bears to the sphere of the fixed stars. For he adapts the proofs of his results to a hypothesis of this kind, and in particular he appears to suppose the magnitude of the sphere in which he represents the earth as moving to be equal to what we call the ‘universe.’

Archimedes

I say then that, even if a sphere were made up of the sand, as great as Aristarchus supposes the sphere of the fixed stars to be, I shall still prove that, of the numbers named in the Principles [a ‘lost’ work of Archimedes], some exceed in multitude the number of the sand which is equal in magnitude to the sphere referred to, provided that the following assumptions be made…

Archimedes

The perimeter of the earth is about 3,000,000 stadia and not greater. It is true that some have tried, as you are of course aware, to prove that the said perimeter is about 300,000 stadia. But I go further and, putting the magnitude of the earth at ten times the size that my predecessors thought it, I suppose its perimeter to be about 3,000,000 stadia and not greater.

Archimedes

The diameter of the earth is greater than the diameter of the moon, and the diameter of the sun is greater than the diameter of the earth. In this assumption I follow most of the earlier astronomers.

Archimedes

The diameter of the sun is about 30 times the diameter of the moon and not greater. It is true that, of the earlier astronomers, Eudoxus declared it to be about nine times as great, and Phedias my father twelve times, while Aristarchus tried to prove that the diameter of the sun is greater than 18 times but less than 20 times the diameter of the moon. But I go even further than Aristarchus, in order that the truth of my proposition may be established beyond dispute, and I suppose the diameter of the sun to be about 30 times that of the moon and not greater.

Archimedes

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