A Quote by Pierre de Fermat
It is impossible for any number which is a power greater than the second to be written as a sum of two like powers. I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain.
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But it is impossible to divide a cube into two cubes, or a fourth power into fourth powers, or generally any power beyond the square into like powers; of this I have found a remarkable demonstration. This margin is too narrow to contain it.
I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain.
To divide a cube into two other cubes, a fourth power, or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it.
I have discovered a truly marvelous proof of this, which however the margin is not large enough to contain.
About Thomas Hobbes: He was 40 years old before he looked on geometry; which happened accidentally. Being in a gentleman's library, Euclid's Elements lay open, and "twas the 47 El. libri I" [Pythagoras' Theorem]. He read the proposition "By God", sayd he, "this is impossible:" So he reads the demonstration of it, which referred him back to such a proposition; which proposition he read. That referred him back to another, which he also read. Et sic deinceps, that at last he was demonstratively convinced of that truth. This made him in love with geometry.
The greater the state, the more wrong and cruel its patriotism, and the greater is the sum of suffering upon which its power is founded.
THE Constitution proposed by the convention may be considered under two general points of view. The FIRST relates to the sum or quantity of power which it vests in the government, including the restraints imposed on the States. The SECOND, to the particular structure of the government, and the distribution of this power among its branches.
Many people believe that the grains of sand are infinite in multitude ... Others think that although their number is not without limit, no number can ever be named which will be greater than the number of grains of sand. But I shall try to prove to you that among the numbers which I have named there are those which exceed the number of grains in a heap of sand the size not only of the earth, but even of the universe
Carnal embrace is sexual congress, which is the insertion of the male genital organ into the female genital organ for purposes of procreation and pleasure. Fermat’s last theorem, by contrast, asserts that when x, y and z are whole numbers each raised to power of n, the sum of the first two can never equal the third when n is greater than 2.
Every work of art reaches man in his inner powers. It reaches him more profoundly and insidiously than any rational proposition, either cogent demonstration or sophistry. For it strikes him with two terrible weapons, Intuition and Beauty, and at the single root in him of all his energies... Art and Poetry awaken the dreams of man, and his longings, and reveal to him some of the abysses he has in himself.
A true proposition is a proposition belief which would never lead to such disappointment so long as the proposition is not understood otherwise than it was intended.
The number of the fixed stars which observers have been able to see without artificial powers of sight up to this day can be counted. It is therefore decidedly a great feat to add to their number, and to set distinctly before the eyes other stars in myriads, which have never been seen before, and which surpass the old, previously known stars in number more than ten times.
The fundamental proposition of the apriorist theory is that knowledge is made up of two sorts of elements, which cannot be reduced into one another, and which are like two distinct layers superimposed one upon the other.
In my study I can lay my hand on the Bible in the pitch dark. All truly inspired ideas come from God. The powers from which all truly great composers like Mozart, Schubert, Bach and Beethoven drew their inspirations is the same power that enabled Jesus to do his miracles.
I go further, and affirm that bills of rights, in the sense and to the extent in which they are contended for, are not only unnecessary in the proposed Constitution, but would even be dangerous. They would contain various exceptions to powers not granted; and on this very account, would afford a colorable pretext to claim more than were granted. For why declare that things shall not be done which there is no power to do?
To make our position clearer, we may formulate it in another way. Let us call a proposition which records an actual or possible observation an experiential proposition. Then we may say that it is the mark of a genuine factual proposition, not that it should be equivalent to an experiential proposition, or any finite number of experiential propositions, but simply that some experiential propositions can be deduced from it in conjunction with certain other premises without being deducible from those other premises alone.
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