As a square number is known to be the product of a number multiplied by itself, so every polygonal number, multiplied by one number and added to another, both of which depend upon the number of its angles, produces a square number. I shall prove this, and shall show also how from a given side to find its polygon and conversely. Some auxiliary propositions must first be proved.
DiophantusRelated topics
auxiliary find given known multiply number polygon product prove show side squareRelated quotes
We must not forget that when radium was discovered no one knew that it would prove useful in hospitals. The work was one of pure science. And this is a proof that scientific work must not be considered from the point of view of the direct usefulness of it. It must be done for itself, for the beauty of science, and then there is always the chance that a scientific discovery may become like the radium a benefit for humanity.
Marie Curie
How very paltry and limited the normal human intellect is, and how little lucidity there is in the human consciousness, may be judged from the fact that, despite the ephemeral brevity of human life, the uncertainty of our existence and the countless enigmas which press upon us from all sides, everyone does not continually and ceaselessly philosophize, but that only the rarest of exceptions do.
Arthur Schopenhauer
We grow great by dreams. All big men are dreamers. They see things in the soft haze of a spring day or in the red fire of a long winter's evening. Some of us let these dreams die, but others nourish and protect them nurse them through bad days till they bring them to the sunshine and light which comes always to those who hope that their dreams will come true.
Woodrow Wilson
Holy Tradition is neither a tradition of men, nor a philosophy, nor some kind of trickery, but is the word of God that He delivered to us personally. The great Apostle Paul teaches and exhorts us to keep with vigour the traditions, saving; "Therefore, brethren, stand fast, and hold the traditions which ye have been taught, whether by word, or our epistle."
Cleopa Ilie
A soul that is nurtured by hatred toward man can not be at peace with God, Who has said: If you forgive not men their sins, neither shall your Father forgive your sins (Matt. 6:15). If a man does not want to be reconciled, you must at least guard yourself from hating, praying with a pure heart for him, and speaking no evil of him.
Maximus the Confessor
