Arithmetic and geometry, according to Plato, are the two wings of the mathematician. The object indeed of all mathematical questions, is to determine the ratios of numbers, or of magnitudes ; and it may even be said, to continue the comparison of the ancient philosopher, that arithmetic is the mathematician's right wing; for it is an incontestable truth, that geometrical determinations would, for the most part, present nothing satisfactory to the mind, if the ratios thus determined could not be reduced to numerical ratios. This justifies the common practice, which we shall here follow, of beginning with arithmetic.
Jacques OzanamRelated topics
ancient arithmetic beginning common comparison continue follow geometry mathematician mind nothing numbers numerical object philosopher practice present right satisfactory say thus truth wing wings plato questionsRelated quotes
This is on the basis of the Aryan invasion theory according to which 'Aryans' invaded India in the early second millennium BC, and conquered it from the 'natives'. This theory is based purely on an eighteenth century linguistic proposition, and has no basis either in archaeology, or in literature, or in the racial-ethnic composition of India. What concerns us more, so far as this present volume is concerned, is the attempt to brand Hindu religious texts, on the basis of this theory, as 'invader' texts: a UNESCO publication characterises the Rigveda as 'the epic of the destruction of one of the great cultures of the ancient world.
Shrikant Talageri
I would teach the world how the Greeks proved, more than 2,000 years ago, that there are infinitely many prime numbers. In my mind, this discovery is the beginning of mathematics – when humankind realised that, by pure thought alone, it could prove eternal truths of the universe.
Prime numbers are the indivisible numbers, numbers that can be divided only by themselves and one. They are the most important numbers in mathematics, because every number is built by multiplying prime numbers together – for example, 60 = 2 x 2 x 3 x 5. They are like the atoms of arithmetic, the hydrogen and oxygen of the world of numbers.
Marcus du Sautoy
At that moment Marx puts himself in a position where he becomes the necessary target of all who have a special interest in maintaining the old-similar to Democritus before him, whose work was burned by Plato and his disciples, the ideologues of Athenian slave aristocracy. Beginning with the revolutionary Marx, a political group with concrete ideas establishes itself. Basing itself on the giants, Marx and Engels, and developing through successive steps with personalities like Lenin, Stalin, Mao Tse-tung and the new Soviet and Chinese rulers, it establishes a body of doctrine and, let us say, examples to follow.
Che Guevara
Through it all I learned the value of being humble to the dust, reduced to ashes. Everyone should experience that. Before you can recognize you're somebody, you have to know you're nobody. [-] The butterfly was just a lowly worm in its beginning. The worm didn't live with the moment-to-moment expectation of sprouting wings and taking flight. He lived a useful and productive life, the life of a worm. And he had to die a worm in order to be born as an angel! The spinning of the cocoon is, in and of itself, remarkable. It is as wondrous as the emergence and first flight of the butterfly.
Henry Miller
There cannot be a greater mistake than that of looking superciliously upon the practical applications of science. The life and soul of science is its practical application; and just as the great advances in mathematics have been made through the desire of discovering the solution of problems which were of a highly practical kind in mathematical science, so in physical science many of the greatest advances that have been made from the beginning of the world to the present time have been made in earnest desire to turn the knowledge of the properties of matter to some purpose useful to mankind.
William Thomson
