The Ars Magna is a great advance on any algebra previously published. Hitherto algebraists had confined their attention to those roots of equations which were positive. Cardan discussed negative and even complex roots, and proved that the latter would always occur in pairs, though he declined to commit himself to any explanation as to the meaning of these "sophistic" quantities which he said were ingenious though useless.
Gerolamo CardanoRelated topics
advance algebra attention commit complex explanation great latter meaning negative positive say sophistic ars rootsRelated quotes
Fresh pitsand, however, in spite of all its excellence in concrete structures, is not equally useful in stucco, the richness of which, when the lime and straw are mixed with such sand, will cause it to crack as it dries on account of the great strength of the mixture. But river sand, though useless in "signinum" on account of its thinness, becomes perfectly solid in stucco when thoroughly worked by means of polishing instruments.
Vitruvius
I conceived, developed and applied in many areas a new geometry of nature, which finds order in chaotic shapes and processes. It grew without a name until 1975, when I coined a new word to denote it, fractal geometry, from the Latin word for irregular and broken up, fractus. Today you might say that, until fractal geometry became organized, my life had followed a fractal orbit.
Benoît Mandelbrot
I can imagine no greater disservice to the country than to establish a system of censorship that would deny to the people of a free republic like our own their indisputable right to criticise their own public officials. While exercising the great powers of the office I hold, I would regret in a crisis like the one through which we are now passing to lose the benefit of patriotic and intelligent criticism.
Woodrow Wilson
'War,' says Machiavelli, 'ought to be the only study of a prince' and by a prince he means every sort of state, however constituted. 'He ought,' says this great political doctor, 'to consider peace only as a breathing-time, which gives him leisure to contrive, and furnishes ability to execute military plans. 'A meditation on the conduct of political societies made old Hobbes imagine that war was the state of nature.
Edmund Burke
Apollo at Delphi, through the oracular utterance of his priestess, pronounced Socrates the wisest of men. Of him it is related that he said with sagacity and great learning that the human breast should have been furnished with open windows, so that men might not keep their feelings concealed, but have them open to the view. Oh that nature, following his idea, had constructed them thus unfolded and obvious to the view.
Vitruvius
