![When an equation...clearly leads to two negative or imaginary roots, [Diophantus] retraces his steps and shows by how by altering the equation, he can get a new one that has rational roots. ...Diophantus is a pure algebraist; and since algebra in his time did not recognize irrational, negative, and complex numbers, he rejected equations with such solutions. (Morris Kline)](https://cdn.quotesdtb.com/img/quotes_images_webp/78/morris-kline-algebra-algebraist-953578.webp)
When an equation...clearly leads to two negative or imaginary roots, [Diophantus] retraces his steps and shows by how by altering the equation, he can get a new one that has rational roots. ...Diophantus is a pure algebraist; and since algebra in his time did not recognize irrational, negative, and complex numbers, he rejected equations with such solutions.
Morris KlineRelated topics
algebra altering complex equation irrational pure rootsRelated quotes
My algebra was relatively poor. I found it very difficult to use equations that substituted numbers - to which I had a synesthetic and emotional response - for letters, to which I had none. It was because of this that I decided not to continue math at Advanced level, but chose to study history, French and German instead.
Daniel Tammet
Okay, look at it this way: if the evening news has a very high probability of being accurate, then it's highly improbable that they would inaccurately report the numbers chosen in the lottery. That counterbalances any improbability in the choosing of those numbers, so you're quite rational to believe in this highly improbable event.
William Lane Craig
I understand and sympathize with the reasonable needs of a reasonable number of people on a finite continent. All life depends upon other life. But what is happening today, in North America, is not rational use but irrational massacre. Man the Pest, multiplied to the swarming stage, is attacking the remaining forests like a plague of locusts on a field of grain.
Edward Abbey
That this subject [of imaginary magnitudes] has hitherto been considered from the wrong point of view and surrounded by a mysterious obscurity, is to be attributed largely to an ill-adapted notation. If for instance, +1, -1, √-1 had been called direct, inverse, and lateral units, instead of positive, negative, and imaginary (or even impossible) such an obscurity would have been out of question.
Carl Friedrich Gauss
I recognize nothing that is not material. In physics, chemistry and biology I see only mechanics. The Universe is nothing but an infinite and complex mechanism. Its complexity is so great that it borders on willfulness, suddenness, and randomness; it gives the illusion of free will possessed by conscious beings.
Konstantin Tsiolkovsky