The Hindus introduced negative numbers... The first known use is Brahmagupta about 628; he also states the rules for the four operations with negative numbers. Bhāskara points out that the square root of a positive number is twofold, positive and negative. He brings up the matter of the square root of a negative number but says that there is no square root because a negative number is not a square. No definitions, axioms, or theorems are given. The Hindus did not unreservedly accept negative numbers. Even Bhāskara, while giving 50 and -5 as two solutions of a problem, says, "The second value is in this case not to be taken, for it is inadequate; people do not approve of negative solutions."
Morris KlineRelated topics
case four given giving known matter number problem root second square take use value while points Rules States operationsRelated quotes
Do everything simply and meekly. Do nothing with an ulterior motive. Don't say, I'll do this in order to have that result, but do it naturally, without taking cognizance of it. That is, pray simply and don't think about what God will bestow on your soul. Don't make any calculations. You know, of course, what God bestows when you enter into communion with Him, but it is as if you don't know. Don't discuss the matter even with yourself. So when you repeat the prayer, "Lord Jesus Christ, have mercy on me”, say it simply and ingenuously and think of nothing other than the prayer. These are very delicate matters and the intervention of the grace of God is required.
Porphyrios of Kafsokalyvia
As for negative numbers... most mathematicians of the sixteenth and seventeenth centuries did not accept them... In the fifteenth century Nicolas Chuquet and, in the sixteenth, Stifel both spoke of negative numbers as absurd numbers. ...Descartes accepted them, in part. ...he had shown that, given an equation, one can obtain another whose roots are larger than the original one by any given quantity. Thus an equation with negative roots could be transformed into one with positive roots. Since we can turn false roots into real roots, Descartes was willing to accept negative numbers. Pascal regarded the subtraction of 4 from zero as utter nonsense.
Morris Kline
We do not mechanically connect the sensation of white with the idea of light, any more than we connect the sensation of black with the idea of darkness. We admit that a black jewel, even if of a dead black, may be more luminous than the white or pink satin of its case. Loving light, we refuse to measure it, and we avoid the geometrical ideas of the focus and the ray, which imply the repetition-contrary to the principle of variety which guides us-of bright planes and sombre intervals in a given direction. Loving colour, we refuse to limit it, and subdued or dazzling, fresh or muddy, we accept all the possibilities contained between the two extreme points of the spectrum, between the cold and the warm tone.
Jean Metzinger
We also believe that we should have the power to assist voluntary repatriation, that the dependents must be counted against the limits on numbers, and that the total should be further reduced. ... Without the measures outlined, those of us who have studied this question at close quarters are increasingly fearful that an intractable racial problem will be introduced into Britain and may become endemic if we are not careful. This, in our view, must not be allowed. Therefore it is time to bring this problem into the open and not be afraid to talk about it. Those who speak about it in a responsible way should not be charged with racial prejudice.
Alec Douglas-Home
Our tasks are definite. The first to see that no man, woman, or child shall go hungry or unsheltered through the approaching winter.
The second is to see that our great benevolent agencies for character building, for hospitalization, for care of children and all their vast number of agencies of voluntary solicitude for the less fortunate are maintained in full strength.
The third is to maintain the bedrock principle of our liberties by the full mobilization of individual and local resources and responsibilities.
The fourth is that we may maintain the spiritual impulses in our people for generous giving and generous service-in the spirit that each is his brother's keeper.
Herbert Hoover