Now as to what pertains to these Surd numbers (which, as it were by way of reproach and calumny, having no merit of their own are also styled Irrational, Irregular, and Inexplicable) they are by many denied to be numbers properly speaking, and are wont to be banished from arithmetic to another Science, (which yet is no science) viz. algebra.
Isaac BarrowRelated topics
algebra arithmetic calumny having irrational irregular merit now numbers reproach science speaking surd viz way wont yetRelated quotes
Let us pass to the despotic part of the soul, spirit. We must not eliminate it utterly from the youth nor yet allow him to use it all the time. Let us train boys from earliest childhood to be patient when they suffer wrongs themselves, but, if they see another being wronged, to sally forth courageously and aid the sufferer in fitting measure.
John Chrysostom
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
Everywhere Christians are tempted to take the easy path, to seek "peace" and "security" and flee from pain and affliction, to view life as an occasion for the enjoyment of earthly blessings, instead of a time of trial in which our eternal destiny is to be decided. But God expects more than this from those who glory in the name of Orthodox Christians.
Seraphim Rose
The way in which the irrational numbers are usually introduced is based directly upon the conception of extensive magnitudes-which itself is nowhere carefully defined-and explains number as the result of measuring such a magnitude by another of the same kind. Instead of this I demand that arithmetic shall be developed out of itself.
Richard Dedekind
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
