“Which was to be proved.”

—  Euclid , book Elements

Elements, Book I, Proposition 4.
Latin translation: Quod erat demonstrandum (often abbreviated Q.E.D.).
Euclid’s Elements

Original

Ὅπερ ἔδει δεῖξαι.

Adopted from Wikiquote. Last update April 28, 2022. History

Help us to complete the source, original and additional information

Do you have more details about the quote "Which was to be proved." by Euclid?
Euclid photo
Euclid 6
Greek mathematician, inventor of axiomatic geometry -323–-285 BC

Related quotes

Thomas Fuller (writer) photo

“4384. That, which proves too much, proves nothing.”

Thomas Fuller (writer) (1654–1734) British physician, preacher, and intellectual

Introductio ad prudentiam: Part II (1727), Gnomologia (1732)

Mahatma Gandhi photo

“It is beyond my power to induce in you a belief in God. There are certain things which are self proved and certain which are not proved at all.”

Mahatma Gandhi (1869–1948) pre-eminent leader of Indian nationalism during British-ruled India

Young India (24 September 1931); also in Teachings Of Mahatma Gandhi (1945), edited by Jag Parvesh Chander, p. 458 archive.org https://archive.org/stream/teachingsofmahat029222mbp#page/n463/mode/2up
1930s
Context: It is beyond my power to induce in you a belief in God. There are certain things which are self proved and certain which are not proved at all. The existence of God is like a geometrical axiom. It may be beyond our heart grasp. I shall not talk of an intellectual grasp. Intellectual attempts are more or less failures, as a rational explanation cannot give you the faith in a living God. For it is a thing beyond the grasp of reason. It transcends reason. There are numerous phenomena from which you can reason out the existence of God, but I shall not insult your intelligence by offering you a rational explanation of that type. I would have you brush aside all rational explanations and begin with a simple childlike faith in God. If I exist, God exists. With me it is a necessity of my being as it is with millions. They may not be able to talk about it, but from their life you can see that it is a part of their life. I am only asking you to restore the belief that has been undermined. In order to do so, you have to unlearn a lot of literature that dazzles your intelligence and throws you off your feet. Start with the faith which is also a token of humility and an admission that we know nothing, that we are less than atoms in this universe. We are less than atoms, I say, because the atom obeys the law of its being, whereas we in the insolence of our ignorance deny the law of nature. But I have no argument to address to those who have no faith.

Dan Brown photo
Napoleon I of France photo

“Laws which are consistent in theory often prove chaotic in practice.”

Napoleon I of France (1769–1821) French general, First Consul and later Emperor of the French

Napoleon : In His Own Words (1916)

Pliny the Younger photo

“Prosperity proves men to be fortunate, while it is adversity which makes them great.”
Secunda felices, adversa magnos probent.

Pliny the Younger (61–113) Roman writer

XXXI.
Panegyricus

Sydney Smith photo

“Nothing remains, under God, but those passions which have often proved”

Sydney Smith (1771–1845) English writer and clergyman

Lecture XXVIL: On Habit - Part II, in “Elementary Sketches of Moral Philosophy”, delivered at The Royal Institution in the years 1804, 1805, and 1806 by the late Rev. Sydney Smith, M.A. (Spottiswoodes and Shaw (London: 1849)) http://www.archive.org/stream/elementarysketc03smitgoog#page/n438/mode/2up, p. 423-424
Another Variant: The history of the world shows us that men are not to be counted by their numbers, but by the fire and vigour of their passions; by their deep sense of injury; by their memory of past glory; by their eagerness for fresh fame; by their clear and steady resolution of ceasing to live, or of achieving a particular object, which, when it is once formed, strikes off a load of manacles and chains, and gives free space to all heavenly and heroic feelings. All great and extraordinary actions come from the heart. There are seasons in human affairs when qualities, fit enough to conduct the common business of life, are feeble and useless, when men must trust to emotion for that safety which reason at such times can never give. These are the feelings which led the ten thousand over the Carduchian mountains; these are the feelings by which a handful of Greeks broke in pieces the power of Persia; and in the fens of the Dutch, and on the mountains of the Swiss, defended the happiness and revenged the oppressions of man! God calls all the passions out in their keenness and vigour for the present safety of mankind, anger and revenge, and the heroic mind, and a readiness to suffer—all the secret strength, all the invisible array of the feelings—all that nature has reserved for the great scenes of the world. When the usual hopes and the common aids of man are all gone, nothing remains under God but those passions which have often proved the best ministers of His purpose and the surest protectors of the world.
Quoted by Theodore Roosevelt in his " Brotherhood and the Heroic Virtues http://www.theodore-roosevelt.com/images/research/txtspeeches/668.pdf" Address at the Veterans' Reunion, Burlington, Vermont, September 5, 1901 and published in Theodore Roosevelt's "The Strenuous Life: Essays and Addresses" by Dover Publications (April 23, 2009) in its Dover Thrift Editions (ISBN: 978-0486472294), p. 126-127
Elementary Sketches of Moral Philosophy (1849)
Context: The history of the world shows us that men are not to be counted by their numbers, but by the fire and vigour of their passions; by their deep sense of injury; by their memory of past glory; by their eagerness for fresh fame; by their clear and steady resolution of ceasing to live, or of achieving a particular object, which, when it is once formed, strikes off a load of manacles and chains, and gives free space to all heavenly and heroic feelings. All great and extraordinary actions come from the heart. There are seasons in human affairs, when qualities fit enough to conduct the common business of life, are feeble and useless; and when men must trust to emotion, for that safety which reason at such times can never give. These are the feelings which led the ten thousand over the Carduchian mountans; these are the feelings by which a handful of Greeks broke in pieces the power of Persia: they have, by turns, humbled Austria, reduced Spain; and in the fens of the Dutch, and on the mountains of the Swiss, defended the happiness, and revenged the oppressions, of man! God calls all the passions out in their keenness and vigour, for the present safety of mankind. Anger, and revenge, and the heroic mind, and a readiness to suffer;— all the secret strength, all the invisible array, of the feelings,— all that nature has reserved for the great scenes of the world. For the usual hopes, and the common aids of man, are all gone! Kings have perished, armies are subdued, nations mouldered away! Nothing remains, under God, but those passions which have often proved the best ministers of His vengeance, and the surest protectors of the world.

Margaret Cho photo

“Most conservatives also believe in the death penalty, but not abortion, which proves they like to procrastinate.”

Margaret Cho (1968) American stand-up comedian

Source: I Have Chosen to Stay and Fight

James Frazer photo

“Yet perhaps no sacrifice is wholly useless which proves there are men who prefer honour to life.”

Source: The Golden Bough (1890), Chapter 24, The Killing of the Divine King.

“Entitle us to the Liberty of proving the Truth of the Papers, which in the Information are called false, malicious, seditious and scandalous.”

John Peter Zenger (1697–1746) American printer

"Case and Tryal of John Peter Zenger", pg. 17