“Find a fraction which, multiplied by itself, shall give 6, or… find the square root of 6. This can be shown to be an impossible problem; for it can be shown that no fraction whatsoever multiplied by itself, can give a whole number, unless it be itself a whole number disguised in a fractional form, such as 4⁄2 or 21⁄3. To this problem, then, there is but one answer, that it is self-contradictory. But if we propose the following problem,—to find a fraction which, multiplied by itself, shall give a product lying between 6 and 6 + a; we find that this problem admits of solution in every case. It therefore admits of solution however small a may be… as small as you please.”

— Augustus De Morgan

...there is such a thing as the square root of 6, and it is denoted by √<span style="text-decoration: overline">6</span>. But we do not say we actually find this, but that we approximate to it.
The Differential and Integral Calculus (1836)

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "Find a fraction which, multiplied by itself, shall give 6, or… find the square root of 6. This can be shown to be an im…" by Augustus De Morgan?

Augustus De Morgan 41

British mathematician, philosopher and university teacher (… 1806–1871

Related quotes

“As a square number is known to be the product of a number multiplied by itself, so every polygonal number, multiplied by one number and added to another, both of which depend upon the number of its angles, produces a square number. I shall prove this, and shall show also how from a given side to find its polygon and conversely. Some auxiliary propositions must first be proved.”

Diophantus Arithmetica

As quoted by James Gow, A Short History of Greek Mathematics https://books.google.com/books?id=9d8DAAAAMAAJ (1884)
Arithmetica (c. 250 AD)

“What then was the commencement of the whole matter? Existence that multiplied itself for sheer delight of being and plunged into numberless trillions of forms so that it might find itself innumerably.”

Sri Aurobindo (1872–1950) Indian nationalist, freedom fighter, philosopher, yogi, guru and poet

Thoughts and Glimpses (1916-17)

“The circumstance which gives authors an advantage above all these great masters, is this, that they can multiply their originals; or rather, can make copies of their works, to what number they please, which shall be as valuable as the originals themselves.”

Joseph Addison (1672–1719) politician, writer and playwright

No. 166 (10 September 1711).
The Spectator (1711–1714)

“Things look as they do because of the field organization to which the proximal stimulus distribution gives rise. This answer is final and can be so only because it contains the whole problem of organization itself.”

Kurt Koffka (1886–1941) German psychologist

Source: Principles of Gestalt Psychology, 1935, p. 98

“The world which we perceive is a tiny fraction of the world which we can perceive, which is a tiny fraction of the perceivable world, you see.”

Terence McKenna (1946–2000) American ethnobotanist

"Understanding and Imagination in the Light of Nature"
Variant: The world which we perceive is a tiny fraction of the world which we can perceive, which is a tiny fraction of the perceivable world...
Context: Because the fact is, what blinds us to the presence of alien intelligence is linguistic and cultural bias operating on ourselves. The world which we perceive is a tiny fraction of the world which we can perceive, which is a tiny fraction of the perceivable world, you see. We operate on a very narrow slice based on cultural conventions. So the important thing, if synergizing progress is the notion to be maximized (and I think it's the notion to be maximized), is to try and locate the blind spot in the culture — the place where the culture isn't looking, because it dare not — because if it were to look there, its previous values would dissolve, you see. For Western Civilization that place is the psychedelic experience as it emerges out of nature.