The depressed cubic equation is a cubic equation of the form $x^3+px+q=0$. This expression sounds strange especially for someone that English is not his mother tongue. Why this equation is called "depressed"? What is so depressing in it? Thanks!
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The coefficient of the quadratic term has been "depressed" to zero. – smcc Jul 20 '16 at 13:04
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1In the Merriam-Webster dictionary the third meaning of depress is "press down". So the equation is not sad but downgraded. – zoli Jul 20 '16 at 13:05
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To depress something is to push it downward.$\qquad$ – Michael Hardy Jul 20 '16 at 15:03
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I'd like using reduced cubic. See another answer of mine. – Ng Chung Tak Jul 20 '16 at 19:14
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The coefficient of the quadratic term has been "depressed" to zero:
https://en.wikipedia.org/wiki/Cubic_function#Reduction_to_a_depressed_cubic
Depress also has the meaning of "reduce":
smcc
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Why this equation is called "depressed"?
It is from latin deprimitur : lowered.
It seems that the terminology was intoduced by François Viète (1540 – 1603) into his posthumous :
Anastrophe [anastrophe] is the transformation of inverse negative equations into their correlatives. It is carried out so that the original equation, with the help of its correlative, can be reduced [reducatur ad depressiorem] [...] to a lower [power] and, therefore, be more easily solved. [...] The work of anastrophe is performed this way : [...] and the equation, otherwise soluble only with difficulty, can depressed [deprimitur] to one that is easily solved by means of a pretty operation.
Mauro ALLEGRANZA
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