„He gave more elegant rules for the sum of the squares and cubes of an initial segment of the positive integers. The sixth part of the product of three quantities consisting of the number of terms, the number of terms plus one, and twice the number of terms plus one is the sum of the squares. The square of the sum of the series is the sum of the cubes.“

—  Aryabhata

Roger Cooke in: The history of mathematics: a brief course http://books.google.co.in/books?id=z-ruAAAAMAAJ, Wiley, 7 October 1997, p. 207.

Ultimo aggiornamento 22 Maggio 2020. Storia
Aryabhata photo
Aryabhata
matematico, astronomo e astrologo indiano 476 - 550

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„Let as many Numbers, as you please, be proposed to be Combined: Suppose Five, which we will call a b c d e. Put, in so many Lines, Numbers, in duple proportion, beginning with 1. The Sum (31) is the Number of Sumptions, or Elections; wherein, one or more of them, may several ways be taken. Hence subduct (5) the Number of the Numbers proposed; because each of them may once be taken singly. And the Remainder (26) shews how many ways they may be taken in Combination; (namely, Two or more at once.) And, consequently, how many Products may be had by the Multiplication of any two or more of them so taken. But the same Sum (31) without such Subduction, shews how many Aliquot Parts there are in the greatest of those Products, (that is, in the Number made by the continual Multiplication of all the Numbers proposed,) a b c d e. For every one of those Sumptions, are Aliquot Parts of a b c d e, except the last, (which is the whole,) and instead thereof, 1 is also an Aliquot Part; which makes the number of Aliquot Parts, the same with the Number of Sumptions. Only here is to be understood, (which the Rule should have intimated;) that, all the Numbers proposed, are to be Prime Numbers, and each distinct from the other. For if any of them be Compound Numbers, or any Two of them be the same, the Rule for Aliquot Parts will not hold.“

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Origine: A Discourse of Combinations, Alterations, and Aliquot Parts (1685), Ch.I Of the variety of Elections, or Choice, in taking or leaving One or more, out of a certain Number of things proposed.

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Origine: A Discourse of Combinations, Alterations, and Aliquot Parts (1685), Ch.I Of the variety of Elections, or Choice, in taking or leaving One or more, out of a certain Number of things proposed.

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Origine: Principles of Gestalt Psychology, 1935, p. 176
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„William inherited very large possessions, part of which consisted of crown debts, due to the vice-admiral for sums he had advanced for the sea-service.“

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Variants:
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The History of the Quakers (1762)
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