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“It is not unknown to those who know any Thing of publike Affairs, of how great Concernment it is, especially in civill Commotions, for those who are to manage such Transactions, to be furnished with continuall Intelligence from their Correspondents, yet so as to conceal their Councells and Resolutions from the adverse Party. And to this Purpose, in all Ages, much Care and lndustry hath been still used, how in Matters of Consequence, to convey Intelligence safely and secretly to those with whom they hold Correspondence, so as not to bee intercepted by the Enemy, or if intercepted, at least not discovered. And as this is no where of more Concernment, so no where more difficult, than in civill Wars, where the intermingling of opposite Parties makes it difficult, if not impossible, to distinguish Friends and Foes.”

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John Wallis

p, 125
An Essay on the Art of Decyphering (1737)

“If any ask, with what Confidence I durst adventure upon a Task so unusuall, as interpreting of Letters committed to Cipher; I shall only give this plain Account thereof.”

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John Wallis

p, 125
An Essay on the Art of Decyphering (1737)

“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.”

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John Wallis

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.
Quelle: 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.

“This method of mine takes its beginnings where Cavalieri ends his Method of indivisibles.”

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John Wallis

...for as his was the Geometry of indivisibles, so I have chosen to call my method the Arithmetic of infinitesimals.
Arithmetica Infinitorum (1656)