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Euler's Elements of Algebra Mystery Cache

This cache has been archived.

WelshJargan: Due to new work commitments, I will not be able to maintain any caches. With regret, archiving this one.

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Hidden : 2/1/2014
Difficulty:
4 out of 5
Terrain:
1.5 out of 5

Size: Size:   other (other)

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Geocache Description:

This puzzle cache links Leonhard Euler with Georges Perec and Ernest Vincent Wright. In the 1880's, Euler named the orthogonal Latin squares as Graeco-Latin squares. Inspired by this, Perec used a 10x10 Graeco-Latin square to construct his most famous novel (Life A User's Manual). His second most famous work (A Void) was inspired by Wright's earlier book (Gadsby), and contains a character called Lord Gadsby V. Wright.

Using the principles of A Void and Gadsby, the following excerpt from Euler's Elements of Algebra has been re-written. From the text, identifty the 15 characters to fill in the northings and westings.

If something is capable of increase or diminution, is called a quantity.  A sum of money is a quantity, as it may grow or diminish.  It is similar with a weight, and other things of this kind.  From this definition, it is conspicuous that all contrasting kinds of quantity must be so various, as to furnish it difficult to account them and this is the origin of the differing arms of Mathematics, individually focussed on a particular kind of quantity.  Mathematics, in total analysis then, is the science of quantity; or, the science of measuring quantity.  Now, we cannot measure or survey any quantity, without considering another quantity of matching kind as known, and point out their mutual relation.  Allow us, for illustration, in trying to confirm the quantity of a sum of money, to start with a known quantity of money, as a louis, a crown, a ducat, or other coin, and show how many parts are contained in total sum.  In a similar way, a quantity of mass is a sum of known parts, such as pound or dram, within a total body of mass.  Again, a span is a sum of known parts, such as a foot or inch.  So that calculation of quantity of all kinds, consists of this: fix upon any singular known quantity of similar kind with that which is calculated, and think of it as a unit; then, calculate what proportion of this total quantity is of this known unit.  This proportion is always shown by digits; so that total is nothing but a proportion of a quantity to a known, distinct, quantity, arbitrarily shown as a unit.  From this it is known that any quantity may be shown through numbers; and this foundation of all Mathematical Sciences must be laid in a global discussion or analysis, and in a factual analysis of the varying methods of calculation.  This fundamental part of Mathematical Science is called Analysis, or Algebra.  In Algebra we consider only numbers, which show quantities, without regarding the different kinds of quantity.  These are the focus of other arms of mathematics.

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Additional Hints (Decrypt)

[puzzle] Snhygl yvcbtenz [cache] Fvg qbja. YUF. Zntargvp.

Decryption Key

A|B|C|D|E|F|G|H|I|J|K|L|M
-------------------------
N|O|P|Q|R|S|T|U|V|W|X|Y|Z

(letter above equals below, and vice versa)