Re: Leibniz -- De Arte Combinatoria

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DAC.  Note 4

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| From 'Of the Art of Combination' (cont.)
|
| 10.  For a certain complexion to be determined, the greater whole must be
|      divided into equal parts assumed as the smallest (that is, which now
|      at any rate are not divided further), from which there is composed and
|      by whose variation there varies the complexion -- i.e. the lesser whole.
|      Because the lesser whole is greater or less as more parts enter into it
|      at one time, the number of parts or unities to be taken together at one
|      and the same time we shall call the "exponent", after the example of
|      geometrical progression.
|
|      For example, let the whole be ABCD.  If the lesser wholes are to consist
|      of two parts -- e.g. AB, AC, AD, BC, BD, CD -- the exponent will be two;
|      if of three -- e.g. ABC, ABD, ACD, BCD -- the exponent will be three.
|
| 11.  Given an exponent, we shall write the complexions as follows.
|      If the exponent is two, we shall write "com2nation" (combination);
|      if three, "con3nation" (conternation);  if four "con4nation", &c.
|
| 12.  "Complexions 'simpliciter'" are all the complexions computed
|      for all the exponents;  e.g. for the number four, fifteen.
|      These are composed of four (by union), six (by com2nation),
|      four (by con3nation), and one (by con4nation) ...
|
| Leibniz, DAC, p. 2.
|
| Leibniz, 'Logical Papers', A Selection Translated and
| Edited with an Introduction by G.H.R. Parkinson (ed.),
| Oxford University Press, London, UK, 1966.

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