“Ten Practical Experiments
1. Spacing (use gray appearance charcoal)
2. Shape (in varying proportions)
3. Arrangement
4. Rhythm
5. Drawn Line (charcoal and brush)
6. Masses(Chinese and Japanese ink painting)
7. Tone (difference)
8. Color ( suggested by stain glass)
9. Dark and Light(crayon on black paper)
10. Intensities”

— Arthur Wesley Dow

A Course in Fine Arts- Arthur Dow- Bulletin of College of Art of Association of America Vol 1 no 4 September 1918
A Course in Fine Arts

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Arthur Wesley Dow 7

painter from the United States 1857–1922

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“Suppose we a certain Number of things exposed, different each from other, as a, b, c, d, e, &c.; The question is, how many ways the order of these may be varied? as, for instance, how many changes may be Rung upon a certain Number of Bells; or, how many ways (by way of Anagram) a certain Number of (different) Letters may be differently ordered?
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2) If Two be exposed, as a, b, it is also manifest, that they may be taken in a double order, as ab, ba, and no more. That is 1 x 2 = 2. Alt.3
3) If Three be exposed; as a, b, c: Then, beginning with a, the other two b, c, may (by art. 2,) be disposed according to Two different orders, as bc, cb; whence arise Two Changes (or varieties of order) beginning with a as abc, acb: And, in like manner it may be shewed, that there be as many beginning with b; because the other two, a, c, may be so varied, as bac, bca. And again as many beginning with c as cab, cba. And therefore, in all, Three times Two. That is 1 x 2, x 3 = 6.
Alt.34) If Four be exposed as a, b, c, d; Then, beginning with a, the other Three may (by art. preceeding) be disposed six several ways. And (by the same reason) as many beginning with b, and as many beginning with c, and as many beginning with d. And therefore, in all, Four times six, or 24. That is, the Number answering to the case next foregoing, so many times taken as is the Number of things here exposed. That is 1 x 2 x 3, x 4 = 6 x 4 = 24.
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Source: A Discourse of Combinations, Alterations, and Aliquot Parts (1685), Ch.II Of Alternations, or the different Change of Order, in any Number of Things proposed.