A Memoir of the Theory of Mathematical Form

A Memoir of the Theory of Mathematical Form

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1886 edition. Excerpt: ...collections will be the collection a, b, c, c, d, d, e, f. 193. The third mode of composition is that in which the derived system has all the self-correspondences which each of a number of systems, of the same number of units, has. We may represent the units of such a system by symbols (Ao... ), (B6... ), (Cc... ), &c, where A, B, C... are units of one of the compounded systems, a, b, c those of another, and so on. General Method of Graphically Representing a System. 194. Let each unit of a system S, each unified column, each unified row, and each element of its tabular representation, be represented by a graphical unit, using different kinds of graphical units in the case of the units of S, the rows, columns, and elements respectively, four kinds in all. Connect each graphical unit which represents an element by links to (I.) the graphical unit representing the unit of S of which the element represents a unit aspect; (2.) the graphical unit representing the unified row in which the element lies; (3.) the graphical unit representing the unified column in which the element lies. We get a graphical representation of a system of 2n--m--mn units, of which S is a component system. 195. It is obviously not always necessary to employ the somewhat cumbrous mode of graphical representation here given; simpler methods can be adopted in special cases. Frequently, as we have already seen, it will not be necessary to have any auxiliary graphical units, but merely those representing the units of S itself. Networks. 196. The pairs of any single collection of pairs are either all component pairs of a single system of- units, or all connecting pairs of two single systems of units. 197. Where a single system P of pairs connects two single systems S and 2, ...show more

Product details

  • Paperback | 26 pages
  • 189 x 246 x 1mm | 68g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236645340
  • 9781236645340