The Philosophy of Arithmetic; Exhibiting a Progressive View of the Theory and Practice of Calculation, with Tables for the Multiplication of Numbers a

The Philosophy of Arithmetic; Exhibiting a Progressive View of the Theory and Practice of Calculation, with Tables for the Multiplication of Numbers a

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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. 1820 edition. Excerpt: ...repeated multiplication is per-formed after the Senary notation, -the 0.521225104 products of the single digits being con-1.25352424 stantly divided by six, while the remain-der is set down, and the quotient car-1.54334544 ried to the next place. The correspond-3.50231504 ing Quaternary notation is therefore, in 4 round numbers, .11011331, the same as 3.521411224 4 what arises from the decimal expression j 3)445344.3810938062. The descending scales now selected for explaining the method of transformation are seldom ever used. But the descending terms of the Denary Scale, or those of the Decimal Subdivision, have at length been very generally adopted into practice, at least in all the calculations connected with mathematical and physical science. The duodecimal system of partition, from its convenience in Mensuration, is employed to a certain extent among traders. It may be proper, therefore, to exemplify the re-.785398 ciprocal transformation of decimals and duodecimals. In this view, let it be required to change the expression.785398, which denotes the ratio of the circle to its circumscribing square, into duodecimals. The operation is performed by multiplying the given fraction by 12, and pointing off the same number of digits; the process being constantly repeated with the several partial excesses. Hence the equivalent expression in the duodecimal notation is.9512010; of which the four first digits, however, may be judged sufficient in practice. Again, the cube root of 2 expressed in duodecimals is 1.315188. To reduce this to decimals, it must 1.315188 undergo a repeated multiplication by ten or 0. It is scarcely necessary to observe, that the notation being now duodenary the whole process is to be carried through that scale, each digital.show more

Product details

  • Paperback | 62 pages
  • 189 x 246 x 3mm | 127g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236546741
  • 9781236546746