Sketches of the History of Man Volume 3

Sketches of the History of Man Volume 3

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1796 edition. Excerpt: ...what are compl-Ix, and consequently makes them appear more natural. It deserves a most serious discuffion, whether the operations of nature be always carried on with the greatest simplicity, or whether we be not mifled by our taile for simplicity to be of' that opinion. No other reasoning affords so clear a notion of the foregoing process, as that which is mathema.. tieal. Equalizy is the only mathematical' relation; and comparison therefore is the only means by which mathematical propositions are ascertain-ed. To that science belong a number of intuitive pro. positions, termed axioms, which are all founded onequality. For example: Divide two equal lines, each of them, into a thousand equal parts, a single part of the one line must be equal to' a V single part of the other. Second: Take ten of these parts from the one line, and as.many from the other, and the remaining parts must be equal; 'which is more shortly expressed thus: From two equal lines take equal parts, and the remainders will be equal; or add equal parts, and the sums will be equal. Third: If two things be, in the same respect, equal to a third, the one is equal to the other in the same respect. I proceed to show the use of these axioms. Two things may be equal without being intuitively so; which is the case of the Cquallty between the three angles of a triangle and two right angles. To demonstrate that truth, it is necessary to search for some' other angles that intuitively are equal to both. If this property cannot be discovered in any one set of angles, we must go more leisurely to work, and try to find angles that are equal to the three' angles of a triangle. These being discovered, we next try to find other angles equal to the angles now discovered; and so on in more

Product details

  • Paperback | 48 pages
  • 189 x 246 x 3mm | 104g
  • United States
  • English
  • black & white illustrations
  • 1236788109
  • 9781236788108