Nicomachus

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1 total works indexed

1. Introduction to Arithmetic

   · 1926 · cited 21x

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Quotes

• “Two other sciences in the same way will accurately treat of 'size': geometry, the part that abides and is at rest, [and] astronomy, that which moves and revolves.”
• “If geometry exists, arithmetic must also needs be implied... But on the contrary 3, 4, and the rest might be 5 without the figures existing to which they give names. Hence arithmetic abolishes geometry along with itself, but is not abolished by it, and while it is implied by geometry, it does not itself imply geometry.”
• “Scientific number, being set over such things as these, should be harmoniously constituted, in accordance with itself; not by any other but by itself.”
• “Everything that is harmoniously constituted is knit together out of opposites...”
• “Number is limited multitude or a combination of units or a flow of quantity made up of units; and the first division of number is even and odd.”
• “The even is that which can be divided into two equal parts without a unit intervening in the middle; and the odd is that which cannot...”

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