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Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

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Egyptians that the death of Osiris happened on the 17th day of<br />

the month, at which time it is especially evident that the moon<br />

is at the full. Hence the Pythagoreans call this day antiphraxis,<br />

obstrzlction, or opposition, and utterly abominate this number.<br />

For 17 falling as a middle number, between the square 16, and<br />

18 an oblong number, (which are the only plain numbers that<br />

have their ambits equal to the spaces contained by the ambitsj<br />

it opposes and disjoins them from each other, and being divided<br />

into unequal portions forms the sesquioctave ratio;" (viz.<br />

by a division into 9 and 8.)<br />

But that the ambits of these two numbers 16 and 18 are<br />

equal to their areas is evident. For 16 is a square each side of<br />

which is 4, and the number of the sides is 4. And 18 may be<br />

conceived to be a parallelogram the four sides of which are 6,<br />

6, 3, 3, the sum of which is 18.<br />

It is observed by Martianus Capella, that if the number 5<br />

either multiplies itself, or any odd number, the product always<br />

ends in 5. And I have observed of 6, which when multiplied<br />

by itself always ends in 6, that if it multiplies an even number,<br />

the product will always end in that even number itself, which<br />

it multiplies, or the final number of it. Thus 2>(6=12; 4x6<br />

=24; 6)(6=36; 8)

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