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Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

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Nothing however which can be dissolved is incomposite, but is<br />

by every necessity a composite.<br />

CHAPTER XI.<br />

On that number which is of itself second and composite, but<br />

with reference to another first and incomposite.<br />

THESE numbers therefore, i.e. the first and incomposite and<br />

the second and composite being separated from each other by<br />

a natural diversity, another number presents itself to the view<br />

in the middle of these, which is indeed itself composite and<br />

second, receives the measure of another, and is therefore capable<br />

of a part with a foreign appellation, but when it is compared<br />

with another number of the same kind, is conjoined with it<br />

by no common measure; nor will these numbers have equivocal<br />

parts. Numbers of this description, are such as 9 and 25;<br />

for these have no common measure, except unity, which is the<br />

common measure of all numbers. They likewise have no equivocal<br />

parts. For that which in 9 is the third part is not in 25,<br />

and that which in 25 is the fifth part is not in 9. Hence both<br />

these numbers are naturally second and composite, but when<br />

compared with each other, they arc rendered first and incomposite,<br />

because each has no other measure than unity, which is<br />

denominated from each; for in 9 it is the ninth, and in 25, the<br />

twenty-fifth part.<br />

CHAPTER XII.<br />

On the generation of the first and incomposite, of the second<br />

and composite numbers, and of that number which is of itself<br />

second and composite, but with reference to another first and<br />

rncom posite.

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