Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

1-nf inittcrn, the order of superparticularity will be appropriately
discovered.
If, likewise, the superparticulars which were formed by conversion,
are themselves converted according to these rules, superpartient
ratios will be immediately produced. And from
the sesquialter indeed, the superbipartient, but from the sesquitertian,
the supertripartient ratio will be generated. The rest
also will be produced according to the common species of denomination
without any innovation of order. Let the superparticulars,
therefore, be disposed as follows:
Let the first therefore be equal to the first, i.e. to 9. But the
second, to the first and second, i.e. to 15. And the third, to
the first, to twice the second, and to the third.
And superbipartient ratio will, as is evident, be produced.
But if after the same manner the sesquitertian ratio is
changed, the superpartient order will present itself to the view.
Let the converted sesquitertian terms therefore be :
Let the first therefore be equal to the first, i.e. to 16. But the
second to the first and second, i.e. to 28. And the third, to
the first, to twice the second, and to the third, i.e. to 49. And
the ratio, as is evident, will be supertripartient:
Again, by converting after the same manner the sesquiquar-