Any quantity, commensurable or incommensurable, can be expressed uniquely as a simple continued fraction, terminating in the case of a commensurable quantity, non-terminating in the case of an incommensurable quantity.

This ratio, invariably denoted by 7r, is constant for all circles, but it does not admit of exact arithmetical expression, being of the nature of an incommensurable number.

Furthermore, incommensurable numbers are defined as the limits arrived at as the result of certain procedures with rational numbers.

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If the number is incommensurable or consists of more than seven figures, we can take the first seven figures of it (or multiply and divide the result by any factor, and take the first seven figures of the result) and proceed as before.

His incommensurable and indescribable masterpiece of mingled humour, wisdom, satire, erudition, indecency, profundity, levity, imagination, realism, reflects the whole age in its mirror of hyperAristophanic farce.

But an investigation of dependent lines which are often incommensurable forces us to adopt the contradictory fiction of partially overlapping, i.e.

In the introduction to his work Von der Weltseele, however, he argues in favour of the possibility of a transmutation of species in periods incommensurable with ours.

Arithmetic, algebra, and the infinitesimal calculus, are sciences directly concerned with integral numbers, rational (or fractional) numbers, and real numbers generally, which include incommensurable numbers.