On the other, he assigned to vas with its insight into rationality too high a function with regard to the concrete in which the surd was present, a power to certify the truth of scientific principles.

G guttural is replaced as a final letter by surd c (longa, but lone; trigar, but Inch).

Since the fraction is infinite it cannot be commensurable and therefore its value is a quadratic surd number.

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Thus the concrete fact required to enable us to pass arithmetically from the conception of a fractional number to the conception of a surd is the fact of performing calculations by means of logarithms.

Muir, The Expression of a Quadratic Surd as a Continued Fraction (Glasgow, 1874).

In the same way the supporting vowel, which is regularly an e in CataIan, is often written a, especially after r (abra, ar bore m; astra, a s t r u m; para, p a t r e in); one may say that in the actual state of the language post-tonic e and a become indistinguishable in a surd sound intermediate between the French a and mute e.

B is replaced by the surd pat the end of a word (trobar in the infinitive, but trop in the present tense); so also in the interiOr of a word when it precedes a consonant (supvensr, s u b v e n i re, sopte, s u b t 0).

Conversely every positive quadratic surd number, when expressed as a simple continued fraction, will give rise to a recurring fraction.