How to use Surd in a sentence
Since the fraction is infinite it cannot be commensurable and therefore its value is a quadratic surd number.
Conversely every positive quadratic surd number, when expressed as a simple continued fraction, will give rise to a recurring fraction.
The second case illustrates a feature of the recurring continued fraction which represents a complete quadratic surd.
A number of this kind is called a surd; the surd which is the pth root of N is written ¦JN, but if the index is 2 it is usually omitted, so that the square root of N is written, /N.
This e is neither open nor close, but a surd e the pronunciation of which comes very near a.Advertisement
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.
Final d after a vowel has produced u (pea, p e d e in; niu, n i d u m; mou, to o d u m); buf when the d, in consequence of the disappearance of the preceding vowel, rests upon a consonant, it remains and passes into the corresponding surd; f r I g i d u s gives fred (pronounced fret).
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).
G guttural is replaced as a final letter by surd c (longa, but lone; trigar, but Inch).
The substitution of these interdental and guttural sounds for the surd and sonant spirants respectively did certainly not take place simultaneously, but the vacillations of the old orthography, and afterwards the decision of the Spanish Academy, which suppressed x (= I; x was retained for cs) and allows only c and g before e and i, I and j before a, a, a, make it impossible for us to follow, with the help of the written texts, the course of the transformation.Advertisement
One of the most notable differences between normal Portugiiese and Gahician is the substitution of the surd spirant in place of the sonant spirant for the Lat.
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.
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.
On the one hand Aristotle by his doctrine of matter admitted a surd into his system.