# Surd sentence example

surd
• Since the fraction is infinite it cannot be commensurable and therefore its value is a quadratic surd number.
• Consideration of the binomial theorem for fractional index, or of the continued fraction representing a surd, or of theorems such as Wallis's theorem (ï¿½ 64), shows that a sequence, every term of which is rational, may have as its limit an irrational number, i.e.
• 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.
• 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).