Muir, The Expression of a Quadratic Surdas a Continued Fraction (Glasgow, 1874).
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.
Surd mutes and linguals are so frequently exchanged in this district that locatives must be relied upon to identify names.
The dialectic exchange of N and R, and of the surd mutes k and t are clear in comparing Nanakan on the Hudson, Naratic-on on the Delaware, and Raritan on the Raritan.
Other dialectic peculiarities seem to appear in the exchange of the sonant g for the hard sound of the surd mute k, and of p for g, s for g, and t for d, st for gk, etc.
The letter t in the name is simply an exchange of the surdmutes k and l.
Secondly, Vieta understood the transformation of equations, so as to clear them from coefficients or surd roots, or to eliminate the second term.
Luca di Borgo perceived, in a certain sense, the application of algebra to geometry, observing, that the rules as to surd roots are referrible to incommensurable magnitudes.
When a surd follows the sonant or vice versa, either in the same word or in two neighboring words, then either the surdchanges into a sonant or the sonant into a surd so that they are both of the same quality.
On the one hand Aristotle by his doctrine of matter admitted a surd into his system.
On the other, he assigned to [Greek: nous] 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.
I do not exactly share the misgivings that a surd mute might be mistaken for a deaf and dumb letter, but I think the name is awkward.
There are various ways of testing the original surd or sonant nature of final consonants in Sanskrit.
They have proved that all Aryan languages show traces of an original distinction between a guttural surd check, k, frequently palatalized in the Southeastern Branch (Sk.
In front of me stood Professor Surd himself, looking down with a not unpleasant smile.
Abscissa Surd was as perfectly symmetrical as Giotto's circle, and as pure, withal, as the mathematics her father taught.
The intelligible, however, lies at the periphery of experience, the surd at its core; and intelligence is but one centrifugal ray darting from the slime to the stars.
In truth, the surd conditions not merely the being of objects but their possible quantity, the time and place of their appearance, and their degree of perfection compared with the ideals they suggest.
We may say that the sonant consonant and its corresponding surd are the hard and soft forms of the same sound.
The rule of surd to surd and sonant to sonant is neglected in most of the factitious specimens of broken English.
The t of out, disturb, and the first one in street, is due to the surd s beside it, or in the German aus and strasze.
