OBS. 20.—­As to what constitutes the subject of the verb in multiplication, I have already noticed three different opinions.  There are yet three or four more, which must not be overlooked in a general examination of this grammatical dispute.  Dr. Bullions’s notion on this point, is stated with so little consistency, that one can hardly say what it is.  At first, he seems to find his nominative in the multiplicand, “used as a singular noun;” but, when he ponders a little on the text, “Twice two is four,” he finds the leading term not to be the word “two,” but the word “number,” understood.  He resolves, indeed, that no one of the four words used, “is in construction with” any of the rest; for he thinks, “The meaning is, ’The number two taken twice is equal to four.’” Here, then, is a fourth opinion in relation to the subject of the verb:  it must be “number” understood.  Again, it is conceded by the same hand, that, “When numerals denoting more than one, are used as adjectives, with a substantive expressed or understood, they must have a plural construction.”  Now who can show that this is not the case in general with the numerals of multiplication?  To explain the syntax of “Twice two are four,” what can be more rational than to say, “The sense is, ’Twice two units, or things, are four?’” Is it not plain, that twice two things, of any sort, are four things of that same sort, and only so?  Twice two duads are how many?  Answer:  Four duads, or eight units.  Here, then, is a fifth opinion,—­and a very fair one too,—­according to which we have for the subject of the verb, not “two” nor “twice” nor “twice two,” nor “number,” understood before “two,” but the plural noun “units” or “things" implied in or after the multiplicand.

OBS. 21.—­It is a doctrine taught by sundry grammarians, and to some extent true, that a neuter verb between two nominatives “may agree with either of them.” (See Note 5th to Rule 14th, and the footnote.) When, therefore, a person who knows this, meets with such examples as, “Twice one are two;”—­“Twice one unit are two units;”—­“Thrice one are three;”—­he will of course be apt to refer the verb to the nominative which follows it, rather than to that which precedes it; taking the meaning to be, “Two are twice one;”—­“Two units are twice one unit;”—­“Three are thrice one.”  Now, if such is the sense, the construction in each of these instances is right, because it accords with such sense; the interpretation is right also, because it is the only one adapted to such a construction; and we have, concerning the subject of the verb, a sixth opinion,—­a very proper one too,—­that it is found, not where it is most natural to look for it, in the expression of the factors, but in a noun which is either uttered or implied in the product.