iplicand.

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_. But, no doubt, it is better to avoid this
construction, by using such a verb as may be said to agree with the number
multiplied. Again, and lastly, there may be, touching all such cases as,
"Twice _one are_ two," a _seventh opinion_, that the subject of the verb is
the product taken _substantively_, and not as a numeral _adjective_. This
idea, or the more comprehensive one, that all abstract numbers are nouns
substantive, settles nothing concerning the main question, What form of the
verb is required by an abstract number above unity? If the number be
supposed an adjective, referring to the implied term _units_, or _things_,
the verb must of course be plural; but if it be called a _collective noun_,
the verb only follows and fixes "the idea of plurality," or "the idea of
unity," as the writer or speaker chooses to adopt the one or the other.

OBS. 22.--It is marvellous, that four or five monosyllables, uttered
together in a common simple sentence, could give rise to all this diversity
of opinion concerning the subject of the verb; but, after all, the chief
difficulty presented by the phraseology of multiplication, is that of
ascertaining, not "the grammatical subject of the verb," but the
grammatical relation between the multiplier and the multiplicand--the true
way of parsing the terms _once, twice, three times_, &c., but especially
the word _times_. That there must be