Belmont chronicle. [volume] (St. Clairsville, Ohio) 1855-1973, 1869-04-15
EDUCATIONA Al.
Twice Two IL Four
ny W. D. HExK1E, SALEM, OHIO.

EDCCAIlON L..
Twice Two is Four
BY W. D. HENKLE, SALEM, OHIO.
There are many expressions in arith
metical language in which there is 9
doubt whether the singular or plura
form of the verb should be used Before
discussing the subject, l shall present 8
variety of forms selected almost entire.
ly from different mathematical works
1t must not be supposed that l have
given all the authorities for each mode
of expression, but only such as 1 have
happened to observe in my examina-
ton. ---
Adams, ID. P. Colburn, Daily, Davies,
Dean, Docharty, Dodd, Eaton, F. Emer-
son, Encyclopedias Britannica, Felter,
Greenleaf, Leach and Swan, Elias
Loomis, Mann and Chase, Mayo, Nay
lor, Nelson, Orton, Parke, Pike, Quack-
enbos, Ray, III. n. Robinson. Herbert
Spencer, Schell. r. c. Smith, Smith
and Duke, Stoddard, J. B. Thompson,
James Thompson, Vogdes, Voster, and
Walton, say. ''2 and are 5''.
Babcock, Pike, Quacken hos, and Ward
lin 1874, say, "2 and 3 is 81.
Blakelock, Daily, aud E Loomis, say,
''2 and 3 make 81; ID. p. Colburn, Dean,
Eaton, Felter, and Leach and Swan,
say, "2 plus 8 are"
Adams, F. Emerson, Greenleaf, Hut
ton, Ray, and Quackenbos, say, - plus
8 ISL.
Blakeleck, D. P. Colburn, Felter,
Mann and Chase. Ray, and Schuyler,
say, .'2 plus equap'.
Brooks, u. p. CoIburn. Dean, Eaton,
Nelson, Quackenbos, Ray, Stoddard,
and Walton, say, ''2 plus equdls''.
Blakelock says. - plus 3 erceeds"
and Heath, % plus 8 contains"
Dean says, twice 0 are OF; Dean and
Eaton, twice l are 2''; and Vogdes,
twice make ~.
Eaton says, twice are A.; twice 2
is A. is found on p. l59 ofSir VIM. Ham
ilton's Philosophy, and in the Encyclo-
padia Britannica.
Pike, Talbot, and Vogdes. say, twice
2 make 4"; Rainey Says. twice = equals
Adams, Felter, Greenleaf, Jas. Rob
inson. and Smith and Duke, say. two
times are OF; and f. Leomi., ''2 times
0 make o.. ..
Adams, Chase, Davies, Dean, Felter,
E. Loomis. .Naylor. Nelson,
Ray, Jas. Robinson, Schell. smith and
Duke, Stoddari, r. c. Smith. j. B.
Thomson, Wilson. and Walton, say,
''2 times l are ~; and Pike and Quack-
enbos, ''2 times / is o.
Adams, Chase, w. Colburn, Davies,
Dean, Eaton, +. Emerson, Felter,
Greenleaf, Leach and Swan, S. l.. Loo
mis-, Z. Loomis, Nelson, Rainey, Ray
Schell. Schuyler, Smith and Duke, John
Smith, Stoddard, J. B. Thomson, Jas.
Thomson Irish), Tracy, Voster, and
say, ''2 times 2 are AZ; Adams,
Brooks, Dodd, Greenleaf, En-
cyclop9dia Britannica, Heath, Hutton,
Geo. Peacock, Quackenbos, I'll. n. Rob-
inson, Stoddard, and Ward lin 1734),
say, "2 times 2 is AZ.
Dalby, f. Loomis, and Ray, say. "2
times make ~; and Hutton ai.d Pike,
''2 times makes 4''
Dean and Rainey say, .'2 times 2
equdP'; and Brooks and Stoddard, 2
times 2 eqaals":
"The number eight, etc., is considered col
lective noun conveying the idea of unity, and
therefore requires verb in the singular num-
ber."-IJ. B. Thomson, 1s47.
The practice of using the singular form of
expression in reading proportion is very COM
mon. but its propriety is doubtful for the num-
bers T. etc. certainly express plurality of idea;
and especially so when used applicately. As 2
ydrds is 10 yards, is dollars to6 dollars sounds
very much like doing violence to one of the
leading rules Of syntax; and yet some object to
the expression, As are TO so are to G. psdsn-
tic. Neither does 1t seem clear that there is less
in an abstract than in an applicate
number. that is less plural number than 3
men or houses. In the above the singular is
used in Difference 10 custom. 1t is true that we
sometimes consider even large number as a
unit, or simply as a number, but it does not
seem that the size of numbers can be thus COM
pared, unless we consider numbers as represen-
tativss Of magnitude and not as made up of
many distinct parts."-[Parl1er's Philosophy Of
Arithmetic, 1872, p. los; 1919. p. log,
I'VE presume some, at first, will object to this
form of expression, as heretofore the plural verb
(are) has generally been used; but We believe a
reflection will convince them that
the form used by us 2 times is 2 times is 4,
etc., is correct. 1t will be observed that the
word times is not the nopsi,.astpe or subject of
the verb; nor is this word in connection with
the word preceding it, but that phrase, Onclud-
Ing the word preceding and the word following
times, Is the simple single subject of the verb
and therefore requires Its singular form.''-
TWebb's Second Reader, p. 20, 1858. -..
"In some arithmetics the language employed
In the operation OF multiplying-such as Twice
two are four. twice three are skis incorrect
It should be, Twice two is FOUR ETC.; for the
word t,cO is used as singular noun-the name
ofa number. The adveb twice is not in con-
struction with it, and consequently does not
make it plural. The meaning Is, The number
two taken twice is equal to FOUR For the same
reason we should say, Three times t,Uo is six,n
because the meaning is, Ttco taken three times
Is six five say, Three times one are three
we make times the subject ofthe verb, whereas
the subject of the verb really is one' and times
Is in the objective of number. 2:4::6:I2
should be read, 'As is to !, SO is 8 to l2;' not
As two are to four, so are etc. But when nu-
merals denoting more than one are used as ad-
lectives, with substantive expressed or under
stood. they must have plural construction. -
[Bnllions's Analyt. and Practical Grammer, p.
80. 1852. H.. -
FINES, Three times the sons age is equal
to the fathers Five times four are twenty
Five times enc are five.'
There is an inconsistency in the foregoing
modes ofexpression. Custom. however, seems
determined TO uphold them all. To parse them
as they are. apply Rule VI "A Noun or Pronoun
that limits the meaning of a verb. an adjective,
pr an adverb, Is sometimes used in the objective
case without a proposition expressedl to times
in the first example. and to four and one in the
others. The sons age, taken three times, etc.
Five times Of four as TO four 10, regard 10 four
Common School Grammar, p. 24
AZ may use plural verb when it is true of
both its nouns separately, and also when it is
only true of them taken together. Now how is
this in another example? Am to say t,Do and
t,oo are four, or t,oo aud t,oo Jo,r?' Clearly
can not say are in the first explanation, for it
can not be true that two is four and two is four
But how odd the seconds Here as clearly may
be dramatically correct in saying two and
two are four, If, that is, understand something
for the two and the four TO apply to; two apples
and two apples make (ure) four apples But