Owen—Hybrid Parts of Speech. 16 & 
the two dots express a ratio; and a ratio is merely a quantita¬ 
tive—or say, in the present case, a numerical—relation. 
Let me now adapt the proportion formula a bit more closely 
to my purpose. Accordingly 3>2::12>11, in which expres¬ 
sion the previously altogether indefinite ratios are displaced by 
ratios definite to this extent, that they are ratios of excess. In 
this expression it is as obvious that 12 is conceived to exceed 
11, as it is in the isolated mathematical statement “12 >11.”' 
Accordingly, it is strictly proper to render “12 >11” by “twelve 
to exceed eleven.” 
Adopting now the method of those who, in “Astronomers 
declare the sun to exceed the moon,” regard the object of “de¬ 
clare” as “all that follows,” I propose the total “twelve to ex¬ 
ceed eleven” as the object of “equals.” Indeed, completing 
my translation of mathematical into linguistic phraseology, and 
obtaining “Three to exceed two equals twelve to exceed eleven,” 
I move you that the object of “equals” is “all that follows,” and 
also that the subject of “equals” is all that precedes. 
That I have, however, directly antagonized the mathematical 
view, is obvious. A proportion is defined as an equality—that 
is, a particular relation—between two ratios. These ratios also 
are themselves relations, attended moreover by their terms, 40 
and therefore with them constituting thoughts. If accordingly, 
to mathematical apprehension, total thoughts were what should 
pose as equal one to the other, they could hardly have been 
overlooked, being so conspicuously in view. It was doubtless, 
therefore, advisedly that proportion was defined, not at all as 
an equality of thoughts (or, say, equations or inequations, as 
the case may be) but as an equality of ratios-—that is, an 
equality, or special relation, obtaining between a member of 
one thought and a member of another thought. I find accord¬ 
ingly that, in the procedure of Mathematics, not a total thought^ 
but only a single nucleary member thereof, although unsepar¬ 
ated from its fellow terms, is regarded as forming part of an¬ 
other thought. 
It appears accordingly that the method of Grammar and that 
of Mathematics are mutually antagonized. Personally cher- 
40 Indeed the ratios can not be identified without their terms. 
