PRO 
therefore, he substitutes a -yicious and pre- 
carious one. To give a just idea of the pro- 
nunciation of a language, it seems necessary^ 
to fix as nearly as possible all the several 
sounds employed in the pronunciation of 
that language. 
Pronunciation is also used for the fifth 
and last part of rhetoric, which consists in 
varying and regulating the voice agreeably 
to the matter and words, so as most effec- 
tually to persuade and touch the hearers. 
It is much the same with what is otherwise 
called emphasis. 
This emphasis is a considerable stress or 
force of voice, laid upon that word in a sen- 
tence by which the sense of the whole is 
regulated : thus, suppose you were asked, 
“ are you determined to vvalk this day to 
London?” If the emphasis be placed on 
the word you, the answer may be, “ yes, I 
go myself;” or “ no, I shall send my son.” 
Again, if it be placed on the word walk, the 
answer is, “ yes, I am;.” or “ no, I shall 
ride if on the words to-day, then the an- 
swer is, “ yes or “ no, I shall go to-mor- 
row and lastly, if the emphasis be placed 
on the word London, the answer may be, 
“ no, I shall go to Richmond only.” 
Quintilian advises his pupils to study the 
principles of pronunciation under a come- 
dian. There are three things which come 
under the pronunciation, viz. the memory, 
voice, and gesture. 
PROOF, in arithmetic, an operation 
whereby the truth and Justness of a calcula- 
tion is examined and ascertained. The pro- 
per proof is always by the contrary rule : 
thus subtraction is the proof of addition, 
and multiplication of division; and vice 
versa. 
Proof, in military affairs, is a trial 
whether the piece will stand the quantity 
of powder allotted for that purpo.se. 
PROPAGO, in botany, properly a slip, 
layer, or cutting of a vine or other tree. 
PROPORTION. When two quantities 
are compared one with another, in respect 
.of their greatness or smallness, the compari- 
son is called ratio, reason, rate, or propor- 
tion; but when more than two quantities 
are compared, then the comparison is more 
usually called the proportion that they have 
to one another. The words ratio and pro- 
portion are frequently used promiscuously. 
When two quantities only are compared, 
the former term is called the antecedent, 
and the latter the consequent, 'file relation 
pf two homogeneous quantities one to ano- 
ther, may be considered either, 1. By how 
PRO 
much the one exceeds the other, which is 
called their difference. Thus 5 exceeds 3 
by the difference 2. Or, 2. What part or 
parts one is of another, which is called ratio. 
Thus the ratio of 6 to 3 is | = or double ; 
and the ratio of 3 to 6 is -| = t, or subduple. 
When two differences are equal, the 
terms that compose them are said to be 
arithmetically proportional. Thus suppose 
the term to be a and b, their difference d. 
If a be the last term, then a-\-d—b. And 
if a be the greatest, then a—d = h. 
But when two ratios are equal, the terms 
that compose them are said to be geome- 
trically proportional. For suppose a and 
b to be the terms of any ratio ; if a be the 
least term, put rs:-, then arz=:b by equal 
multiplication: but if b be the least term, 
putr = ^, then hr = a by equal multipli- 
cation, and j^~b by equal division. 
Thus the ratio of two quantities, or of two; 
numbers, in geometrical proportion, is found 
by dividing the antecedent by the conse- 
quent, and the quotient is the exponent or 
denominator of the ratio. 
If when four quantities are considered, 
you find that the first hath as much great- 
ness or smallness in respect to the second, 
as the third hath in respect to the fourth : 
those four quantities are called propor- 
tionals, and are thus expressed. 
. t A : B C : D ) , . 
i ^ 2 ::16: 4 S ^ ® 
tains B = 2 four times, so C = 16 contains 
D = 4, tour times ; and therefore A has the 
same ratio to B as C has to D; and conse- 
quently these four quantities having equal 
ratios, are proportionals. 
Proportion consists of three terms at least, 
whereof the second supplies the place of 
two. 
When three magnitudes. A, B, C, are 
proportional, the first. A, has a duplicate 
ratio to the third, C, of. that it hath to the 
second, B ; but when four magnitudes, 
A, B, C, D, are proportional, the first. A, 
has a triplicate ratio to the fourth, D, of 
what it has to the .second, B ; and so always 
in order one more, as the proportion shall 
be extended. 
Duplicate ratio is thus expressed, ^ - 
C B 
twice ; that is, the ratio of A to C is dupli- 
cate of the ratio of A to B. For let A _ 2, 
B = 4, C = 8 ; then the ratio of 2 to 8 is 
