PRO
430
PRO
have baen part of the business of the prophets on the Sabbath -daysand festivals. It is probable that God generally chose the pro-phets, whom he inspired, out of these schools.
PROPHETESS, [prophetesse, Fr. from prophet,] a womanthat foretels future events.
PROPPIYLACTICE, [wp«fux«KTix^,] in medicine, that partthereof which instructs as to the method of preserving health, andaverting diseases.
PROPITIATION, in theology, a sacrifice offered to God toassuage his wrath, and render him propitious. Among the Jews there were both ordinary and public sacrifices, as holocausts, &c.offered by way of thanksgiving ; and extraordinary ones, offeredby particular persons guilty of any crime, by way of propitiation.
R he Roman Catholics believe the mass to be a sacrifice of propi-tiation for the living and the dead. The reformed churches allowof no propitiation but that one offered by Jesus Christ on the cross, iSee Sacrifice. j
PROPITIATORY, anything rendering God propitious; as jpropitiatory sacrifices, in contradistinction to eucharistical. Among |the Jews the propitiatory was the cover or lid of the ark of the co- !venant; which was lined both within and without with plates of igold, insomuch that there Was no wood to be seen. This propi-tiatory was a type or figure of Christ , whom St. Paul calls the pro-pitiatory ordained from all ages. See Ark.
PROPLASM, is sometimes used for a mould where any metalor soft matter, which will afterwards grow hard, is cast: hence,
PROPLAS PICE, [irfosXar'x'i,] the art of maxing moulds forcasting.
which the bees stop up all the holes or cracks in the sides of theirhives. See Ree.
PROPONTIS, or the Sea of Marmora , a part of the Medi.terranean, dividing Europe from Asia; it has the Hellespont , orcanal of the Dardanelles, on the S. VV. whereby it communicateswith the Archipelago, and the ancient Bosphorus of Thrace , orStrait of Constantinople , on the N.E, communicating with the: Black or Euxine Sea .
I PROPORTION, the identity or similitude of two ratios,j Hence quantities that have the same ratio between them are said: to be proportional; c. gr. if A be to. B as C to D, or 8 lie to 4 as30 to 15; A, B, C, D, and 8, 4, 30, and 15, are said to be inproportion, or are simply called proportionals. Proportion is fre-quently confounded with ratio; yet the two convey in realityvery different ideas, which ought by all means to be distinguished.Ratio is properly that relation or habitude of two things, whichdetermines the quantity of one from the quantity of another, with-out the intervention of any third: thus we say the ratio of 5 and10 is 2, the ratio of 12 and 24 is 2. Proportion is the sameness orlikeness of two such relations: thus the relations between 5 and 10and 12 and 24 being the same, or equal, the four terms are said tobe in proportion. Hence ratio exists between two numbers, butproportion requires at least three. Proportion, in fine, is the habi-tude or relation of two ratios when compared together ; as ratio isof two quantities. See Algebra, Arithmetic, and Geometry .If four quantities are proportional, they will also be proportionalin alternation, inversion, composition, division, conversion, equa-lity, &c. (Euclid, 5 Def. 13, 14, 15, 10, 17, 18, 19, 20,) as inthe following table:
A TABLE OF PROPORTIONALS.
13
As nx : x : : nz : z in direct proportion.Alternation,nx : nz : : x : z.
Alternate reason is, when we compare the antecedents one with the other,as also the consequents,
14
Inversion,x : nx : : z : nz*
Inverse proportion, or reason, is a comparison of the consequents to theantecedents.
15
Composition.nx-{- x : x : : nz +Z : z.
Composition of reason is a comparison ol the antecedent and consequent
taken together, to the consequent alone.
16
Division.
nx x : x : nz — z : z.
Division of reason is the comparison ol the excess of the antecedent abovethe consequent to the same consequent.
17
Conversion.
ni : nx — x :: nz : nz — z.
Conversion of reason is the comparison of the antecedent to the differenceof the terms.
18
Equality.
(nx:x::nz\z. }
If < mnx : mx : : muz : viz. >
(?w: z : : mux ; viz. )
Proportion of equality is a comparison of the extreme quantities by leav-ing out those in the middle.
19
Ordinate Proportion.
nx : x :: mnx : mx.
x : nz :: mx : mnz.nz : z : mnz : mz.
Ordinate proportion is that in which one compares the terms in thesame manner .of order, as in the preceding example.
i
' 20i
J
Inordinate Proportion.
, ( nlr. nx. mx. \
“i !•
n 9 x : nx : : nz : z.
v*
nx : mx :: — z : nz.m
Inordinate proportion is the comparing the terms in the one rank ofproportionals, in a retrograde, or backward, order, with these ot an-other.
Proportion, or Rule of Three . See Arithmetic.
Proportion, Arithmetical. See Algebra .
Proportion, Compass of, a name by which the French , andafter them some English , authors call the sector.
Proportion, Geometrical. See Geometry .
Proportion, IIarmonical, or Musical Proportion, isthat in which the first term is to the third, as the difference of the 1first and second is to the difference of the second and third ; or jwhen the first, the third, and the said two differences, are in geo- ;metrical proportion. Or, four terms are in barmonical proportion •when the first is to the fourth as the difference of the first and se- icond is to the difference of the third and fourth. Thus 2, 3, 6,
are in harmonical proportion, because 2 : 6 : : 1 : 3. And thefour terms 9, 12, 16, 24 are in harmonical proportion, because 9 :24: : 3: 8. If the proportional terms be continued in the lormercase, they will form an harmonical progression, or series. 1. Thereciprocals of an arithmetical progression are in harmonical pro-gression ; and, conversely, the . reciprocals of hurmonicals arearitluncticals. Tims the reciprocals ot the harmouicals 2, 3, 6, are
-i-, 3-, ~, which are arithmetical ; for -j = and
*-— = * also : and the reciprocals ol the arithmetioals 1,