Page:Cyclopaedia, Chambers - Volume 2.djvu/517

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In the Greek Church, the leffer Prophets are placed in order before the great ones ; apparently becaufe many of the leffer Prophets are more antient than the greater.

Among the Greeks too, Daniel isrank'd among the leffer

Trofhets. . •, ,

In the 48th Chapter of Eccleftaflicusjfaiah is particularly call'd the great Prophet; both on account of the great things he foretold, and the magnificent Manner wherein he did ir. . - ,.

Spinoza fays, the feveral Trofhets prophefied according to their refpective Humours; Jeremiah, e.gr. melancholy, and dejected with the Miferies of Life, prophefied nothing but Misfortunes. .

Dacier obferves, that among the Antients the Name Poet is fometimes given to Prophets ; as that of Prophet is at other times given to Poets. See Poet.

The Word is derived from the Greek paw, faid ; whence the latins derive their fatus, fpdken. SeeVATEs

PROPHYLACTICS, rpyvlMimiu, that part of the Art of Medicine which direBs the preventing or preferving from Difeafes. See Medicine, Preservative, i§c.

PROPITIATION, in Religion, a Sacrifice offer'd to God to affuage his Wrath, and render him propitious. See

Sacrifice. .-.-,-. j u.

Among the 7e«is there were both ordinary and public Sacrifices, as Holocaufts, i3c. offer'd by way of Thankf- eiving 5 and extraordinary ones offer'd by particular Per- sons guilty of any Crime, by way of Propitiation ■

If it were a Crime of Ignorance, they offer'd a Lamb or a Kid ; if done wittingly, they offer'd a Sheep : For the Poor, a pair of Turtles was enjoin'd as a Propitiation.

The RomiJIi Church believe the Mafs to be a Sacrifice of Propitiation for the Living and the Dead. The Reform'd Churches allow of no Propitiation but that one offer'd by Jefis Chrilt on the Crofs.

Propitiation is alfo a folemn Feaft among the jte-ws, celebrared on the tenth of the Month Ttfri, which is their feventh Month, and anfwers ro our September.

Itwasinftiruted ro preferve the Memory of the Pardon proclaimed to their Fore-fathers by Mofes on the part of God ; who thereby remitted the Punilhment due for their Worfhip of the golden Calf.

PROPITIATORY, among the jfe'XS, was the Cover or Lid of the Ark ; which was lined both within and without- fide, with Plates of Gold ; infomuch that there was no Wood to be feen. See Ark.

Some even take it to have been one piece of maflive Gold. The Cherubim fpread their Wings over the Pro- pitiatory.

This Propitiatory was the Type or Figure of Uiritt, whom St. 'Paul calls the Propitiatory ordain 'd from all

PROPLASM, Froplafma, wfoTWfut, is ufed for a Mould, wherein any Metal or foft Matter, which will afterwards grow hard, is call. See Mould.

PROPLAST1CE, strnnrmS, the Art of making Moulds, for calling things in. See Mould, Founder*,

seje

PROPOLIS, a Virgin-Wax, of a reddilh or yellowi/h Colour, wherewith the Bees Hop up the Holes and Crannies of their Hives, to keep out the cold Air,£/c See Wax.

The Propolis is a friable Matter, elleem'd fovereign in Difeafcs of the Nerves. It is alfo ufed to make Holes in Abfceffes ; and being heated on the Fire, its Vapour is re- ceived for inveterate Coughs.

PROPORTION, in Arithmetic, the Identity or Simili- tude of two Ratios. SeeRATio.

Hence, Quantities that have the fame Ratio between 'em, are faid to be Proportional : e. gr. If A, be to B ; as C, to D : or 8, be to 4 ; as 30, to 1 5 ; A,B, C, D, and 8, 4, 30, and 1 5 , are faid ro be in Proportion, or are fimply call'd Proportionals. See Proportional.

Proportion is frequently confounded with Ratio ; yet have the two, in reality, very different Ideas ; which ought by all means to be diftinguifh'd.

Ratiois, properly, that Relation or Habitude of two things which determines rhe Quantity of one from the Quantity of another without the Intervention of any third : Thus we fay, the Ratio of 5 and 10 is 5 ; the Ratio of la and 24 is 12.

Proportion is the Samenefs or Liken efs of two fuch Re- lations : Thus, the Relations between 5 and 10, and 12 and 24 being the fame, or equal ; the four Terms are faid to be in Proportion. Hence, Ratio exifts between two Numbers ; but Proportion requires atleaft three.

Proportion, in fine, is the Habitude or Relation of two Ratios, when compared together; as Ratio is of two Quantities. See Quantity.

Proportion, again, is frequently confounded with Pro- grrjfion. In effect, the two often coincide ; the difference between 'em only confiding in this, that Progreflion is a particular Species of Proportion, wherein the. fecond of

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three Terms is a mean Proportional between the other two or has the fame Ratio to the third which the firft has to the fecond.

Add to this, that Proportion is confin'd to three Terms • but Progreflion goes on to infinity ; (fo that Progreflion is I iSeries or Continuation of Proportions :) And that in f uur Terms 3, 6, 12, 24, Proportion is only between the two Couples 3 and 6, and 12 and 24; bur Progreflion is bc- tweenall thefour Terms. SeepROGRESsloN.

Proportion is faid to be continual, when the Confequent of the firft Ratio is the fame with the Antecedent of the f e. cond ; as, if 3 be to S, as 6 to 12. See Continual.

The Proportion is faid to be Hifirete, or Interrupted • when the Confequent of the firft Ratio differs from the An- tecedent of the fecond ; as, if 3 be to 6, as 4 to 8.

Prop&rtioHfigila, is either faid to be Arithmetical, or Geometrical ; as the Ratios are.

Arithmetical Proportion, is the Equality_ of two or more Arithmetical Ratios ; or the Equality of difference between three feveral Quantities.

' Thus, 1, 2, 3 ; and 2, 5, 8, are in Arithmetical Propor- tion ; becaufe there is the fame difference betwixt the Numbers compared, which are 1 to 2, and 2 to 3 j or 2 to 5, and 5 to 8.

If every Term have the fame Ratio to the next as the firft has to the fecond ; the Terms are faid to be in continual Arithmetical Proportion ; as 5, 7, 9, 12, 15.

If the Ratio between any two Terms differ from that of any others ; the Terms are faid to be in Arithmetical Pro- portion difcrete, or interrupted; as where 2 : 5 : 6 : 0, the Ratios of 5 and 6 being different from that of 2 and 5.

A Series of more than four Terms in Arithmetical Pro- portion, form an Arithmetical Progreflion. S:e Pro- gression.

Properties of Arithmetical Proportion.

i°. If three Numbers be in Arithmetical Proportion, tU Sum of the Extremes is equal to double the middle Term. Thus, in 3, 7, 11 j the Sum of 3 and 11 is equal to twice 7 ; viz. 14.

Hence we have a Rule for finding a mean Proportional Arithmetical between two given Numbers; half thcSum of the two being the Mean required : Thus half the Sum of 1 1 and 3, viz. 14, is 7.

2°. If four Numbers be in ArithmsticalPropcrtion,th& Sum of the Extremes is equal to the Sum of the middle Terms. Thus, in 2 : 3 : 4 : 5 ; the Sum of 5 and 2 is equal to the Sum of 3 and 4, viz. 7.

Hence, four Terms in Arithmetical Proportion, are ftill proportional if taken inverfely 5 : 4 : 3 : 2 ; or alternately, thus, 2:4:3:5; or, inverfeJy, and alternately 5 thus, 5:3:4:2.

3 . If two Numbers in Arithmetical Proportion be added to other two ; the lefs to the lefs, SSc. their difference is in a duplicate Ratio, i. e. double that of the refpef.ive parts added : Thus, if to 3 : 5 be added 7 : 9, the Sums are 10: 14; whofe difference 4 is double the difference of 3 : 5, or 7 : 9. And if to this Sum you add other two, the difference of the laft Sum will be triple the difference of the firft two, and fo on.

If two Arithmetical Proportionals be fubftracled from two others in the fame Ratio, the lefs from rhe lefs, Sic. the Arithmetical Ratio of the Remainder is o. Thus from o : 7 taking 3:5, the Remainders are 4, 4.

Hence, if Arithmetical Proportionals be multiply'd by the fame Number, the difference of their Produces will contain the firft difference as oft as the Multiplier con- tains Unity. Thus 3: 5 multiply'd by 4, produce 12, 20, whofe difference 8 is equal to 4 times 2, the difference of

3 and 5.

4 Q. If twoNumbers in Arithmetical Proportion be added to, or multiply'd by, other two, in another Ratio of the fame kind, lefs by lefs, &c. the Sums are in a Ratio which is the Sum of the Ratios added or multiply'd. Thus, 2 : 4 and 3 : 9 being added ; the Sums are 5:13, whofe diffe- rence is 8, the Sum of 2 and 6, the differences of the Numbers given.

GecwzernctfiPROPoRTioN, is the Equality of two Geo- metrical Ratios, or Comparifons of rwo Couples of Quan- tities. See Geometrical Proportion.

Thus 4: 8 : : 12 : 24, are in Geometrical Proportion i the Ratio of 4 and 8 being equal to that of 12 and 24; i.e.

4 being contain'd as often in 8, as 12 is in 24. Again, 9, 3, 1 are in Geometrical Proportion, 9 being triple of 5, as 3 is of 1.

If in a Series of Terms, there be the fame Ratio be- tween every rwo Terms that there is between the firft ana fecond ; they are faid to be Continual Geometrical Pro- portionals : As 1 : 1 ; 4 : 8. ,

If any two Terms have a different Ratio from thatot tns firft and fecond, they are (aid to be in DisjuiiH, °' I " te ''j