Page:Cyclopaedia, Chambers - Volume 2.djvu/578

 RAT

( 9 6i )

RAT

£. gr. if the Exponent be \, then 5:8 = 1;,; whence it munition, Bread, Drink, or Forrage, distributed to each Soldi- flnnears the Ratio is call'd Subfupertripartiens qtmttas. er and Seaman for his daily Sublicence. See Ammunition,

As to Names of Irrational Ratio's, no-body ever attempted cjyc. • em The Rations of Bread are regulated by Weight.— The Officers

Sam, or Identic Ratio's, are thofe whofe Antecedents have an have feveral Rations according to their Quality, and the Number equal refpedt to their Confequents, i. e. whofe Antecedents di- of Attendants they are obliged to keep.

vided by their Confequents, give equal Exponents. See IdeN- The Horfe have Rations of Hay and Oats, when they cannot

go out to Forrage. — The Ship's Crews have their Rations of

Bisket, Pulfe, and Water, proportioned according to their Stock.

When the Ration is augmented on Occalions of Rejoycing,

it is call'd double Ration.

The ufual Ration at Sea, particularly among the Portugeze, &c.

TlTY*

And hence may the Identity of Irrational Ratio's be concei- ved.

Hence, Firjf, as oft as the Antecedent of one Ratio contains its Confequent, or what ever Part it contains of its Confequent,

fo oft, or 'fuch Part of the other Confequent does the Antece- is a Pound and half of Bisket, a Pint of Wine, and a Quart of

Sent of the other Ratio contain: Or, as oft as the Antecedent frefii Water per Day, And each Month an Arrobe or 31 Pound

of the one is contain'd in its Confequent, fo oft is the Antece- of Salt Meat, with fome dried Fifti and Onions,

dent of the other contain'd in its Confequent. Some write Ration, and borrow the Word from the Spanifb

Secondly, If A be to B as C to D, then will A : B : : C : D ; or Ration. But they both come from the Latin Ratio ; and in fome

A ; B = C : D. The former of which is the ufual Manner of Parts of the Sea they call it Reafon.

rep'refenring the Identity of Ratio's; the latter is that of the ex- RATIONABIL1 parte bomrum, a Writ which lies for the

cellent Wolfius ; which has the Advantage of the former, in that the Wile, againft the Executors of her Husband denying her the

middle Charafier =, which denotes the famenefs, is fcieniifical, third Part of her Husband's Goods, alter Debts and Funeral Ex-

e. expreffes the Relation of the thing reprefenced, which the other : : does not. See Character.

Two equal Ratio's, e. gr. B : C =S D : E, we have already ob- served, do conffitute a Proportion: Of two unequal Ratio's, e. gr. A:B and C D we call A:B the Greater; if A: B> C: D; on the contrary we call C:D the lejjer, if C:D < A:B.

Hence, we exprefs a greater and lefs Ratio thus. E. gr. 6 to of the Country makes for it. 13 has ^greater Ratio, than 5 to 4; for, 6: 3 (— 2) > 5 : 4. RATION AB1LES Expeufie, Reafinable Expences; the Com- (=; ij), But 3 to 6 has a lefs Ratio than 4 to 5, for 4 = * mons in Parliament, as well as the Prodors of the Clergy in Con- ^ 4 vocation, were amiently allow'd Rationabiles Expenfas ; that is,

1 he Ratio is faid to be compounded of two or more other Ra- fuch Allowance as the King, conlidering the Prices of all things, tie's, which the Fadum of the Antecedents of two or more fhall judge meet to impofe on the People, to pay for the Sub- Ratio's lias to the Fadum of their Confequents. Thus 6 to 7 is fiftance of their Representatives. SeeREFREsENTATivE, ef 1

pences paid. See Goods.

Fitzherbcrt quotes Magna Cbarta and Glunville, to prove that by the Common Law or England, the Goods of the deceafed, his Debts firft paid, fhould be divided into three Parts ; whereof his Wife to have one, his Children a f.cond, and the Executors a third. Adding, that this Writ lies as well for the Children, &c. as the Wife. But it feems only to obtain where the Cuftom

This in the 17th of Edivard II. was 10 Groats per Day for Knights, and 5 for Burgeiles. Afterwards, 4 Shillings a Day for Knights, and 2 Shillings for Burgeffes; which was then deem'd an ample Retribution both for Expences, for Labour, Atten- dance, Neglect of their own Affairs, &c. See Parliament.

RATION ABILIBUS divifs, is a Writ that lies where two

Lords have the Seigneuries joining together, for him that finds

his Waff e encroached upon, within the Memory of Man, againft

the Encroacher ; thereby to rectify the Bounds of the Seigneu-

Thfi, Ratio's fimilar to the fame third, are alfo fimilar to one ries: in which Refpeft Fitzherbert calls it, in its own Nature, a

mother ; and thofe fimilar to Similar, are alfo fimilar to one an- Writ of Right.

^ ' RATIONAL, Reafinable. See Reason.

Secondly, If A : B = C : D ; then, inverfely, B : A =: D : C. Rational, or true Horizon, is that whofe Plane is conceived Thirdly, Similar Parts P and p have the fame Ratio to Wholes to pals through the Centre of the Earth ; and which therefore T and t; and if the Wholes have the lame Ratio, the Parts are dividesthe Globe into two equal Portions, or Hemifpheres. See

_l a Ratio compounded of 2 to 6, and 3 to 12.

Particularly, if it be compounded of two, it. is call'd a Dupli- cate Ratio ; if of three, a Triplicate; if of four, Quadruplicate; and in the general Multiplicate, if it be compofed of feveral fi- milar Ratio's. Thus 48 : 3 is a duplicate llatio of 4 : I and 12:3.

Properties of Ratio'* of Quantities.

fimilar.

Fourthly, If A : B = C : D ; then, alternately, A : C = B : D. And hence, A = C ; hence, alfo, if A : B = C : D ; and A : F = C ■ G ; we (hall have B : F = D : G. Hence, again, if A : B = C:D; andF:A = G:C; we mail have F : B = G : D.

Fifthly, Thole things which have the fame Ratio to the fame, or equal things, are equal : <& w verfa.

Horizon.

'Tis call'd the Rational Horizon, becaufe only conceived by fheUnderftanding; in oppofition to the finfibh or apparent Ho- rizon, which is vilible to the Eye. See Sensible.

Rational Quantity or Number, a Quantity or Number Com- menfurable to Unity. See Number and Unity.

Suppofing any Quantity to be 1, there are infinite other Quan-

Si'xtbly, If"you multiply any Quantities, as A and B, by the titles, fome whereof are Commenfurable to it either (imply, or in

fameor equal Quantities; their ProdudsD and E will be to each Power; thefe Euclid calls, Rational Quantities. See Qjjan-

Seventhly, If you divide any Quantities as A and B, by the The reft, that are Incommenfurable to 1, he calls, Irrational

fame or equal Quantities, die Quotients F and G will be to each Quantities, or Suras. See Surd.

other as A and B. Rational Integer, or -whole Number, is that whereof Unity

Eighthly, The Exponent of a compound Ratio is equal to the is an aliquot Part. See Number and Aliquot Fart

Fadum of the Exponents of the (imple Ratio. See Expo- Rationalise, or broken Number, is that equal to fome

NENT aliquot Part or Parts of Unity. See Fraction.

Ninthly, If you divide either the Antecedents, or the Confe- Rational mxt Number, is that confiding of an Integer and a

quents of fimilar Ratio's, A : B and C : D by the fame E ; in the Fradion, or of Unity, and a broken Number,

former Cafe, the Quotients F and G will have the fame Ratio Commenfurable Quantities are defined by being to one ano-

to the Confequents B and D; in the latter, the Antecedents A ther, as one Rational 'Number to another. ,_,„,..-.

and B will have the fame Ratio to the Quotients H and K. For Unity is an aliquot Part of Unity; and a Fradion has

Tenthly, If there be feveral Quantities in the fame continued fome aliquot Part common with Unity : In things, therefore, that

Ratio A, B, C, D, E, dye. the firft, A is to the third, C, in a are as a Rational to a Rational Number, either the one is anali-

ckplicate Ratio, to the fourth, D, in a Triplicate, to the fifth E, in quot Part of the other, or there 13 fome common aliquot Pare

iS)uaarupl,cate, &c. Ratio of the Ratio of the firft, A, to of both : Therefore they are Commenfurable. bee Commen-

cond B SURABLE.

E'kventhly, If there be any Series of Quantities in the fame Hence, if a S^oW Number be divided by a Rational, the

Ratio, A, B, C, D, E, F, 6-c. the Ratio of the firft, A, to the Quotient is a Rational .„,.,_ „ .. .

laft, F, is compounded of the intermediate Ratio's, A : B, B : C, RATIONAL Ratio, is a Rat.o whofe Terms are Rattonal

C : D, D : E, E : F, &c

Tuxlfthly, Ratio's compounded of Ratio's, whereof each is e- qual to another, are equal among themfelves. Thus the Ratio's 90:3 — 060:32 are compounded of 6: 3=: 4:2, and 3: It=i2 : 4; and 5 : 1 ^20:4. Forother Properties of fimilar or equalitarw's, fee Proportion.

Ratk

Law Writers, is ufed for a Reafon, or Judg- Reafon

Quantities ; or a Ratio which is as one R^roWNumber to ano- ther, e. gr. as 3 to <>. See Ratio.

The Exponent of a Rational Ratio is a Rational Quantity. See Exponent.

RATIONALE, an Account, or Solution of fome Opinion, Adion, Hypothefis, Phenomenon, or the like, on Principles of

ment gi ve n in a Caufe. Hence, ponere ad rationent, is to Cite one to appear in Judgment, Walfng ' flatus, RagioNE deflate.

Rati

RATIOCINATION Reasoning,

See Reason of State. the" Adion of Reasoning. See

Hence Rationale has become the Title of feveral Books; the moft confiderable is the Rationale of the Divine Office, by Gutll. Durandus, a celebrated School Divine, Bifhopof Mende; finlfhd in 1286, as he himfelf tells us.

Rationale, is alfo an antient facerdotal Veftment, wore by

RATION, ia the Forces, a Pittance, or Proportion of Am- the High-Prieft under the old Law; and call'd by theHfir ™^n>