Page:Cyclopaedia, Chambers - Volume 2.djvu/799

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hended abundance of Adjectives, iignifying a Number of people agreeing in Ibme common Attribute ; as, the Learned, tn e Great, the Devout, the Brave, the Diffolute, ($c. But rjje is here to be regarded ; for we don't iky the Eloquent, as we lay the Learned ; but Elegant Writers, gfa 'Tis Cuftom, and the Ear alone, that are to decide about thefe Differences.

Again, Adjectives taken fubftantk-ely, for other Things befide Men, are either fo ufed, to fignify a Number or Set of Things that have Ibme common Quality ; or to exprefs an abftracf Quality. ]n both which, as in thofe of Men, there are ibme authorized by Cuftom, and others form'd every Day on their Model.

"With regard to which laft, Ufe, again, and theEar, are to decide. Here All the Adjectives of Colours, are yxie&fubftan- twely i as the White, Black, Green, £cJc. Some of thofe of Qualities; as the Cold, %$c. Thofe of Time; as the Paft, Prefenr, Future: And many of other Matters ; as the Agree- able, the Sublime, the Principal, i£c. Nor is it only in the Pofitive, but alio in the Comparative and Superlative Degrees, that Adject ives are ufed fubftantively ; as, The Utter of the two ■■ The left of it, &.

SUBSTITUTE, a Petfon appointed to officiate for an- other, in cafe of Abfence, or other legal Impediment.

In the French Law, the ^Frocureurs, or Procfors, are obliged to name two of their Brethren for Substitutes, whofe Names are wrote after theirs in the Lift; to receive Signi- fications and Summons's made in their Ablence.

The Word is form'd from the Latin, fub, under, and Jfatuo, I appoint, edablifh.

Substitute, in Medicine, aDrug, or Remedy that may be ufed in lieu of another ; or that fupplies the Place of an- other of like Virtue, which is not to be had ; call'd alfo a Sttccedaneum. See Succedaneum.

The Root of the great Centaureum, and fometimes Monk's Rhubarb, are ufed as Substitutes to Rhapontic.

SUBSTITUTION, in Grammar, the ufing of one Word for another; or a Mode, State, Manner, Perfou or Number of a Word for that of another. This the Gram- marians orherwife call Sylleffts. See Syllepsis.

Substitution, in the Civil Law, a Difpofition of a Teftator, whereby he Subftitules one Heir to another, who has only the Ufu-fruit, and not the Property of the Thing left him.

Subftittttion is a kind of Inheritance, call'd Fiduciary, or Tidei-commiffto, in regard the immediate Inheritor has only the Ufe or Fruit of the Thing; the Body thereof being fubftituted and affected to certain Perfbns, who are likewiie to have the Ufu-fruit in their Times, but never the Property. In iome Countries, the Subftittttion is perpetual ; in France, it only holds to the fourth Generation.

Subfiitution an'fwcrs to Remainder, in our common Law. See Remainder.

Among the Romans, there were abundance of thefe Fidu- ciary Heirs ; who enjoy'd Inheritances, till they returned them into the Hands of the right Heir ; and the Reafon why they did not likewiie retlore the Fruits, or that the Fruits were not deem'd to make a Part of the Inheritance, but only of the Thing, was, that the Fiduciary was obliged to run the Risks, and to {land the Charge of the Culture of the Land.

Substitution, in Algebra, Fracfions, t£c. is the putting in the Room of any Quantity in an Equation, fome other Quantity, which is equal, but exprefs 'd after another Man- ner. See Quantity.

SUBSTRACTION, in Arithmetic, the fecond Rule, or rather Operation, in Arithmetic ; whereby we deducf a lefs Number from a greater, to learn the precife Difference :

Or, more juftly, Subtraction is the finding of a certain Number from two Homogeneous ones given ; which, with one of the given Numbers, is equal to the other. See Arith- metic.

The Dodlrine of SubftraBion is as follows ;

TofiibftraB a lefs Number from a greater.

\° Write the lets Number under the greater, in fuch Man- ner, as that homogeneous anfwer to homogeneous Figures, i.e. Unites to Unites, Tens to Ten, £5?f. as we have directed under Ann it ion. 2° Under the two Numbers, draw a Line. 3° SubfttaB, fevcrally, Unites from Unites, Tens from Tens, Hundreds from Hundreds ; beginning at the right Hand, and proceeding to the Left ; and write the feveral Remainders in their correfuondent Places, under the Line. 4 If a greater Figure come to be fubtraBed from a lefs ; borrow an Unite from the next Left-hand Place ; this is equivalent to 10, and added to the lefs Number, the Subtraction is to be made from the Sum : Or if a Cypher chance to be in the next Left-hand Place, borrow the Unite from the next further Place. By thefe Rules, any Number may be fubtraBed out of another greater. For Example 5

If it be requited, from To Subtract

9800403459 4743865263

The Remainder will be found 5056538 196

For, beginning with the right Hand Figure, and taking i from 9, there remains 6 Unites, to be wrote underneath the Line : Going then to the next Place, 6 I find, can't be taken from 5 ; wherefore, from the Place of Hundreds 4, I borrow one, which is equivalent to Ten, in the Place of Tens; and from the Sum of this 10 and 5, viz. 15, fubtraBing 6, I find 9 Tens remaining, to be put down under the Line. Pro- ceeding to the Place of Hundreds, 2 with the 1 borrowed at the lafl Place, make 3, which fubtraBed from 4, leave 1. Again, 5 in the Place of Thoufands, cannot be fubtraBed from 3 ; for which Reafon, taking one from 4, in the Place of Hundreds of Thoufands, into the empty Place of Tens of Thoufands, the Cypher is converted into Ten Tens of Thoufands, whence one Ten being borrowed, and added to the 3, and from the Sum 13 Thoufand, 8 Thoufand being fubtracled, we fhall have 8 Thoufand to enter under the Line : Then fubtraBing 6 Tens of Thoufands from 9, there remain 3. Coming now to take 8 from 4 ; frum the 8 further on the Left, I borrow one, by means whereof, the two Cyphers will be turned each into 9. And after the like Man- ner, is the reft of the SubftraBion eafily perform'd.

If heterogeneous Numbers be to be fubftraBed from each other ; the Unites borrow'd, r are not to be equal to Ten ; but to fo many as there go of Unites of the lefs Kind, to con- ftitute an Unite of the Greater. For Example ;

I. s. d. 4? 16 6 2719 9

17 16 9

For fince 9 Pence cannot be fubftraBed from 6 Pence ; of the 16 Shillings, one is converted into 12 Pence; by which means, for 6 we have tS Pence; whence 9 bemgfubtraBed, there remains 9. In like Manner, as 19 Shillings cannot be fubtraBed from the remaining 15; one of the 45 Pounds is converted into 20 Shillings, from which, added to the 15, 19 bang fubtracled; the Remainder is 16 Shillings. Laftly, 27 Pounds fubtraBed from 44 Pounds, there remains 17.

If a greater Number be required to be fubtracled from a lefs, 'tis evident the Thing is impoffible. The lefs Number, therefore, in that Cafe, is to be fubtracled from the greater ; and the Defect to be noted by the negative Character. E.gr. If I am requir'd to pay 8 Pounds, and am only Matter of 3 ; when the Three are paid, there will ftill remain 5 behind ; which are to be noted, 5.

SubftraBion is prov'd, by adding the Remainder to the Subtrahend, or Number to be fubfiraSed : For if the Sum be equal to the Number whence the other is to be fubtraBed, the SubftraBion is juftly perform'd : For Example 5

I. s. d. q. 9800403459 156 11 jj

4743865263 Subtrahend 21 17 2 1 Subtrahend

5056538196 Remainder 134 14

9800403459

156 11 3 i

Suestraction, in Algebra, is perform'd by conned! ing the Quantities with all the Signs of the Subtrahend changed ; and at the fame time uniting fuch as may be united ; as is done in Addition. Thus --7 a fubftraBed from -f- 9 a, makes --9*1 — 7 aor ia.

In the SubftraBion of Compound algebraic Quantities ; the Characters of the Subtrahend, are to be changed into the con- trary ones, ra'3.-|-into — ; and — into -(-. See Quantity.

To SubftraB fpecimts Numbers, or Quantities front one another ; both thofe affiBed with the fame, and thofe with contrary CharaBers.

1° If the Quantities defign'd by the fame Letter, have the feme Signs ; and the lefs be to be fubftraBed from the greater ; the SubftraBion is perform'd as in common Arith- metic, e.gr.

5b+ 4 d-f =5j&.+4/.-~ j ib+d —f = 1 f B .-]-ip.—i

3& 3^-0 3 — [-3/.

2° If a greater Quantity be to be fubftraBed out of a lefs ; the lefs muft be fubftraBed out of the greater, and to the Remainder, muft be prehVd the Sign —, if the Quantities be affecfed with the Sign + ; or the Sign -j-, if they be affected with —.

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