Page:Cyclopaedia, Chambers - Volume 2.djvu/29

 IN

D A- Every thing that promotes Salvation is advanta- geous :

R I- There are AfBicfions which promote Salvation ; I. Therefore there are Afflictions which are advan- tageous.

D A- Every thing that promotes Salvation is advanta- geous :

B I- There are Afflictions which promote Salvation j TIS. Therefore fome things promoting Salvation are

Afflictions, or ami&ing. t INDIVIDUAL, or INDIViDUUM, in Logic, is a par- ticular Being of any Species, or that which can't be di- vided into two or more Beings, equal or alike. The ufu- al Divifion in Logic is made into Genera, or Genus's, thofe Genera into Species, and thofe Species into Indivi- duals. The Schoolmen make a fourfold Diltinftion of In- dividuals : (i.) Indevidaum Vagttm, is that, which tho' it figni- fiesbut one thing, yet may be any of that kind j as when we fay a Man, a certain Perfon, or one faid fo and fo, tho' but one Perfon is meant, yet that Perfon, for ought that appears to the contrary, may be any body. (2.) ht- dtvidttum Determinatitm, is when the thing is named and determined 5 as Alexander, the River Nile, ckc. this is alfo called Sigizatum. (3.) Individuum Demonji rativum, is when fome demonstrative Pronoun is ufed in the ExprefTion ; as this Man, that Woman. (4.) Individuum ex Hypotbeji, orvby Supposition, when an univcrfal Name or Term is re- trained, by the Supposition, to a particular thing; as when we fay, the Son of fuch an one, and it be known that he had but one Son.

INDIVISIBLES, in Geometry, are underftood of fuch Elements or Principles, as any Body or Figure may ulti- mately be refolved into j and thefe Elements, or hidivi- Jibles, are, in each peculiar Figure, fuppofed to be infi- nitely fmall. With regard to which Notion, a Line may be faid to confirt of Points, a Surface of parallel Lines, and a Solid of parallel and fimilar Surfaces ; and then becaufe each of thefe Elements is fuppofed indivifible,if in any Figure,a Line be drawn thro' the Elements perpendicu- larly, the Number cf Points in that Line will be thefame, as the Number of the Elements. Whence we may fee, that a Parallelogram, Prifm, or Cylinder, is refolvable into Elements or Indiv/ftbles, all equal to each other, pa- rallel, and like to the Bafe : A Triangle into Lines pa- rallel to the Bafe, but decreasing in Arithmetical Propor- tion ; and fo are the Circles, which constitute the Parabo- lic Conoid, and thofe which conliiture the Plane of a Cir- cle, or the Surface of an Ifoceles Cone. A Cylinder may be refolved into Cylindrical Curve Surfaces, having all the fame Height, and continually decreafing inwards, as the Circles of the Bafe do, on which they infill. This Method of hidiv-fibks is only the antient Method of Ex- haustion, a little difguifed and contracted, and is now allowed to be of excellent Ufe in the fiiortning of Ma- thematical Demonflrations. Of which take the following Instance in that famous Proposition of Archimedes, That a Sphere is two Thirds of a Cylinder circumfcribing it. For fuppofe (as in the Figure) a Cylinder, Hemifphcre, and an inverted Cone to have the fame Bafe and Altitude, and

(380

IN

to be cut by infinite Planes, all parallel' to the Bafe, of which d g is one ; it is plain, the Square of db will every where be equal to the Square of k c (the Radius of the Sphere) ,he Square hc=eb fquare ; and confe- <I ue ™y foce Circles are to one another as the Squares of the Kadi, all ,he Circles of the Hemifphcre will be equal to all thofe of the Cylinder, deducting thence all thofe of the Cone: wherefore the Cylinder, deducting the Cone, is equal to the Hemifphere ; but it is known, that the Cone .s one Third of the Cylinder, and confequenfly the Sphere mud be two Thirds of it.

INDORSEMENT is any thing written on the Back of a Deed or Inftrurnent ; as a Condition, written on the Hack ot an Obligation, is commonly called an Indorse- ment, from in and Dorl'um, Bad'.

INDUCTION, in Logic, a Confcqeence drawn in lealoning from feveral efiabli/hed Principles. Thus the Jjonclufion of a Syllogifm is an InduSion made from the

be°a Svl'i t" '"r" P JZ' i"> WCT «> ™y te jaftly faid to be a Sjllogifm of itfelf, being a kind of Medium between anEnthymemeand a Gradation, in regard it wants a

Propofit.on (which, however, is underftood) as in the En thymeme, and abounds in Aflumptions (which yet collateral, or of the fame degree) which is the Cafe L. jradat.on. Thus, forinftance, every Terrettrial Animal

are a

lives, every Aerial Animal alfo lives

every Aquatic Ani-

mal lira, and every Reptile Animal lives ;" therefore every Annual lives There are, it may be obferved, va- rious Aflumptions, from the more general Species of the Animal Kind collected into one, which this Proportion is iuppoled to precede, viz. every Animal is either Ter- rettrial, Aerial, Aquatic, or Reptile.

■SmAu reckons three kinds of InduSion ; that iult men- tioned, which concludes or gathers fome general Pro.oft- t.on from an Enumeration of all the Particulars of a kind he calls the Dialectic luduShn. The fecond, which pro- ceeds by Interrogation, and concludes probably or with a Vcr.fimilitudc, by the Greeks called .^.^yr, and Was that which Socrates ordinarily made ufe of, "as Cicero in his Topics, and Qttmtiliaphuve obferved. The third kind of InduHim is properly rhetorical ; being a Concluhon drawn from fome Example or Authority. This is a very imper- fect Indaflion, all its Force lving in a Propofition which is concealed, and which will hardly bear being exprefled. Thus he that fays, aims died bravely for his Country, therefore I mutt die bravely for my Country, proves no- thing, unlefs this Propofition be carried in mind, that I mutt do the fame with (Mm. Again, Archimedes, and the other Mathematicians fay, the Sun is much bigger than the Earth ; therefore it mutt be owned the Sun^'is much bigger than the Earth. Where the Propofition is under- flood, via. whatever Archimedes and the other Mathemati- cians fay is true,

INDUCTION, ; n, n E.^Cuftoms, is ufually ta- ken for the giving Pofleflion to an Incumbent of his Church, by leading him into it, and delivering him the Keys by the Commiffary or Bifhop's Deputy, and by his ringing one of the Bells. When a Clerk is militated into a Benefice, he is to exhibite his Mandate from the Bifhop tothe Arch Deacon, or other Perfon to whom it is di- rected, and hath a Right thereby to be induced into his Living ; and if he be refufed Induction, he hath a Reme- dy both in the Ecclefia'lical Court, and alfo an Action of the Cafe in the Common Law, againtt the Arch-Deacon If the Induaor, or Perfon to be inducted, be kept out of the Church or Foufe by Laymen, the Writ de w Laica lies for the Clerk, which is directed out of the Chancery to the Sheriff of the County, to remove the Force c>r. If another Clergyman, prefented by the fame Patt'on, keep poffefiion, a Spoliation is grantablo out of the fpiritual Coutt, whereby the Tithes, 15c /hall be fequeftred, till the Right be determined. The Arch-Deacon rarely in- ducts a Clerk by himfelf in Perfon, but iffues out a War- rant to all Clerks and Lettered Perfons within the Arch- Deaconry, impowering any of them to do it in his ttead. The ufual Form and Manner of InduSmn, is, for the In- ductor to take the Clerk by the Hand, and then to lay it on the Key of the Church, which muft be then in the Door, and to fay, ' By virtue of this Inftrument, I induct ' you into the real, actual, and corporal Poffcffion of the

' Rectory or Vicarage of, with all its Fruits, Profits

'Members, and Appurtenances.' This done, he oDens the Door, and puts the Clerk in poffeffion of the Church and (huts the Door upon him ; who after he hath tolled a Bell (if there be any) comes out, and defires the In- ductor to indorfe a Certificate of hvdndu&Stfo on the Arch- Deacon's Warrant, and that all prefent will fignify i t un- der their Hands. If the Church-Key cannot be had it is fufficicnt that the Clerk lays hold of the Ri'.g of the Door, and within the time' limited read the Common- Prayer, and Thirty-nine Articles of the Church in the Church-Porch. Within two Months after this, the Clerk mutt read the Thirty-nine Articles, and all the Service of the Day, both at Morning and Evening-Prayers, and de- clare his Affent and Confent ; he muft alfo then read the Bi/hop's Enghfi Certificate, in which is the Declara- tion of his Conformity ; and of all this hemufthave two or three good Witnefles, who muft fign that they heard him do it, and be ready to atteft it, viva voce, if required ; and within three Months after hiduffim, he muft alfo take the Abjuration-Oath at the Quarter-Scflions, or in fome one of the Courts at Ifcftminjier-Ha!l. The word InduSim is derived from the Latin in, and diico, to lend. ■- INDULGENCE, in the Romifli Theology, h the Re- miffion of the Punifhment due to a Sin, granted by the Church, and fuppofed to fave the Sinner from Purgatory. They found their Indulgences en the infinite Trcaiure of the Merits of Jefus Ch'rift, the Holy Virgin, and all the Saints, which they fuppofe the Church has a right of dillributing, by virtue of the Communion of Saints' Tho Roman Jubilee carries with it a plenary or full Indulgence for all the Crimes committed therein. The Pope alfo giants Bulls of plenary Indidrence to feveral Churches Fffff 1W