Page:Cyclopaedia, Chambers - Volume 2.djvu/520

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In thefe the great Pieces, which ferve to form the Body, are to be fet out in Meafures agreeable to the Height ; on- ly diversifying them by their Bignefs.

In the Rule of Proportions, it is to be obferv'd, that there is a difference in the Contours of fome parts, when

fiut in different Pofturcs. Thus when the Arm is bent, 'tis irger than when ftraight ; the fame is true of the Foot and Knee, as is ihewn by Leonardo da Vinci.

Rule of Proportion, in Arithmetic, a Rule whereby we find a fourth Proportional to three Numbers given.

This is popularly call'd, The Golden Rule, and fome- times, The Rule of Three. See Rule.

Compafs of Proportion, a Name by which the French, and after them Come Euglifn Authors, call the SeHicr.

See its ConftruBion and Ufe, under the Article Sector.

PROPORTIONAL, a Quantity, either Linear or Nu- meral ; which bears the fame Ratio, or Relation to a third, that the firit does to the fecond. See Proportion.

t.To find a fourth Proportional to three given Lines, AB, AC, andBD. (Tab. Geometry, fig.Cs.)

Draw an Angle FAG at pleafure ; from A fet off the firit of the Lines to B; from A, the fecond to C ; and from B, to D, the third : draw B C ; and in D make an Angle, equal to A B C : then is C E the fourth Proportional fought 5 andAB: AC: : B D : C E.

2. If a third Proportional be requir'd to two given Lines, AB, and AC; make BD equal to AC, i.e. let ACbe repeated twice: then AB:AC::AC:CE.

5. To find a mean Proportional between two given Lines, AB and BE (fig, 63. J join the two given Lines, into one continued right Line, and biffect it in C. From C, with the Interval of A C, defcribe a Semi-circle A D E 5 and from B erett a Perpendicular B D ; this is the mean proportional fought; andAB: BD:: BD: BE.

The Geometricians have been thefe two thoufand Years in fearch of a Method, for finding two mean Propor- tionals. See Mean.

The Antients perform'd it mechanically, by the Mefo- labe, defcrib'd by Eutochius 5 and many of them attempted to give the Demonflration ; fome by the folid Loci, as Menechtnus; others by the plain Loci, as Nicomedes, T)io- cles, and in our Times, Vieta ; and others by implicit Mo- tions, as Plato, Architas, Pappus, and Sforus ; others ten- tatively, by the Defcription of Circles, as Hero and Apollo- nius,&c. But all in vain. See Problem and Quadra- ture.

4. To find a mean 'Proportional between two Numbers : Half the Sum of the two given Numbers is an arithmeti- cal mean 'Proportional ; and the fquare Root of their Pro- duct, a Geometrical mean Proportional. See Proportion Arithmetical and Geometrical.

To find a mean harmonical Proportional. See Propor- tion Harmonical.

Proportional Compaffes, an Inftrument for the ready drawing of Lines, and Figures, in any given Ratio to other Lines, or Figures.

See their Construction and Ufe, under the Article Com- passes.

Proportional Scales, call'd alfo Logarithmical Scales, fte the Artificial Numbers or Logarithms, placed on Lines, for the Eafe and Advantage of Multiplying, Dividing, Sgc. by means of Compaffes, or of Sliding- Rules. See Logarithm and Scale.

They are, in effect, only fo many Lines of Numbers, as they are call'd by Gunter $ but made tingle, double, triple, or quadruple; beyond which they feldom go. See Num- bers, Gunter's Scale, &c.

PROPORTIONALITY, a Term ufed by Gregory iSt. Vincent for the Proportion that is between the Exponents of four Ratios. See Exponent and Ratio.

PROPORTUM, Proport, or Purport, in our Law- Books, the Intention or Meaning of any thing. Secundum Proportum diSi Chirographi inter eos confetti.

PROPOSITION, Propositio, call'd alfo Enuncia- tion, in Logic, part of an Argument, wherein fome Qua- lity, either Negative or Pofitive, is attributed to a Subject. See Enunciation, Attribute, &c.

Chauvin defines a Proportion, a complcat, confiftent Sentence, indicating or expreffing fomething either true or

falfe, without ambiguity : -As, Xantippe is a bad Wife 5

—If an Afsfiy, he has Wings.

Others, more Philofophically, define it a Speech utter'd, or produced to fignify fome Judgment of the Mind. See Judgment.

A Propofition confifls of two Terms ; the one, that, whereof we affirm or deny ; call'd the Subject : The other the thing affirmed or denied, call'd the Attribute or Predicate. See Subject and Predicate.

Thefe two are either join'd, orfeparated, by the Inter- vention of fome Copula or Disjunct ive. See Copula.

Thus in the Proportion, God is jujt j the Subject, God,

is joined with the Attribute fafl by the Verb fubftantiva is.

The Schoolmen call the two Terms the Matter, and the Copula theForm of the Propofition. See Form, g?c

Now, as Terms may be either Angular ; or common, and univerial ; if the Subject of a Propofition be a common Term, taken in all its extent ; the Propofition is call'd Umverfal: As, Every Athcift is blind. See Universal.

If the common Term be only taken in an indeterminate part of its Extent, the Propofition is call'd particular : As, Some Atheift are wicked. See Particular.

It the Subjcft of the Propofition be lingular, thePropo- fition is call'd fmgular: As, George is King .'/England. See Singular.

Thofe Propofiticns which have only one Subject, and one Attribute, are cM'dfimple ; thofe that have feveral Sub- jects, or Attributes, are call'd compound. See Compound.

A Syllogifm conftits of three Proportions, Major, Minor, and Conclufion. See Syllogism.

An Enthymeme, of two. See Enthymeme.

The Schoolmen make feveral other Species and Dlvifions of Proportions ; as,

A Proposition de prima adjaccnte, where the Subject and Predicate are both included under the Verb ; fuch are, Veni, Vidi, Viei.

A Proposition de fecundo adjacente, is, where either, the Subject or Predicate is included in the Verb ; as, I love -I write.

A Proposition de tertio adjacsnte, is, where both the Subject and Predicate are exprefs, and (land dittincl from the Verb ; as, The King is jufl.

Thispropojiriou is the Rule or Standard of all the other j fo that whatever Propofition can be reduced thereto, is le- gitimate ; and what cannot, is not.

Propofitions, again, are divided into three Claffes : The firit, regarding the Matter ; the fecond, the Form ; the third, the Thought.

Thofe of thefirlf Clafs are fubdivided into, finite and in- finite ; direcf and indirect ; fingie and manifold.

A finite or definite Proposition, is that which declares fomething determinate on a Subject ; as, Man is aSipede. — The Wind is not vifible.

An infinite or indefinite Proposition, is that where either one or both of the Terms are infinite, or have a Ne- gative prefixed to 'em ; as, Nou homo efi albus—Homo efi non albus.

Adirect Proposition, is that wherein a higher or more general is predicated of a lower and more particular ; as, Man is an Animal. Others will have it, that wherein the Subject Hands as a Matter, receiving, and the Predicate, as a Form, received ; as, Peter is learned.

An indirect Proposition, according to fome, is that wherein an inferior is predicated of a higher ; as, An Animal is Man. According to others, it is that wherein the Sub- ject Hands as the Form, and the Predicate as the Matter ; as, Every Rational is Man.

Afngle Proposition is fuch, either Simply, or by Con- junction : Simply, when it affirms or denies one thing of one other thing; as, The Sun pines : By Conjuniiion, when feveral Propofitions are join'd and coupled together ; thus, The Sun fames, and it is" Day ; are two Propofitions, which conjoin'd make this one, Jf the Sun ffjines, it it T)ay.

Of fuch conjunct Propofiticns there are divers kinds, viz. Hypothetical, Disjunctive, Copulative, Sf?c.

Hypothetical Propofition, is that confining of feveral fimple ones, affected with fome conditional one ; as, Jf the Sun be fet, it is Night.

T)is]unctive Propofition, is that confining of feveral, af- fected with a disjunctive Conjunction ; as, It is either T)ay or Night.

A copulative Proportion, is that confiding of feveral af- fected with a Conjunction Copulative 5 as, Peter does not fiand, and fit.

Some add, Difcrete or Adverfative Proportions ; as, He is rich, but covetous.

A compottnd?Ro?osirioti, is that where one or both the Terms excite feveral Ideas in the Mind ; as, A Man is Sody and Soul, and both together : Or,, a Foundation, Walls, and Roof, are a Houfe.

A manifold Proposition, is that confining of feveral Subjects; as, Peter and Paul preach 'd: Or, feveral Predi»- cates ; as, Simon reads and walks : Or both ; as-, Petef and Paul preach and pray.

In refpect of Form, Propofitions are divided into Affir- mative, and Negative 5 True, and Falfe 5 Pure, and Modal.

An Affirmative Proposition, is that whofe Attribute is join'd to the Subject ; as, God isaSpirtt.

A Negative Proposition, is that whofe Attribute is fe- parated from the Subrefl ; as, Man is not t Stone, r i. T A