^j . then wi
CON C 313 )
II AC = /r<» : +£'J. Let AC=»z; then And therefore * = —; confequently ,
CON
C] . siippofe * = --—"• On AB, (Fig. ».) defcribe a
vircle.ancf therein fet off AC = £.
then wiii*=r' conrec i» cntl y. c = '»
10. Suppo'e*
Since the Triangle . Let CB = S!
f«
af-j-bc
Szy,h:a::f:L?i and b f0±.c=bj Then will bc-\-af=bh. Hence, » =
fi+'tZ/^fa'+c/l) : t. Find betwixt AC = c, (Fig.
1 anil C B = d, a Mean Proportional C D = •/ c it. Let Pgsrij; then will D£=Yfs' — c^J. Call this m 5 then
■11 v== t-; confequently, h : m \\ m-.x.
To Covft'tiE? a quadratic Equation Geometrically. Since Ouadraticfc Equations may be reduced to fimple ones, (fee TiuATloN;) thofe may likewife be conflrv.Bed from the Methods already laid down : For if the Equation be pure, s^tllt; then will a : x : : x : b; wherefore, we fhall find »'=/ 8 ^ i 'f between AC=«, (Fig. 4..) and BC=: i we find a Mean Proportional D C. If this Equation be jjfefled, **. ax = b"; Then will x=-ia (1/ \a~- b' ) that is, either x-=ia-\-</ (^a 1 -\- V) or, *= / f-J/8' + f)~&,Mx=^a-\-'/(\a ± — b*) or x^=\ a — \/(-^a z — b- ' ).
The whole Myftery, therefore, of coxjirufting Quadra- ticks comes to this; that the Value of \/ 4 a' -\- b', and al- io the Value of \/ ^a'—b* be found; both of which are (hewn in the preceding Article. For, if in the Rectangular Triangle, (Fig. 1.) AB = i« and BC=i; then will AC s/ls' + b*. But if on AB = i<t, (Fig. z.) be defen- ded a Semicircle; and therein applied AC = S; CB~ ^/ ja 1 — 1>% as was /hewn in the Article preceding. See Eqjta-
IION.
Construction, or Syntax, in Grammar, the arranging and connecting the Words of a Sentence; according to the Rules of the Language. See Grammar, Word, Sentence, Syntax, &c.
The Cmfirutlion is generally more fimple, eafy, and di- rect in the modern Tongues than in the antient : we have very few of thofe Inveriions which occafion fo much Em- hatras and Obfcurity in the Latin; our Thoughts are nCrallydeliver'd in the fame Order wherein the Imagination conceives 'em : The Nominative Cafe, for Inftance, always precedes the Verb, and the Verb goes before the oblique Cafes it governs.
The Greeks and Latins, M. St. Evremont obferves, ufually end their Periods, where, in good Senfe and Rcafon, they ftould have begun; and the Elegance of their Language conflli, in fome meafute, in this capricious Arrangment, m rather in this tranfpofal and diforder of the Words. See Lanouage.
CuftrutJion is either Simple or Figurative : Simple, is mat wherein all the Terms, or Parts of the Difcourfe are placed in their natural Order.
Figurative ConftruSion, is that wherein we recede from 'nis Simplicity, and ufe certain Expreftions, ihorter, and
- >re elegant than Nature affords. See Figure.
Toe Syntax, or Conftrutlion of Words, is diftinguiftYd in- to iwo Parts, Concord, and Regimen, or Government. See "word, and Regimen.'
WJNSOALIA, Feafts held among the Antients, in ho- "w of the God Confus, i.e. Neptune. See Feast. j Iney were introduced with a magnificent Cavalcade, or h™,™? " on Horfeback; by reafon Neptune was reputed to «»e Brit taught Men the ufe of Horfes; whence his Sir- Ml ™ of 'Ito©-, Equeftrii.
K tit"' ' S faicl t0 haVC e ' a in(1 ' tuted tilis Feafi : IC W3S
tc», J b? R <"»"li", nnder the Name of Confus; in
rh»,"r" was l? me God under the Denomination of Confus,
,£ - " WA * mine uocl under the uenomination 0] "'"Sgefled to him the Rape of the Sabines.
•Me" I ' t ' 1at was "^ a ^*' ew t0 'h's Rape, . ctn at F.Qjblidiment. This, however, is certa
that he
~ .i.iiiucl.1, niio, however, is certain, that
'aid -, t0 q Fea ^ a 'l bis Neighbours were invited; when, the 4 ai " a ev= °f the Solemnities and Sacrifices, he feiz'd gave ° m ° n ' T draw the greater Concourfe of People, he
- chT' ■ he had found an Altar hlA under Ground,
lo»l '"tended to confecrate, with Sacrifices to the God
y™ ^ had b H ca , *^° ra ke on 'em" to explain the Myfteties of the is a c E " ,' hcolo Sy, lay, That the Altar hid under Ground
%tbotir' XD- thC feCret Dcf ' gn ° f Rmmlm t0 feize his Vei K _?"S ml "' w - erc oft!ie Number of Feafts call'd So-
0,;„ ■?, ein S eonfecrated to a Divinity.
CS V hefe Fea,ls ana Games we m ">ofe of the Circus . whcncc . t . Sj
were not diitinguifli'd Valerius Maximus
fays, that the Rape of the Sabines was effefled at the Games of the Citcus. See Circus.
'Plutarch obfetves, that during the Days of this Solemnity^ Horfes and Affes were left at reft, and were drefs'd out with divers Crowns, i$c. on account of its being the Feafl oh Nejnunus Equejirts. Feftus lays, the Cavalcade was per- formed with Mules; it being an Opinion, that this was the firft Animal ufed to draw the Car.
Servius gives us to underftand, that the Ccnfiialia fell on the 13 th of Jug uft; but 'Plutarch and 1)to?:yfius place it in the Month of March.
The Confualia differ'd from other Feafts of the fame Deity, call'd Neptiwalta. See Neptunalia.
CONSUBSTANTIAL, in Theology, a Term of equal import with Ce-cjfeutial; denoting fomething of the fame Subftance with another. See Substance.
Thus, the Orthodox believe, the Son of God to be con- fubftantial with the Father. See Trinitv, Father, efo
The Term ipixtri©-, Confubftantial, was firft adopted by the Fathers of the Council ol'Nice, to exprefs the Orthodox Doctrine the more precifely, and to ferve as a Barrier and Precaution againlt the Errors and Subtilties of the Arians; who own'd every thing excepting the Confubftanliality.
The Jrians declared that the Word was God, as' having been made God; but denied that he was the fame God, and of the fame Subftance with the Father : Accordingly, they exerted themfelves to the utmoft to abulifh the Ufe of the Word. The Emperor Conftantine ufed all his Authority with the Bi/liops, to have it expung'd out of the Symbols; but it ftill maintain'd it felf, and is at this Day, as it was then, the diftingutfhing Criterion between an Athanafian and an Arian.
Sandius will have it, the Word Confubftantial was un- known till the Time of the Council of Nice; but 'tis cer- tain it had been before propos'd to the Council of Antioch, wherein 'Paulus Samofatanus had been before condemn'd; tho it had there the fortune to be rejected. Courccl, on the other hand, maintains, that it was an Innovation in Doctrine in the Council of Nice, to admit an ExprcfTion, the ufe whereof had been abolifh'd by the Council of Antioch.
According to S. Athanafius, the Word Confubftantial was only condemn'd in the Council of Antioch; inafmuch as it contain'd the Idea of a pre-exiltent Matter, prior to tho Things form'd thereof: Now, in this Senfe, 'tis certain, the Father and the Son are not Confubftantial, there having been no pre-exiftent Matter.
CONSUBSTANTIATION, a Tenet of the Lutheran Church, with regard to the manner of the Change made in the Bread and Wine in the Eucharift. The Divines of that Profcffion maintain, that after Confecration, the Body and Blood of our Saviour are fubftantially prefent, together with the Subftance of the Bread and Wine; which is call'd Cou- fubftantiation, or Impanation. See Impanation, Transub-
STANTIATION, LuTHERANISM, &C.
CONSUETUDINIBUS 55? Servitiis, in Law, a Writ of Right, which lies againft the Tenant that deforceth hi3 Lord of the Rent or Service due to him.
CONSUL, the chief Magiftrate of the Roman Common- wealth.
The Confuls were the chief of the Senate; they com- manded the Armies of the Republick, and were fupreme Judges of the Differences between the Citizens. In regard, however, they had made fome abufe of this Power, it was allow'd, by the Valerian Law, for the Party aggriev'd to ap- peal from their Tribunal to the People; efpecially in Cafes where the Life of a Roman Citizen was concern'd.
In progrefs of Time, the Confuls being too much taken up with the grand Affairs of State, or at the Heads of Ar- mies, there were other Magiftrates created for the Diftribu- tion of Juftice to the People, in lieu of the Confuls. See Prjetor.
After the Romans had expell'd their Kings, they were govern'd by two Confuls, eftablifli'd in the lear of Rome 240; having their Name a confulendo. 'Brutus and Colla- tinus were the firft, elected by an Affembly of the People : Their Office was to hold a Year 5 and if either of 'em died in the Courfe of the Year of theit Confulate, a new one was elected.
To be elected Conful, it was tequir'd that the Candidate iTrould be at leaft 43 Years old. The Election was held in the Month of January, in the Campus Martins; afterwards in the Capitol.
Confuls wete even continu'd under the Emperors, after the Republick was deftroy'd : But the Office of Conful was here little elfe but an honourable Title; which, however, the People were fond of keeping up j as efteeming it fome Re- main of their antient Liberty.
It dwindled for a long time; and at iaft, became abfolute- ly extinct in the Time of Juflinian; after whom, no Em- peror either created any Conful, or aflumed the Dignity himfelf.
M ra m m
■Bafil
