DEM
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DEM
or tie Angle the two Courtins would make, were they thus protraaed to meet in the Baftion. See Gorge.
T)%ui-Lmie, Half-Moon, in Fortification, an Out- work, as EFGHK {-fab. Fortific. Ftg.'j.) confiftmg of Faces, and Flanks ; frequently built before the Angle ot a Baftion, and fometimes alfo before the Courtine, tho now much difufed. See Outwork.
DEMi-^cawr, is aNote inMufick ; twoot which are equal to the Quaver. See Quaver, an d Note.
DEMISE, in Law, is applied to an Eftate, either in Fee-fimple, Fee-tail, or for Term of Life, and fo it is commonly taken in many Writs : The King's Death is in Law termed, The 'Demise of 'the King.
DEMOCRACY, a Form of Government, wherein the Sovereignty, or fupreme Authority, is lodged in the Peo- ple, who exercife ihe fame by Perfons of their own Order, deputed for that Purpofe. This is the moft ancient Form of Government.
The moft flourifhing Democracies were thofe of Rome and Athens. The modern Republicks, as Venice, and the United 'Provinces, are rather Ariftocracies than 'De- mocracies. The Government of Safll, however, is a Democracy ; fo are fomc of the free Cities in Germany.
The Word is form'd of the Greek Jlny-of, 'People, and KpetTzh) command.
DEMON, or DjEMON, a Name the Ancients gave to certain Spirits, or Genii, which appeared to Men, ei- ther to do them Service, or to hurt them. See Genius.
The firft Notion of Demons was brought from Chal- Atta ; Whence it fpread it felf among the 'Perfians, Egyptians, and Greeks. 'Pythagoras and Thales were trie firft, who introduced Demons into Greece. 'Pla.to fell in with the Notion, and explain'd it more diftinctly, and fully, than any of the former Philofophers had done. By Demons, he underftood Spirits inferior to Gods, and yet fuperior to Men ; which inhabiting the middle Region of the Air, kept up the Communication between Gods and Men, 'carrying the Offerings and Prayers ofMen to the Gods', and bringing the Will of the Gods to Men. But he allowed of none'but good, and beneficent Ones. Tho' his Difciples, afterwards, finding themfelves unable to give the Reafon of Evil, adopted another Sort of De- mons, who were Enemies to Men.
There is nothing more common in the Heathen Theo- logy, than thefe good, and evilGenM. And the fame fuperftitious Notion got footing among the Jfraelites, by their Commerce with the Chaldeans. But by Demons, they did not mean the Devil, or a wicked Spirit : They never took the Word Demon in that Scnle, nor was it ever ufed in fuch a Signification, but by the Evangelifts, and fome modern Jews. The Word is Greek, S-cu^as.
Gale endeavours to fhew, that the Origin, and Infti- tuticn of Demons, was an Imitation of the Meffiah. The •Pbtmiciaus call'd them O'tya 'Baalim. For they had one fupreme Being, whom they call'd Baal and Moloch, and various inferior Deities, call'd Baalim, whereof we find frequent mention in the Old Teftament. The firft Demon of the Egyptians was Mercury, or Tbeut. The fame Author finds fome Refemblance between the feve- ral Offices afcribed to the Demons, and thofe of the Meffiah.
DEMONIAC, orDjEMONIAC, is applied to a Per- fon poffefs'd with a Spirir, or Demon.
In the Romifi Church, there is a particular Office for theExorcifm of Demoniacs. See Exorcism.
Demoniacs, are alfo a Party, or Branch of the Ana- baptifts, whofe diftinguifhing Tenet it is, that the Devils fliall be faved at the End of the World.
DEMONSTRABLE, a Term chiefly ufed in the Schools, fignifying fomewhat that may be clearly and evidently proved. It is demonftrable, that the Side of a Square is incommenfurable with the Diagonal. The Pro- blem of the Motion, ot Reft of the Earth, is not demon- ftrable, by reafon the fame Appearances refult from ei- ther Suppofition.
DEMONSTRATION, in Philofophy, a Syllogifm in Form, containing a clear and invincible Proof of a Pro- pofition : Or, a convincing Argument, the two firft Propo- sitions whereof are certain, clear, and evident 5 whence of Neceffity arifes an infallible Conclufion. See Syelocism. A Demonftratiou ufually confifts of 5 Parts : The Ex- plication, Preparation, and Conclufion. The Explica- tion is the laying down the Things fuppofed to be given, or granted ; from which the Demonstration is to be made. The 'Preparation is a Suppofition to be made, according to the Nature of the Demonftration intended. The Conclufion is a Propofition that concludes the Thing to be demonftrated, fully perfwading, and convincing the Mind. See Conclusion.
TheMethod of demonftrating Things inMathematicks, is the fame with that of drawing Condufions from Prin-
ciples in Logicks. In Effefl the Demonstrations of Ma thematicians, are no other rhan a Series of Enthymemes- fo that every Thing is concluded by Force of SyuViffn' only omitting the Premiffes, which cither occur oftheir own Accord, or are recollected by means of Quotations To have the Demonftration perfect, the Premiffes of the' Syllogifms fhould be proved by new Syllogifms, till at length you arrive at a §yilogifm wherein the Premieres are either Definitions, or Identic Propofitions.
Indeed it might be demonfirated, that there cannot be a genuine Demonftration, 'i?e: , fiich a one as fhall give full Conviclion, unlefs the Thoughts be directed therein ac- cording to the Rules of Syllogifm. Clavius, 'tis known to every body, refolved iheDemonftration of the firftPro- pofition of Euclid into Syllogifm : Herlinus, and Da- fipodius, demonftrated the whole fix firft Books of Euclid and Henifchius, all Arithmetic, in the Syllogiftic Form.
Yet People, and even Mathematicians, ufually imagi- ned, that Mathematical Demonftrations are concluded in a Manner far remote from the Laws of Syllogifm 5 fo far are they from allowing, that thofe derive all their Force and Conviction from thefe. But we have Men of the firft Rank on our Side the Queftion. Mr. Leibnitz, f or Inftance, declares that Demonftration to be firm and valid, which retains that Form prefcribed by Logic. And Dr. Wallis confeffes, that what is propofed to be proved in Mathematicks, is deduced by means of one, or more Syllogifms. The great Ruygens too obferves, that Paralogifms frequently happen inMathematicks, through Want of obferving the Syllogiftic Form. See Syleocism.
Problems confift of three Parts : A 'Propofition, Re- folution, and Demonftration.
In the 'Propofition is indicated the Thing to be done. See Proposition.
In the Refolution, the feveral Steps are orderly rehear- fed, whereby the Thing propofed is perform 'd. See Re- solution.
Laftly, in the Demonftration it is fhewed, that the Things injoyned by the Refolution being done, that re- quired in the Propofition is effect ed. As often, therefore, as a Problem is to be demonftrated, it is converted into a Theorem, the Refolution being the Hypothefis, and the 'Propofition the Thefts : For the general Tenor of all Pro- blems to be demonftrated is this, that the Thing pre- fcrib'd in the Refolution being perform 'd, the Thing re- quired is done. See Problem.
The School-Men make two Kinds of 'Demonftration : The one Ami, or, propter quod ; wherein an Effect is proved by the next Caufe : As when it is prov'd, that the Moon is eclypfed, by reafon the Earth is then be- tween the Sun and Moon. The fecond on, or, quia 5 wherein the Caufe is proved from a remote Effect : As when it is proved, that Fire is hot, becaufe it bums 5 Or, that 'Plains don't breath, becaufe they are not Animals.
Affirmative Demonstration, is that, which proce- dingby affirmative and evident Propofition, dependent on each other, ends in the Thing to be demonftrated.
A Negative Demonstration, is that, whereby we fhew a Thing to be fuch from fome Abfurdity that would follow if it were otherwife. This we alfo call a Demon- ftration ab impoffibili.
A Geometrical Demonstration, is that, framed of Reafoning drawn from the Elements of Euclid.
A Mechanical Demonstration, is that, theRea- fonings whereof are drawn from the Rules of Mechanicks.
A Demonstration A priori, is that, whereby an Effect is proved from a Caufe, either a next, or remote one 5 or a Conclufion proved by fomething previous, whether it be a Caufe, or only an Antecedent.
A Demonstration A pofteriori, is that, whereby either a Caufe is proved from an Effect ; or a Conclu- fion is proved by fomething poll erior, whether it be an Effect, or only a Confequent.
DEMONSTRATIVE, in Rhetoric, one of the Genera, or Kinds of Eloquence ; being that ufed in the Compofing of Panegyricks, Invectives, c5c. See Panegyric.
Rhetoric is divided into three Parts; Deliberative, De- monftrative, and Judiciary. See Rhetoric.
Demonstrative, inGrammar, is applied to Pronouns that ferve to fhew, point out, or indicate a Thing ; As, This here, That there, Thofe yonder, &c. See Pro- noun.
DEMURRAGE, inTraffick, is an Allowance to the Matter of a Ship, by the Merchants, for flaying in a Port longer than the Time firft appointed for his Departure.
DEMURRER, in Law, from the French Demeurer, to ftay, or dwell, is a Kind of Paufe, or Stop, put to the Proceeding of any Action, upon fome difficult Point, which muft be determin'd by the Court, 'ere any further Pro- ceedings can be had therein. .
