COM
one third of the given Line. In the
Line be divided into another number of Farts.
For the Ufe of the Line of Polygons : Suppofe, v.g. a Pentagon requir'd to be inferib'd in a Circle ; pufh the Cur- for till the middle of the Screw be againft 5, the number of Sides in a Pentagon ; between the fhorteft Parts of the Legs take the Semidiameter of the Circle: the Legs thus open'd, the diftance between the Points of the longctt Parts, will be the fide of the Pentagon to be inferib'd in the Cir- cle. And thus for a Figure of any other number of Sides.
'Proportional Compasses with the SeBor Lines. The Strufture of thefe is fo like that of the common Proportio- nal Compares, only a little nicer, that it needs no parti- cular Description. See Plate Geometry, Fig. 4.
The Lines on the fir [I Face, are the Line of Lines, mark'd Lines : it is divided into 100 unequal Parts, every tenth number'd : And the Line of Chords, which goes to 60° ; and is mark'd Chords. On the other Face are a Line of Sines to 90°, and a Line of Tangents to 45°. On the firft fide are the Tangents from 45 to 7i°.34' 5 on 'he other Se- cants from o° to 7o°.3o'. _ _
For the Ufe of thefe Compaffes. 1. To divide a Line into any number of equal Parts, lefs than 100: Divide 100 by the number of Parts requir'd ; flip the Curfor till the Line on the flidinp Dove-tail be againft the Quotient on the Line of Lines: Then, the whole Line being taken between the Points of the Compaffes mod remote from the Centre ; the Aper- ture of the other will be the Divifion requir'd. 2. A right Line given, fuppofed to be divided into 100 Parts, to take any number of thofe Parts : Slip the Line on the Aiding Dove-tail to the number of Parrs requir'd : the whole Line being taken between the Points furtheft from the Centre, the Aperture of the other two will include the number of Divi- fions requir'd. 3. The Radius being given, to find the Chord of any Arch under 6o° : Slip the Line on the Aiding Dove-tail to the Degrees requir'd on the Line of Chords : the Radius being taken between the Points furtheft from the Centre of the Curfor ; the Aperture of the other Line will be the Chord rcquir'd ; provided the number of Degrees be greater than 29 : if it be lefs, the Aperture taken from the'Radius will leave the Chord requir'd. 4. If the Chord of an Arch under fTo be given, and the Radius requir'd ; flip the Line on the Dove-tail to the Degrees given on the Line of Chords : the given Chord being taken between the two Points next the Curfor, the Aperture of the other will be the Radius requir'd. ;. The Radius being given, to find the Sine of any number of Degrees. Slip the Line on the Dove-tail to the Degree on the Line of Sines whofe Sine is requir'd : The Radius taken between the Points fur- theft from the Cutfor ; the Aperture of the other will give the Sine of the Angle requir'd. But if the Sine fought be lefs than 30 , the Difference of the Apertures of the oppo- fite Points, will be the Sine requir'd. 6. The Radius be- in? given, to find the Tangent of any number of Degrees under 71 : If the Tangent requir'd be under 16°. 30', flip the Line on the Dove-tail to the Degree propofed on the Tangent-Line : the Radius taken between the Points fur- theft from the Curfor ; the Aperture of the others, will be the Tangent of the Degrees requir'd : If the Tangent re- quir'd be above 26°. 30', but under 45 5 the Line on the Curfor muft be flip'd to the Degrees given on the Tangent- Line : then the Radius being taken between the Points fur- theft from the Curfor ; the Aperture of the others will be the Tangent. If the Tangent requir'd be greater than 45 °, but lefs than 55°. 20' ; flip the Notch on the Tangent-fide of the turn'd Cheek to the Degree o in the Tangent-line on the Side of the Compafs .- the Radius taken between the Points furtheft from the Curfor ; the difference between the Aper- ture of the other, and thefe, added together, will be the Tangent requir'd. Thus, for the Tangents of other De- grees under 7 1 . After the like manner may the Secant of any number of Degrees under 7 1 be found.
Lapidary's Compasses, a piece of Wood in form of the Shaft of a Plane, cleft a-top, as far as half its length ; wherewith they meafure the Angles, &c. of the precious S rones as they cut 'em.
In the Cleft is a little brafs Rule, faften'd there, at one end, by a Pin ; but fo as it may be mov'd in the manner of a Bevel : with this kind of Square they take the Angles of the Stones, laying 'em on the Shaft as they cut them.
COMPATIBLE, fomething that mayfuit, or confift with another. See Incompatible.
COMPENDIUM, an Abttraft, Epitome, or Reduction of a large Matter into a little compafs. See Epitome.
COMPENSATION, an Action whereby any thing is ad- mitted as a Parallel, or an Equivalent to another.
Compenfation, in the Civil Law, is a kind of Right, whereby a Debtor purfu'd by his Creditor, for the Payment of a Debt, demands that the Debt may be compenfated with what is owing him by the Creditor.
Compenfation is equivalent to Payment.
COMPETENCE, in Law, the Authority, or Right, of a
( 288 ) COM
me manner may the Judge for taking Cognizance of any certain Matter. S c,
Jurisdiction.
COMPITALITIA, Fcafts held among the Antients i„ honour of the Lares. See Feast, and Lares.
The Word comes from the Latin Compitum, a Ctofs-way. by reafon the Feaft was held in the Meetings of f CVcr<i j Roads.
This Feaft is more antienr than the building of fie,,,,. liionyfius Halicamajfeus and Pliny, indeed, fay, they were inftitutedby Senilis lilllius ; but this onlyfignifies thit they were then introdue'd into Rome.
Notwithstanding what Dion relates, that the Compitaliti), were celebrated a little after the Saturnalia ■ and that the Roman Calendar fixes 'em on the 12th of January ; i t a „ pears that they had not any fix'd Day ; at leaft, not in th« time of Varro, as is obferv'd by Cafaubon.
The Feaft being thus moveable, the Day whereon it was to be held, was proclaim'd every Year. It was ordinarily held on the 4th of the Nones of February, i. e. on the 2d of that Month.
Microtias obferves, that they were held not only i n 1 10 . nour of the Lares, but alfo of Mania, Madnefs. The Prie|i s who officiated at 'em were Slaves and Literti ; and the Si. crifice a Sow.
They were re-eftablifh'd, after a long negleft, by Tar. quin the Proud ; and on occafion of an anlwer of the Ora- cle, That they Jhould facrifice Heads for Heads, i. e. for the Health and Profperity of each Family, Children were ordain'd to be facrificed : But Srutus, after expelling the Kings, in lieu of thofe barbarous Victims, fubftituted the Heads of Garlick and Poppy ; thus fatisfying the Oracle which had enjoin'd Heads, Capita.
During the Celebration of this Feaft, each Family placed at the Door of their Houfe, the Statue of the Goddeis Ms- ilia : They alfo hung up at their Doors Figures of Wool, re- presenting Men and Women ; accompanying them with Sup- plications that the Lares and Mania would be contented with thofe Figures, and fpare the People of the Houfe.
As for Slaves, in lieu of the Figures of Men, they offer'd Balls, or Fleeces of Wool. Servius Tullius order'd, that the Slaves who affifted at the Compitalitia, fhould be free du- ring the whole Time of the Feaft. Auguftus order'd the Statues of the Lares, placed in the Crofs-way, to be adorn'd with Flowers twice a Year.
COMPLAINANT, in Law, a Plaintiff, or one who pre- fers a Complaint againft another, to be reliev'd by Juliice, or Equity. See Plaintiff.
COMPLEMENT, in Geometry, is what remains of a Quadrant of a Circle, or of 90 Deg. after a certain Arch has been retrench'd from it. See Arch.
Thus, if an Arch or an Angle be 30 Deg. w&fay its Ctnt- plement is (To Deg. fince 60+30= 90.
The Arch and its Complement are Relatives; and are only ufed with regard to each other.
The Sine of the Complement of an Arch, is call'd the Co- fine ; of a Tangent, the Co-tangent, &c. See Co-sine, Co- tangent, £ffc.
We fometimes alfo fay, the Complement of an Angle; meaning fo much as it wants of a right Angle, or 90 Deg. See Angle.
Complement of the Courfe, in Navigation, is the Num- ber of Points the Courfe wants of 90 Deg. or 8 Points, viz. of a Quarter of the Compafs. See Course.
Complement, in Aftronomy, is ufed for the diftance of a Star from the Zenith 5 or the Arch comprehended between the Place of a Star above the Horizon, and the Zenith. See Zenith, Star, i$c.
Complement of the Curtain, in Fortification. The in- ner Polygon confifts of the Curtain and two Demigorges : The Complement of the Curtain, therefore, to the inner Po- lygon, is the Demigorges. See Curtain, and Demigorge.
Complement of the Line of Defence, is the Remainder of the Line of Defence, after you have taken away the An- gle of the Flank. See Defence:
Complements of a Parallelogram, are the two leffer Pa- rallelograms, made by drawing two right Lines parallel to each fide of the Figure, thro' a given Point in the Diagonal.
Such are the Parallelograms C and M, (Piute Geometry, Fit*. 5.)
- T5i demonftrated, that in every Parallelogram, * c ^?,"
plements C and M are equal : For Z+C + = R+ a -f X ; as making up on each fide the great Triangle, »* = by the Diagonal ; of which, Z = R, and = X, [<£ caufe the Diagonal makes them lb ;) wherefore, the remain- ing Parallelogram C = M.
"COMPLEX, a Term ordinarily ufed as fynonymou_s Compound ; tho, ftriflly fpeaking, there be fome difference between 'em. . ,.
Complex may be applied where a thing contains divm others, or confifts of divers Parts, not really diftinct from
th
one another ; but only imaginably, or in our Conception.-
In
