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EqueRies are particularly ufed among us, for Officers cF the King's Stables ; who when his Majefty goes Abroad, ride in the leading Coach 5 are in Waiting one at a Time monthly, and have a Table with the Gentlemen Uflicrs du- ring the Time.
They ufed to ride on Horfe-back by the Coach-Side, when the King travelled 3 but that being more expenfive to them, than neceffary to the Sovereign, it has been dif- continued. There are Six of them, and their Salary is 300 /. per Annum each.
"7h" Equeries of the Crown Stable have that diftinct Appellation, as being imployed in managing and breaking the Saddle Horfes, and preparing them for the King's Riding.
One of them is, or always fliould be, in clofe Waiting at Court ; and when his Majefty rides, holds the Stirrup, whilll the Mailer of the Horfe, or one of the Equeries, in his Abfence, affifts in mounting him 5 or when his Majefty rides, they ufually attend him. They are two, and their Salary is 256"/. per Annum each.
EQUES Auratus, is ufed to fignifie a Knight Batchelor ; call'd AurdiUS, becaufe anciently none but Knights might gild or beautify their Armour, or other Habiliments of War, with Gold. See Knight.
However, in Law, this Term is not ufed 5 but inftead of. it Miles 5 and iometimes Chevalier. See Miles, Che- valier, ££c
EQUESTR15, Equestrian, a Term rarely ufed, but jn the Phrafe Equeftrian Statue, which fignifies a Statue reprefenting a Perfon mounted on Horfeback. See Sta- tue.
The Fortuna EqUeftris, in ancient Rome, was a Statue of that Goddefs on Horfeback.
We fometime alfo fay, Equeftrian Column. See Co- lumn.
And Equeftrian Order, which fignified, among the "Romans, the Order of Knights, or Equites. See Knight,
The Word is form'd of the Latin, Eques, Knight, Horfemar, 3 of Equus, Horfe.
EQUIANGULAR, or Equiangular, in Geometry, is applied to Figures whofe Angles are all equal. See Angle.
A Square is an Equiangular Figure. See Square.
All equilateral Triangles are alfo Equiangular. See Equilateral.
When the three Angles of one Triangle, are fevcrally equal to the three Angles of another Triangle 5 the Tri- angles are alfo faid to be Equiangular. See 'Triangle.
EQU1CULUS, Equuleus, or Equus minor, a Conftel- lation of the Northern Hemifphere. See Equuleus.
EQUICRURAL, or Eqjjicrural Triangle, is what we more ufually call an IJqfceles. See Isosceles.
EQUIDIFFERENT, or JEquidieferent, in Arith- metic. If in a Series of three Quantities, there be the fame Difference between the firft and fecond, as between the fecond and third, they are faid to be continually Equidifferent : But if in a Series of four Quantities, there be the fame Difference between the firfl and fecond, as between the third and fourth, they are faid to be difcretely Equidipfcrent. Thus, 3, <r, 7, and 10, are dif- cretely Equidifferent; and 3, 6, and j>, continually Equi- different.
EQUIDISTANT, or Equidistant, in Geometry, a Term of Relation between two Things, which are every where at an equal, or the fame, Diilance from each other. See Distance.
Thus parallel Lines are faid to be Equidiftant, as they neither approach nor recede.
Parallel Walls are Equidiftant from each other. See Parallel.
EQUILATERAL, or Equilateral, is applied to any Thing whofe Sides are all equal. Thus, an Equi- lateral Triangle, is that whofe Sides are all of equal Length. In an Equilateral Triangle, all the Angles are likewife equal. See Triangle.
All regular Polygons, and regular Bodies, are Equilate- ral. See Polygon.
An Equilateral Hyperbola, is that wherein the conjugate Axes, asAB, andDE, are.cqual. (Tab.Couick's Fig. 20.)
Hence, as the Parameter ii a .rf Proportional to the conjugate Axes, it is alfo equal thereto. Confcquently, in the Equation y' = bs; + b»':a, make b = a 3 And the Equation y- = aa? + *S defines the Nature of an Equi- lateral Hyperbola. See Hyperbola.
EQUILIBRIUM, 01 Equilibrium, in Mechanicks, a Term implying an exact Equality of Weight between two Bodies, compared with each other. See Weight.
Thus, we fay a Balance is in Equilibrio; when the two Ends are fo exaftly pois'd, that neither of 'em
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afcends or defcends, but both retain their parallel Pofition to the Horizon. From which Circumflance the Word is originally taken 3 as being a Compound of aquus, equal and libra. Balance.
Whence we frequently ufe the Word Balance in lieu thereof. See Balance.
The Equilibrium of Fluids makes a considerable Part of the Doctrine of Hydroftaticks. See Fluid.
The Term Equilibrium, is alfo ufed figuratively on other Occafions. A Painter muft take Care to obfervc the Equilibrium of his Figures, i. e. to difpofe 'em well on their Center of Gravity, that they mayn't feem ill fupport- ed, or ready to tumble.
Thus, e. gr. if one Arm be moving forward, the other muft be proportionably backward to poife the Figure.
In a Picture, there ihould be an Equilibrium between one Part and another: That is, the Objefls are to be diftributed fo, as to balance, and contraft each other 5 and not too many, e. gr. be crowded on one Side, and the other left bare. — Peace is never well fecured, unlefs the Neighbouring Srates are in Equilibrio.
EQUIMULTIPLE, in Arithmetic and Geometry, is applied to fimpie Magnitudes, when multiplied equally, i. e. by equal Quantities, or Multiplycrs. See Multipli- cation.
Thus, taking A as many Times as B; or multiplying 'em equally, there will flill remain the fame Ratio between the Magnitudes thus multiplied, as between the primitive Magnitudes before Multiplication.
Now, thofe Magnitudes, thus equally multiplied, are call'd Equimultiples of the original ones A and B : Whence we fay, that Equimultiples have the fame Ratio as the fimpie Quantities. See Ratio.
In Arithmetic, we generally ufe the Term Equimultiples for Numbers -which contain equally, or an equal Number of Times, their Submnltiples.
Thus 12 and 6 are Equimultiples of their Sub-multiples 4 and 23 inafmuch as each of them contains its Submul- tiple three Times. See Submultiple.
EQUINOCTIAL, or Equinoctial, in Aftronomy, a great and immoveable Circle of the Sphere, under which the Equator moves in its diurnal Motion. Sec Sphere.
The Equinotlial, or Equinotlial Line, is ordinarily confounded with the Equator 5 but there is a Difference: the Equator being moveable, and the Equinotlial immove- able 3 and the Equator drawn about the Convex Surface of the Sphere, but the Equinotlial on the Concave Surface of the Magnus Orbis. Sec Equator.
The Equinotlial is conceiv'd, by fuppofing a Semi-dia- meter of the Sphere, produced thro' a Point of the Equator, and there, by the Rotation of the Sphere about its Axis, defcribing a Circle on the immoveable Surface of the prirauni Mobile.
Whenever the Sun, in his Progrefs thro' the Ecliptic, comes to this Circle, it makes equal Days and Nights all around the Globe 3 as then arifing due Eaft, and letting due Weft, which he never does at any other Time of the Year. Sec Day.
And hence the Denomination, from tequus, and nox, Nights quia equat diem notli. See Day and Night.
The Equinotlial, then, is the Circle which the Sun defcribes, or appears to defcribe, at the Time of the Equi- noxes 5 that is, when the Length of the Day is every where equal ro that of the Night 5 which happens twice per Annum. Sec Equinox.
Equinoctial, in Geography. See Equator.
People who live under this Circle, by Geographers and Navigators call'd the Line, have their Days and Nights conftantly equal. And at Noon, the Sun is in their Zenith, and cafts no Shadow. See Ascu.
From this Circle, is the Declination, or Latitude of Places, accounted in Degrees of rhc Meridian. See Lati- tude, &c.
Equinoctial 'Points, are the two Points wherein the Equator and Ecliptic interfect each other. The one, being in the firfl: Point of Aries, call'd the Vernal 3 and the other in the firft Point of Libra, call'd the Autumnal 'Point. See Point.
Equinoctial Colure, is that paffing thro' the Equi- notlial Points. See Colure.
Equinoctial Dial, is that whofe Plane lies parallel to the Equinotlial. See Dial.
EQUINOX, or ./Equinox, in Aftronomy, rhe Time when the Sun enters one of the Equinotlial Points.
That when he enters the Vernal Point is particularly denominated the Vernal; and that in the Autumnal Point, the Autumnal Equinox. See Equinoctial 'Points.
The Equinoxes happen when the Sun is in the Equi- noBial Circle 5 when, of Confcqucnce, the Days arc equal to the Nights throughout the World, which is the Cafe
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