QUA
( 9*9 )
QUA
the Stibtingent Into the difference of the Semiordinates. fides -S there Hinds for the Semi-diameter of a Circle,
2 . Therefore the Space E A P M, is to the Space P M S Q_ and 90 for a Line equal to 90 Degrees in the Circumference.
as the difference of the Semiordinates A B and P M to the See Sector.
difference of the Semiordinates PM and S Q. QUADRATUS, in Anatomy, a Name apply'd to feve-
tfote, If a Curve be notfuppofed ; defcribe but only an ral Mufcles, in refpecf of their fquare Figure. Sec
Equation to it given, fo as it don't appear ; e. gr. where Muscle.
the Origin of * is to be fixed, we are to put x=0 in the In- Quadratus FeffioriS) a Member of the Mufcle Qua-
tegral, and expunging what are multiply'd by x, add to it the Remainder, if there be any, under the contraty Sign 5 to have the Quadrature fought.
Quadrature of c Des Cartels Curve, which is defined ty the Equation, b'-.x '=b — * : $. Since, b y= bx ' — *'
y=(bx' — x') : b'
ydx=fbx*dx — x*dx) : b* fydx=x' : 3 b— x* : 4 b' Quadrature of all Curves comprehended under the ge- an d pectoral Mufcle ; whence^ fpr'eading over'toe"Nec"k" it
becomes flefhy, and is inferted partly into the Os Hyoides,
drigeminus, arifing from the Apopbyfis of the Ifibium, and maintaining an equal breadth and bulk to its mfertion jull below the great Trochanter.
This affiits with the other Mufcles of the Quadrigeminus, toturn the Thigh outwards. SeeQuADRiGEMiNus.
Quadratus Gents, or Maxilla inferioris, call'd alfo Montanus, is a broad fquare Mufcle lying immediately un- der the Skin of the Neck It arifes thin and membranous
from the upper part of the Spines of the Vertebra of the Neck and .the Skin of the fuperior parts of the Cucullaris
I Equation y=*</™ (x+a) Since y—x(x-\-a) '
ydx=dx (*+") ' : ». To render the Element integrable ; fuppofe, {x-\-a) ' : m =.y Then will x-[-a=vm
dx=-mv m — 'dv <ydx — mv m dv
and partly into the under Edge of the lower Jaw It
ferves to pull the lower Jaw downward. See Subcuta- neus.
QUADRELS, in Building, a kind of Artificial Stones, perfectly fquare, whence their Name '■, made of a chalky, or whkifli and pliable Earth, £gc. dried in the Shade for two Years.
They were formerly in great requeft among the Italian Architects.
QUADRIGA, in Antiquity, a Car, or Chariot drawn by fourHorfes. S^e Car and Chariot.
On the Rcverfe of Medals we frequently fee Victory, or the Emperor, in a Quadriga, holding the Reins of the Horfes ; whence theie Cjins are call'd among the Curious, Quadrigates, or Viiloriates. See Medal.
Various are the Accounts we have of the Author of the
Quadriga • Cicero makes it the Invention of Minerva.
Hyginus attributes it to ErichtoniuslV. King of the -^fo- nians ; which Sentiment Virgil follows in his Georgics,
lib. iii. v. Li 3. Efchylus gives 'Prometheus the Honour
thereof I'ertullian, ds Spetlac. 1. 9. fays it was in- vented among the Argians, by I'rochilus, in honour of jfuno, and at Rome, by Romulus in honour of Mars, or Quirimts. Aden of Vienna, Chronic. Act 3. will have it to have been invented by one Trocidus, about the time of the eftablifhment of the Kingdom of Athens. Zaziardels, fflfi. Univerf. Epilom. 1. 14. fays the fame of Triptolemus. LalHy, if there be not Opinions enough already, Hero- dotus gives us another 5 and fays the Greeks borrow'd ic
from the Lybians Pliny tells us that his Seal was a
Quadriga, lib. xvi. See Seal.
The Word is form 'd from the Latin, quatuor, four, and \v.gurn, yoak. See Biga.
QUADRIGEMINUS, in Anatomy, a Mufcle, or rather an Affemblage of four Mufcles ; ferving to turn the Thigh outward. See Thigh.
The firft of the conflituent Mufcles of the Quadrigeminus, is the Tyriformis ; the fecond and third the Gemini 5 and the fourth Quadratus Femoris. See each defcribed under S-e its proper Article, Pyriformis, Geminus, $£c.
QUADRILATERAL, in Geometry, a Figure whofe Perimeter c nulls of four right Lines, making four Angles , whence it is alfo call'd a Quadrangular Figure. See Qua- drangular.
If the feveral Angles be right, the Figure Is a retlangular Quadrilateral If oblique, an oblique-angular Quadri- lateral. See Rectangular, cifc.
If the Sides of a Quadrilateral be equal, and the Angles right, the Figure is a Square. See Square.
If the Sides be equal, bur the Angles unequal, the Figute Is a Rhombus. See Rhombus.
If the Angles be equal, and the Sides unequal, the Figure Apfidesof theMoongo backwards, ormove in antecedentiaj is a Ret! angle. See Rectangle. but forwards in the Syzygies. See Apsides. _ If only the oppofite Angles and Sides be equal, the Qna-
The Moon's Orbit undergoes various Alterations in each dri lateral is nRhomboides. See Rhomeoides.
fydx=mv«-\-i = m {x-\-a) •/" (x-\-d). Let *==■<>: The
m-\-i m-\-i
Remainder — r~ a s/™ a- Whence, the Area of the Curve is m-\-t '
Ph 0+0) /» (*+ a) — ma /» tt.
Quadrature, in Aftronomy, that Afpeft, or Situation
of the Moon, when ftte is 90 diftant from the Sun. See
Moon. . . ,
Or, the Qtiadrature is when Die is in the middle Points of her Orbit, between the Points of Conjunction and Oppofition, which happens twice in each Revolution, via. in the firlt and third Quarter. See Orbit, Opposition and Con- junction.
When the Moon isin her Quadrature, me exhibits that Phafis which we call the Half Moon, i. e. ihe Ihines with juft half her Face ; and is faid to be biffected, or 2)ichoto- miz'd. See Phasis and Dichotomy.
In the Moon's Pcogrefsfrom the Syzygies to her Qtiadra- ture, her Gravity towards the Earth is continually increa- fing by the Action of the Sun ; and her Motion retarded for
the fame Reafon Her Motion, then, in her Orbit is
iloweft as her Gravity to the Earth is greateft when in the Quadrature. SccGravity.
in her recefs from the Quadratures to the Syzygies, the Gravity continually decreales, and the Velocity increafes.
The Ratio is thus: As Radius is to the Sum, or Diffe- rence of one and a half the Co-fine of double the diftance of the Moon from the Syzygy, and half the Radius ; fo is the addition of Gravity in the Quadratures to the Dimi- nution or Increafe thereof in any other Situation. Syzygy. .
Hence the Moon's Orbit is more Convex in the Quadra- tures, than in the Syzygies; and hence the Circular fi- gure of the Moon's Orbit is changed into an Oval, whofe gteater Axis goes through the Quadratures; and hence, alfo, the Moon islefs diftant from the Earth at the Syzygies, and more at the Quadratures. See Orbit.
'Tis no wonder, therefore, that the Moon approach nearer the Earth when her Gravity is diminifhed ; that Accefs not being the immediate effect of this Diminution, but of the Inflexion of the Orbit towatds the Quadranires.
In t\\a Quadratures, and within 35 Degrees thereof, the
Revolution Its Excentricity is the greateft when the
Line of the Apfides is in the Syzygies ; leaft, when in the Quadratures. See Excentricity.
Confidering one entire Revolution, the Nodes move flower and flower as the Moon approaches the Quadratures, and reft when ftie is therein : But confidering feveral Re- volutions, the Nodes go back fafteft in the Quadratures. See Node.
The Inclination of the Plane of the Moon's Orbit in- creafes as the Nodes go from the Syzygies, and is greateft when the Nodes are in the Quadratures. See Incli- nation.
QjVhvKkTvRi.-Lines, or Lines o/Quadrature, are two Lines frequently placed on Gltnter's Sector.
They are mark'd with the Letter Q, and the Figures 5, «. 7i 8, 9, to; of which Q_fignifies the fide of a Square, and the other Figures the fides of Polygons of 5, 6, 7, £?r.
If the oppofite Angles and Sides be unequal, \\\zQuadri- lateral is a Trapezium. See Trapezium.
The two oppofite Angles of any Quadrilateral Figure in- fcribed in a Circle, always make two right Angles. See Inscribed.
QUADRILL, Quadrilla, a little Troop or Company of Cavaliers, pompouily drefs'd and mounted 5 for the per- formance of Carroufels, Jouits, Tournaments, Runnings at the Ring, and other gallant Divertifements. See Joust, Tournament, &c.
A regular Carroufel is to have at leaft four, and at mo£t twelve Quadrills.. See Carrousel.
Of thcl'e Quadrills, each is to confift of at leaft three Cavaliers, and at moll of twelve.
The Quadrills are diftinguilh'd by the Form of their Ha- bits, or the Diverfity of their Colour'. See Colour, Li- ye&y, fSc.
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