QUA 



Whence, the area of the curve = 



m i- I 



m + I 



See on the fcbjeft of this article Maclaurin's Fluxions, 

 aad Simpfon's Fhixions, vol. i. feft. 7. p. 121, &c. 



Quadrature, in yyironomy, that afpeft, or fituatinn of 

 the moon, when ftie is go (degrees dillaiit from the fun. 



Or, the quadrature is when (he is in a middle point of her 

 orbit, between the points of conjunftion and oppofition ; 

 which happens twice in each revolution, -viz. in the firll and 

 third quarter. 



When the moon is in her quadrature, flic exhibits tliat 

 phaiis wliich we call the half-moon, i. e. fhe thines with 

 juft half her face ; and is faid to be bifefted, or dichoto- 

 mized. 



In the moon's progrefs from the fyzygies to her quadra- 

 ture, her gravity towards the earth is continually increafing 

 by the atlion of the fun ; and her motion is retarded for the 

 fame reafon. Hei- motion then, in her orbit, is flowell as 

 her gravity to the earth is greateft when in the quadra- 

 tures. 



In her rccefs from the quadratures to the fyzygies, the 

 gravity continually decreafes, and the velocity increafcs. 

 The ratio is thus : as radius is to the fum, or diiTcrence of 

 one and a half the coiine of double the diftance of the moon 

 from the fyzygy, and half the radius; fo is the addition of 

 gravity in the quadratures to the diminution or increafe of it 

 in any other iituation. See SvzYCiY. 



Hence the moon's orbit is more convex in the quadratures, 

 than in the fyzygies ; and hence the circular figure of the 

 moon's orbit is changed into an oval, whofe greater axis 

 goes through the quadratures ; and hence, alfo, the moon 

 is lefs diftant from the earth at the fyzygies, and more at 

 the quadratures. 



It is no wonder, therefore, that the moon (liould ap- 

 proach nearer the earth when her gravity is diminifhed ; 

 that accefs not being the immediate effeft of this diminution, 

 but of the inflexion of the orbit towards the quadi-atures. 



In the quadratures, and within thirty-five degrees of them, 

 the apfides of the moon go backwards, or move in antece- 

 dentia ; but they move forwards in the fyzygies. See Ap- 

 sides. 



The moon's orbit undergoes various alterations in each 

 revolution. Its excentricity is the greateft when the line of 

 the apfides is in the fyzygies ; and the leaft, when in the 

 quadratures. 



Confidering one entire revolution, the nodes move flower 

 and flower as the moon approaches the quadi'atures, and they 

 reft when fhe is in them ; but confidering feveral revolutions, 

 the nodes go back fafter in the quadratures. 



The inclination of the plane of the moon's orbit iacreafes 

 as tlie nodes go from the fyzygies, and is greatefl: when the 

 nodes are in the quadratures. See Moon and Nodes. 



Quadrature Lines, or Lines of Quadrature, are two 

 lines frequently placed on Gunter's ieclor. 



They are marked with the letter Q, and the figures 5, 6, 

 7, 8, 9, 10 ; of which Q fignifies the fide of a fquare, and 

 the other figures the fides of polygons of 5, 6, 7, &c. fides. 

 S there (lands for the femi-diameter of a circle ; and 90 for 

 a line equal to ninety degrees in circumference. 



QUADRATUS, in Biography, an early Chriftian writer, 

 who flouriflied under the reigns of Trajan and Adrian. 

 He is (tyled by Jerome and Eufebius " a difciple of the 

 apoftles," and he was reported to have been endowed with 

 the gift of prophecy. According to Eufebius, Quadratus 



Q U A 



prefentcd to the emperor Adrian, in the year 126, an apo* 

 ix + a) "^ (x- -j- a) logy for llie Chridlan religion, with a view of mitigatinij 

 the fu(fi rings inflicted upon the profeliors of that perioo. 

 This isfuppofcdto have boLMi the (ir(t written apology pre- 

 fentcd on the fame fubjeft to aiiv' of the Roman emperors, 

 and it produced a con(idi.ral)lf e(fect on tlie mind of Adrian. 

 Of this work only a fragment remains, which is preferved by 

 Eufebius, and which is cxtreir.' ly valuable on account of the 

 teftimony which it affords to the reality of the miracles ot 

 Chrid and his apoftles, by afterting that fome of thofe 

 miracles were wrought on perfons who were living at the 

 time when Quadratus wrote. Nothing is known refpedling 

 the time and manner of his death. Lardner. 



QuADKATUs, in Anatomy, a name given to feveral mufcles 

 of the body, on account of their form. 



QuADRATiT.s Fcmoris, le carre, ijchiotrochanlhien ; is 

 fituated at tlie upper and back part of the thigh, and ex- 

 tends from the tuberofity of the ifchium to tlie great tro- 

 chanter. It is flattened, quadrilateral, znd tolerably thick. 

 The pofterior furface is covered by the gluteus maximus, 

 the fciatic nerve, and the femi-mcmbranofus ; the anterior 

 furface covers the obturator externus, the extremity of the 

 tendon of the pfoas magnus, and the back of the trochanter 

 minor. The fuperior edge is parallel to the inferior ge- 

 minus ; and the inferior to the upper fibres of the adduftor 

 magnus. The inner edge, or origin of the mufcle, is fixed 

 to the outer fide of the tuberofity of the ifchium, in front of 

 the femi-membranofus ; the outer is attached to the bony 

 ridge, which runs from the great to the fmall trochanter. 

 It is tendinous at its two attachments, and flelhy in other 

 parts. It will rotate the thigh ouUvards upon the pelvis ; 

 or, if the former be fixed, it will move the pelvis upon the 

 thigh. When the thigli has been carried upwards and out- 

 wards, it will reftore the hmb to its natural pofition. 



Quadratus Gend, a mufcle of the lower lip; fee the 

 article Deglutition, where it is defcribed under the name 

 of dtprejfor lalii inferioris. 



Quadratus Lumborum. See Lumborum. 



Quadratus Occipitis, a name of the pofterior or occi- 

 pital portion of the Epicranius ; which fee. 



QUADRELLA, in Geography, 2l town of Naples, in 

 Lavora ; 20 miles E.N.E. of Naples. 



QUADRELS, in Building, a kind of artificial ftones, 

 perfedlly fquare; whence their name. They are made of a 

 chalky, or whitiih and phable earth, &c. dried in the ftiade 

 for at leaft two years. 



They were formerly in great requeft among the Italian 

 architeAs. 



QUADRICEPS, in Anatomy, a name under which it 

 has been propofed to defcribe the extenfors of the knee- 

 joint, w'z. the vaftus internus and externus, the crurxus, 

 and reftus ; and the addutlors of the thigh, with the pecti- 

 nalis. 



QUADRIGA, formed from quatuor, four, znd jugum, 

 yoie, in Antiquity, a car, or chariot, drawn by four horfes, 

 harnefled abreaft. 



Various are the accounts we have of the inventor of the 

 quadriga. Cicero makes it the invention of Minerva. Hy- 

 ginus attributes it to Erichtlionius IV. king of the Athe- 

 nians ; which fentiment Virgil alfo follows in his Georgics, 

 lib. iii. ver. 113. jEfchyli;s gives Prometheus the honour 

 of it. TcrtuUian, De Spctlac. lib. ix. fays, it was in- 

 vented among the Argians, by Trochilus, in honour of 

 Juno ; and at Rome, by Romulus, in honour of Mars, or 

 Quirinus. Ado of Vienne, Chronic. aA iii. will have it 

 to have been invented by one Procidus, about the time of 

 the eftablilliment of the kingdom of Athens. Laziardels, 



Hift, 



