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 EPI

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EPI

EPPCHEREMA, in Logic, an Argumentation, confiding of four, or more Proportions ; fome whereof are Proofs of others.

Thus, that Oration of Cicero for Milo, may be reduced to the Epicherema. Thofe who Way-lay a Man to kill him, 'tis lawful for him to kill ■-, as is allowed by the Laws of Nature and Nations, and by the Practice of the bell Men : But Ciodius Way-laid Milo with that View ; as appears from his forming an Ambufcade before his Country Houfe, and from his Provifion of Weapons, Sol- diers, £?r. Therefore it was lawful for Milo to kill Ciodius. Sec Sop. ites.

EPICOLIC Regions, from am, fupra, upon, and Colon, the Gut fo called ; a Name gi ven by Dr. Glijfon, to that Space, on both Sides, over the Colon. See Colon.

EPICUREANS, a Sc5t of antient Philofophers, who adhere to the Doctrines and Opinions of Epicurus. See Epicureanism.

The Epicureans have, in all Ages, been decried for their Morals, and their Attachment to the Pleafures of Senfe : Several Authors, particularly, Cicero among the Antients, and Gaffendus among the Moderns, have endeavoured to vindicate them from this Charge; by shewing that the Pleafurc wherein their Mailer Epicurus places the Simnmm bonnm, or fuprcme Happinefs of this Life, was not any fenfual, or brutal Pleafurc, but a Contentment, and Tran- quillity of Mind, exempt from all tumultuary Paffions, (i'c.

This Opinion feems juff, and well grounded ; but, with- out entering into the Qucition, which Gaffendus, 2Ja Rondel, and others have exhauflcd ; 'tis certain, that in the common Ufe of the Word, Epicurean conftantly fig- niilcs a Debauchee, an indolent, foft, effeminate Perfon, who only confults his Pleafure, without concerning hirnfelf with any Thing ferious.

In Effect, there were always two Kinds of Epicureans ; the Rigid and Rcmifs : The Rigid Epicureans, were thofe ftrictly attach'd to the Sentiments of Epicurus, who placed all their Happine's in the pure Pleafures of the Mind, refuliing from the Practice of Vertuc. The Remifs Epicureans, taking the Words of that Philofophcr in a grofs Senfe, placed all their Happinefs in Pleafures of the Body, in Eating, Drinking, Loving, && The former Kind, who were the genuine Epicureans, call'd the other the Sophilts of their Se:f.

The Epicureans take their Name from the Chief of their Sect, Epicurus, whom fome, however, deny to be the Author of the Phiiofophy he taught ; charging him with Retailing for Phyficks, the Doctrine of 23emocritus ; and for Ethicks, that of Arifiippus.

Be this as it will, he was an Athenian, and the Son of Neocles ; born in the 109th Olympiad, and confequently 542 Years before Chrift. He began to form his School at Mitylene and Lamjfachus, about the 32 d Tear of his Lite ; tho' he afterwards remov'd to Athens, where he phiiofophized chiefly in his Garden : And died of the Stone at 72 Years of Age.

EPICUREANISM, or EPICUREAN 'Phiiofophy, the Declare, or Syftcm of Phiiofophy, maintain'd by Epicurus, and his Followers. See Epicureans.

The noble Poet Lucretius, who has given us a beautiful Syitcm of Epicureanifm in fine Latin Verfe, prefers its Father Epicurus, above all other Philofophers, whom, he makes no Scruple to fay, he obfeured, as much as the Sun does the other Stars. Tis faid he firii taught Grammar; till upon reading Serdocritus's Books, he began to apply himfclf to Phiiofophy.

From Democritus he learnt the Doctrine of Atoms, or Corpufcles, which he afterwards made the Bans cf his Phy- ficks. Cltm.Alexaud. Strom. 6. advances, that Epicurus Hole his chief Doclrines from liemocritus. But, 'tis certain, he greatly improved and illuflrated them. 2)iog. Laertius affures us, he compofed an infinite Number of Volumes.

This Phiiofophy confiiled of three Parts : Canonical wmti'i "Phyfical <t<, m S r, and tor.lv, Ethical ; which he explain'd briefly in three Epiftlcs.

The firft, as Laertius relates, was about the Canons, or Rules of Judging ; wherein, rejecting the Ufe of Logic, he eilablilh'd the Senfcs, Paffions, and Anticipations, as the Critenons, or Judges of Truth. See Criterion, Sense, &c.

In the fecond, he laid down Atoms, Space and Gravity, as the firfl principles of all Things. The Univerfe he taught, confilted of Atoms, or Corpufcles, of various Forms, Magnitudes and Weights, which having been difperfed at Random thro' the immenfe Inane, or Space, fortuituoufly concurred into innumerable Syftems, or Worlds which were thus form'd, and afterwards, from Time to Time incrcas'd changed, and diffolved again, without any certain Caufe', or Deiign ; without the Intervention of any Deitv, or the Intendance of any Providence. See Atom and Corpuscle.

Not that he denied the Exiilence of a God : On the contrary, he afferted it ; but thought it beneath the

Majelfy of the Deity to concern it felf with human Af- fairs : Laertius allures us, he held him, ™ ^ivjeisv £ afyZafliv, «7* auii ir&yua-ni tyj 87* akhv craasvJ A Slejfed, Immortal Being, having no Affairs of his' own to take Care of, and above taking Care of thofe of others. See Corpuscular, Space, Gravity, Element, iS c \

As to Ethicks ; his finl Principle, or the fupreme Felicity of Man, he held, was Pleafure. Which fome, as already obferved, underfland of Mental, and others of Carnal P lca. lure. See Epicureans.

EPICYXLE, in the antient Aftronomy. As the Aftro- nomcrs have invented an Eccentric Circle, to folvc the apparent Irregularity of the Planets, and their different Diftances from the Earth ; they have likewife invented a little Circle to folve the Stations, and Retrogradations of the Planets. This little Circle which they call Eujcycle, has its Centre in the Circumference of another greater which is the Eccentric of a Planet. See Eccentric.

In this Eccentric, the Centre of the Epicycle moves - carrying with it the Planet fix'd in its Circumference, the Centre of the Planet, all the Way, moving regularly alon-r the Circumference of the Epicycle, when downwards, according to the Order of the Signs, and when upwards, contrary to it.

The higheil Point of the Epicycle is call'd the Apoa-ee, and the loweil the 'Perigee. See Apogee and Pericee!

The great Circle, in whofe Circumference the Centre of Ax Epicycle is plac'd, is call'd the ^Deferent of the Epicycle, as carrying the Epicycle along with it. Sec Deferent!

Thus, the Moon is fuppofed to move in an Epicycle', whofe Centre is in the Orbit of the Earth, according to' the Hypothefis of Copernicus : But in that of 'Ptolemy, who fuppofed the Heavens folid, the Epicycle was a Sphere, which revolved with the Moon, of the Thicknefs -al- lowed its Heaven or Orbit ; and which, fometimes fhcw'd it higher, and fometimes lower. See 'Ptolemaic System.

' The Aftronomers, who deny the Motion of the Earth - ' in Order to render the Phamomcna of the Motions of the ' Planets more confiflent with the Motion of the Sun ' have affix'd the Orbit of the Earth, as an Epicycle, to' ' the Orbit of the Planets : So that the Planet fhould ' proceed in an Epicycle, while it is carried through its ' Orbit round the Sun : But this is far from anfwering ' their Expectations.' Wolf. Elem. Math. T. II. p. 501.

' Ricciolus, tho' a zealous Enemy of the Motion of the ' Earth, cou'd not make any Agronomical Tables that ' fhould but tolerably agree with Obfervation, without ' fuppofmg the Earth to move ; not, tho' he called in all ' the foreign and forced Affiifances of changeable Epicycles, ' inclined to the Ecliptic' S)e Chales Ailrou. Reforif Lib. X C. 1. f. 353, iSc. J
 * liable to continual Increafe and Decreaie, and varioudy

The Word is form'd of the Greek, sir; 3 and xil«A©-. Circle, q. d. a Circle on a Circle.

EPICYCLOID, in Geometry, a Curve generated by the Revolution cf a Point of the Periphery of a Circle, aloni the Convex, or concave Part of another Circle. See Curve

A Point of the Circumference cf a Circle, proceeding along a Plane, m a right Line, and at the Came Time revolving on its Centre, defcribes a Cycloid. See Cycloid.

And the generating Circle, if in lieu of movin» on a right Line, it move along the Circumference of anorher Circle, whether equal or unequal ; the Curve defcribed by any Point in its Circumference is called an Epicycloid.

If the generating Circle proceed along the Convexity of the Periphery it is called an upper, or Exterior Epicycloid ; If along the Concavity, a lower, or Interior Epicycloid.

In an Epicycloid, the Part of the Circle, the seneratina Point moves along, is called the Safe of the Epicycloid: Thus in fab. Geom. Fig. 58. D B is the Safe of the Epicycloid, V its Vertex ; V B its Axis = D P V half of the Exterior Epicycloid; made by the Revolution of the Semi-circle VLB, (which is called the Generam) along the Convex Side of the Bafe, D B : As D P U is the Interior Epicycloid, formed by the Generant's re- volving along the Concave Side of the Bafe.

The Length of any Part of the Curve, which any »iven Point 111 the revolving Circle has defcribed, from the Time it touched the Circle whereon it revolved, is demonffrared to be double the verfed Sine of half the Arch, which all that Time touched the quicfcent Circle, as the Sum of the Diameters of the Circles, to the Semi-diameter of the quicfcent Circle : Provided the revolving Circle moves upon the Convex Side of the quiefcent Ctrcle ; but, if upon the Concave Side, as the Difference of the Diameters, to the Semi-diameter."

Dr. Bailey gives us a general Proportion for meafurin-r all Cycloids and Epicycloids ; thus : The Area of a Cy- cloid, or Epicycloid, either primary, or contracted, or prolate, is to the Area of the generating Circle ; and alfo the Area of the Parts, generated in thofe Curves, to the Areas of anala'gous Segments of the Circle: j\s the Sum of double the Velocity of the Centre, and Velocity of the

' circular