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W, and for the Icofibedron by 20.— The Product is the fuperficial Area. See Area and Superficies.
Proportions of the Sphere, and of the five Regular Bodies infcribed therein : The Diameter of the Sphere being 2.
The Circumference of a great: Circle is,
Surface of a great Circle*
Surface of the Sphere,
Solidity of the Sphere,
Side of the Tetrahedron,
Surface or a Tetrahedron,
Solidity of a Tetrahedron,
Side or a Cube or Hexahedron,
Surface of the Hexahedron,
Solidity of the Hexahedron,
Side of an Octahedron,
Surface of the Octahedron,
Solidity of the Octahedron,
Side of the Dodecahedron,
Surface of the Dodecahedron,
Solidity of the Dodecahedron,
Side of the Icolihedron,
Surface of the Icolihedron,
Solidity of the Icolihedron,
If one of thefe Bodies be required to be cut out of the Sphere of any other Diameter ; fay, as the Diameter of the Sphere 2, is to the Side of any one Solid, inscribed in the fame, (Tuppofe the Cube 1. 1547.) Co is the Diameter of any other Sphere (fup- pofe 8.) to 9. 2376;, the Side of the Cube inferib'd in this latter Sphere.
Let dr> then, (Tab. Geometry, Fig. 81.) be the Diameter of a- ny Sphere, and da £ of it. -~ab-rzbr. Erect the Perpendiculars ae, cf, and bg ■ and draw de, df, er, fr, andgr; then will (1.) re bs as the Side of the Tetrahedron : (2.) df is the Side of the Hexahedron : (3 ) de is the Side of the Octahedron. (4..) And cutting de in extreme and mean Proportion in h, dh will be the Side of the Dodecahedron. (5.) Setting the Diameter dr up perpen- dicularly atr; from the Centre c, to its Top, draw the Line eg* cutting the Circle in g.— Let fall the Perpendicular gb; Co is br the Side of the Icolihedron.
Regular Curves, are fuch whofe Curvity proceeds continually in the fame uniform Geometrical Manner. — Such are the Perime- ters of the Conic Sections. See Curve, Conic Section, Sec.
Such as have a Point of Inflection, or Regrefiion ; and which being continued to a certain Point, turn themfelves a contrary Way, are call'd Irregular Curves* — Such are the Conchoid, and the folid Parabola, which has a Square for its Parameter. See Flexion and Retrogression.
Regular Architecture? Fortification* &c. See Architec- ture and Fortification.
Regular, in the Monaftic Senfe, is a Perfon who has made the Vows in fome Religious Houfe. See Religious and Vow.
Under Regulars are comprehended the whole Body of Monk*. See Monk.
The Denominations of Regular, in this Cafe, arifes hence, that they are bound to obferve the Rule of the Order they are en- ter'dinto. See Rule and Order.
Hence, Regular Priefl is ufed for a Prieft who is in fome Re- ligious Order ; in oppolition to a Secular Prieft, who lives in the world, or at large. See Secular.
A Cardinal is reputed both Regular and Secular, and is enti- tled to the Rights of both. Sec Cardinal.
Regulars may be promoted to Bifhopricks and Archbifhopricks, as well as Seculars ; but their Promotion fecularizes them; the Epifcopal Dignity difpcnfing them from the Obfcrvation of the Rule whereof they have made Profeffion. See Secularisa- tion.
Regular Canons. See Canon.
Regular Benefices, are fuch as can only be held by Monks or Religious ; or at lean 1 :, per cupientem profiteri, a Perfon deiirous K> embrace the Monaftic Life. See Benefice.
Tis a Maxim in the Romi',h Canon Law. — Regularia Regula- WW, i. e. Regular Benefices are to be confer'd on Regular Priefts. —The Abbies that are Chiefs of their refpective Orders are all Regular, and can only be ierved by Monks or Cardinals. See Abby.
All Benefices are prefumed Secular, unlefs they be proved Re- S,uhr,
Amicmly, the Regular Benefices were almoft all confer'd by way of Admin iftrations or Curacies; the Religious Incumbents bc '£g always ad Manum of their Superiours, who difplaced them at rleafure.— Hence the common Maxim among the Canoniits, 0m M Seneficium regulate manuals.
The Benefices affected to Regulars are Abbies, Conventual Tories, Simple Priories, and Clauftral Offices.— They may be confer'd o n Seculars in Conmiendam. See Commendam.
Regular. Places, are thofe within the Boundary or Indo- le ° f tlle Convent ; as the Cloifter, Dormitory, Chapter, and Refectory .-i n oppolition to thofe deftiaed for Guefts., and for
the Necef&ries of the Houfe, which are reputed without tire Inclofure.
REGULATION, a Rule or Order prefcribed by a Superior; for the uniform and orderly Management of fome Branch of Po- licy, Juftice, or the like. See Law and Statute, Ordi- nance, <&c.
REGULATOR, of a Watch, is a fmall Spring belonging to the Balance; ferving to adjuft the going, and make it either pro- ceed fafter or flower. See Watch, &c.
REGULO, a Title given to the Sons of the Emperors of China.
The Emperor's eldeft Son, whom we call the fir fi Regulo, was the only one of all his Children in favour; 'till, of a fudden, Matters took a new Face. From fome new Intelligences, the Emperor learnt the Innocence of the hereditary Prince whom he had depofed, and the Artifices that had been ufed to ruin him : Particularly, that the Regulo, to fucceed therein, had had recourfe to Magick, and at the Inftigation of certain Lama, or Tartar Priefts, had procured a Statue to be buried in Tartary\ accompanying the Ceremony with feveral Magical Operations. Upon this, Orders were inftamly fent to feize the Lama, and to dig up the Statue: The Regulo had his Palace aflign'd him for a Prifon. Let. Edif. & Cur.
REGULUSj petty Kink, in i ourantientCuftoms, a Term fre- quent in the Saxo?i Councils, lignifying a Corns ox Count. See Count and Earl
Hence, Subreguks, was ufed for a Vice-comes, or Vicaunt : Tho* in many Places the two feem ufed indifferently for the fame Dig- nitary.
Thus in the Archives of the Cathedral of Worafler, Uthredus, fometimes ftiles hirnfelf Regulus, and fometimes Sub-regulus of the City of Worceftcr. '•
But in other Places we find Of.i, Rex Merciorum; Uthredus, Regulus; Aldredus, Sabregulus, Sec.
Regulus, in Chymiftry, is the fmeft and pureft Part of a Metal or Mineral, which (inks or precipitates to the bottom of the Crucible or Furnace, in melting' a Mineral, or metallic Ore. See Metal, Mineral, Fusion, &c.
To procure the Regu/us's of Metals, &c. Flux Powders are commonly ufed; as Nitre, Tartar, &c. which purge the fulphu- rous Part adhering to the Metal, by attracting and abforbing it to themfelves. See Flux Poiuder.
Regulus is principally ufed for that of Antimony, which is a ponderous metallic Powder, that upon fufing fome of that Mine- ral in its crude State, finks to the bottom, leaving the Scoria or Impurities a-tbp. See Antimony.
The Alchymifts will have this Matter called Regulus, i. e. 1 little King, as being the firft born of the Royal metallic Blood j which is really a Son, but not a perfect Man, /. e. not yet a per- fect Metal for want of Time and proper Nourifhment.
Antimony purified by Ample Fufion, is call'd Regulus of An- timony ; or Regulus Antimmti fiellatus Philofipho-um.
But the more common way of reducing it into a Regulus is with the Addition of Flux Powders, as Tartar and Nitre. See Flux Poiuder.
The Scoria found at the top of this Regulus is violently emetic, as well as the Regulus itfelf, whereof if Cups or drinking Veffels be caft, the Wine put into them will become vomitive.
Of this Regulus caft in Moulds are made thofe common- ly called the AMtmomd Pills, weighing about eight or ten Grains each, one of which being fwallowed, will operate confiderably both by Vomit and Stool.
Thefe Pills having thus performed their Office, and being dis- charged the Body, will ferve the fame Purpofe again and again; whence they have obtained the Name 0$ perpetual Pills.— The Virtue of this Regulus is not however inexhauftible, as has been imagined; for by repeated Infulions in Wine, though the Liquor be made violently Emetic at firft, yet by Degrees it lofes its Force, and at length ceafes to be Vomitive.
Martial Regulus of Antitnony is a Mixture of the Nails of Horfe's Shoes, melted with the Regulus.
In this Operation the Iron difiblving and abforbing the fulphu- rous Parts of the Antimony, more ftrongly than the Fluxes in the former Cafe ; and turning it into a Crocus; the Antimony is hereby brought to a greater Degree of Puriry, and render'd more efficacious than in the common Regulus See Iron, Sulphur,
This Regulus is fometimes further purified by repeated Fufions and Detonations, with the Addition of frefh Antimony, and more Nitre, alternately.
Regulus, in Aftronomy, is a Star of the firft Magnitude, in the Conftellation Leo ; call'd alfo from its Situation, Cor Leonis, or the Lion's Heart; and by the Chaldeans, Kalbeleced, or Ka/be- leceid, from an Opinion of its influencing the Affairs or the Hea- vens; as isobfervedby Theon. See Star.
The Longitude of Regulus, as fix'd by Mr. Flamflccd, is 25* 31' 20"; and its Latitude o°. 26': 38" North. See Leo.
REHABILITATION, in the Civil and Canon Law, an Acti- on whereby a Prince or Pope, by Difpenfations or Letters Pa- tents, reftore a Delinquent to the Condition he was in before his Delinquency. See Degradation, &c
11 S
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