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For, fiippofe there was given any three Numbers, or Quanti- ties. Geometrically Proportional, as A, B, andC; and that it were required to find a fourth, D, Proportional to them : Since A : B : : C : D, therefore AD^BC, and confequent-
hy, D— — , that is, the fourth Term is equal to the Quotient
of the fecond, multiplied by the third Term, divided by the firft.
Or thus, in Numbers: Suppofe given 12, 4, and 9 ; required a fourth Proportional. Now as 12. : 4 : : 9 : Q: But 12
Qrr4x9^r^. Therefore Q,~^T ( : 3- by dividing both
Sides by 12.
And hence it follows, that if any two Triangles, Paralle- lograms, Prifms, Parallelopipeds, Pyramids, Cones, or Cylin- ders, have their Bafes and Altitudes reciprocally Proportional, thofe two Figures or Solids are equal to one another ; and wee ■verfa, if they are equal, their Bafes and Altitudes are reciprocal- ly proportionable. See Triangle , Parallelopiped, Prism, Cone, Cylinder, &c.
Reciprocal Proportion, is when in four Numbers, the fourth islcfler than the fecond, by fo much as the third is greater than the firft ; and 'vice verfa.
This is the Foundation of the Inverfe, or indirect Rule of Three, thus; 4 : 10 : 8 : 5 : See Rule.
There is great Ufe made of this Reciprocal Proportion, by Sir Jfaac Nevitott, and others, in demonitrating the Laws of Moti- on, See Proportion.
RECITATION, the Act of reciting, or delivering a Difcourfe, either in the way of Narration, Rehearfal, Declamation, or Reading.
RECITATIVE M/fe, a Kind of Singing, that differs but little from ordinary Pronunciation ; fuch as that wherein feveral Parts of the Liturgy are rehears'd in Cathedrals j or that wherein the Actors ordinarily deliver themfelves on the Theatre, at the Opera, &c. See Singing and Opera.
The Italians value themfelves on their Performance in the 'Re- citative Way. The Recitatives, or Recitatives, in our Opera's, ufually tire the Audience, by rcafon they don't understand the Language ; the Songs make them amends. See Song.
Recitative Style, is the Way of Writing accommodated to this Sort of Mufic. See Style.
RECKONING, in Navigation, the eftimating of the Quan- tity of the Ship's Way, or of the run between one Place and an- other. See Sailing and Distance.
This is bell perform'd by means of the Log-Line; the manner of applying which fee under its proper Article, Log-Line.
Yet is this liable to great Irregularities. — Vitruvius advifes an Axis tobepafs'd through the Sides of theShip, with two large Heads propending out of the Ship „■ wherein are to be included Wheels touching the Water, by whofe Revolution the Space pafs'd over in any given time, may be meafured. The fame has been late- ly recommended by Snellius : But there are few who have wrote of Navigation, but have (hewn the infufficiency of this Me- thod.
RECLAMING, or Reclaiming, in our antient Cuitoms, the Action of a Lord purfuing, proiecuting, and recalling his Vaual, who had gone to live in another Place, without his Per- miffion. See Lord and Vassal.
Reclaiming is alfo ufed in a fimilar Senfe, for the demand- ing of a Perfon or thing to be delivered up, or furrender'd, r.o the Prince or State it properly belongs to; when, by any irregu- lar Means it has come into the Poireflion of another. See Claim.
An Officer was fent to reclaim the VefTel feiz'd by the Alge- rines, contrary to the Terms of the Treaty of Peace. The Mi- niftry reclaim'd the late Cafhier of the South-Sea Company, who had refuged himfelf in Flanders,, but in vain.
Reclaiming, in Falconry, is the Calling of a Hawk, or Bird of Prey back to the Fift,
The Sparrow-Hawk, Goffe-Hawk, &c. are reclaimed with the Voice: The Falcon only by making the Lure.
So that Luring, with regard to the Falcon, is more proper than Reclaiming. See Lure.
The Partridge is alfo faid r_o relaim her Young ones, when flie calls them together upon their feathering too much.
RECLINATION, of a Plane in Dialling, the Number of Degrees which a Dial-Plane leans backwards, from an exactly upright or vertical Plane, i. e, from the Zenith. See Plane.
The Redinatiou is eafily found, by means of a Ruler and a Quadrant ; for having drawn an Horizontal Line on the Plane, by a Level or Quadrant, and to it another Line at Right Angles ; apply a Ruler, fo that one End of it may hang over, or reach beyond the Plane : Then will a Quadrant, applied to the under Edge of the Ruler, mew the Degrees and Minutes of the Plane's Redinatiou; accounting from that Side of the Quadrant that is contiguous to the Edge of the Ruler. See Dial, Quadrant,
RECLINER, in Dialling, or Reclining Dial, is a Dial whofe Plane reclines from the Perpendicular ,- i.e. leans from you when you ftand before k. "SeeRECLiNATic-N.
When this Reclination is equal to the Height of the Pole, the Dial is faid to be Equinoctial.
A Declining Recliner, or Declining Reclining Dial, is a Dial which neither ftands perpendicularly, nor oppofite to one of the Cardinal Points. See Decliner.
RECLUSE, among Religious, a Perfon clofe fhut up in a very narrow Cell of a Hermitage, or other Religious Houfej and cut off, not only from all Conversation of the World, but: even of the Houfc. See Hermit, &c.
The Word is chiefly ufed for fuch as thus imprifon themfelves out of Devotion, to do Penance. It is fomctimes alfo applied to incontinent Wives, whom their Husbands procure to be thus kept in a perpetual Prifon in fome Convent. See Convent>
Redufes were antiently very numerous: They were, then, a kind of Solitaries who fhut themfelves up in fome little Cell, with a Vow never to ftir out of it. See Solitary.
None were admitted to this Oath 'till they had given fuffid- ent Proofs of their Abftinencc, and had leave from the Biihop* or the kbbot ot the Monaitery where they were fhut up; for the Cells of the Redufes were always to join to fome Mo- naitery.
The Prelates Permifiion being obtain'd, they were tried for 3 Year in the Monaftery ; out of which, during that time, they never ftirr'd. See Probation.
They were then admitted to their Vow of Stability, in the Church before the Bifhop} which done, and the Reclufe enter'd his little Cell, the Bifhop fet his Seal on the Door.
The Cell was to be very fmall, and very exactly clofed. See Cell.
The Reclufe was to have every thing within it necefTary to life j and, even, if he were a PriefLan Oratory confecrated by the Bifhop, with a Window which lookM into the Church, through which he might make his Offerings at the Mafs, hear the Singing, fmg himfelf with the Communicants, and anfwer thofe who talk'd to him. But this Window was to have Curtains before it, both wkhin-ftde and Without ,■ fo that the Reclufe might neither fee nor be feen.
Indeed he was allow'd a little Garden in his Recluf mt, to Plant a few Herbs, and take frefh Air: Adjoining to his Ceil was that of bis Difciples, which he was very rarely without, with a Win- dow, through which they ferv'd him with Neceflaries, and recei- ved his Infractions.
When it was judg'd proper to have two or three Redufes toge- ther, their Cells were made Contiguous to each other, with Win- dows of Communication : If any Women would confult them, or confefs to them, it was to be in the Church, and in the Face of all the World.
Where there were two or three Redufes together, they were never to hold any Conference, but on fpiricual Matters ; and to confefs to each other : Where there was but one, he was to con- fefs and examine himfelf.
If the Reclufe fell fick, his Door was opened for People to come in and aififl: him ; but he was not allowed to ftir out on any Pretence whatever.
Thefe Articles are extracted from a Rule, compiled for the Redufes, by Grimlaic, a Pricft in the IXth Century.
There were alfo Women Redufes-, who led the fame Life, in Proportion. St. Viborarde lived a Recluf at St. Gall, and was there martyriz'd by the Hungari.-ms in 825. See Reclusion.
RECLUSION, the State of a Recluie; or the Cell and 0- ther Appurtenances thereof. See Recluse.
F. Helyot gives a particular Account of the Ceremonies pra- cticed at the Reduf on of a Woman, in that of the Mother of Cambray, Inftitucrix of the Order of the Prefentation of Notre Dame.
A Cell being built for her in 1625, adjoining to the Church of St. Andrew in Tournay: The Bifhop waited for her early in the Morning at the Church Door. Upon her Arrival, proftra- ting her felf at the Feet of that Prelate, he gave her his Bene- diction, conducted her to the Grand Altar; and, there blellinga Mantle, Veil, and Scapulary, put them on her, and gave her a new Name.
Having here made her Vow, and the Bifhop having haran- gued the People in Praife of the new Reclufe - 7 he conducted hec Proceffionally to her Rcdufon, the Clergy all the way finging, Vent Sponfa Chrifii, &c.
Here the Bifhop bleifing her a-frefh, confecrated the Recluf 'on* and fhut her up in perpetual Confinement.
RECOGNITION, an Acknowledgement.
The Word is particularly ufed in our Law Books, for the Title of the firft Chapter of the Stat. 1 Jacob. I. whereby the Parlia- ment acknowledged the Crown of 'England, after the Death of Queen Elizabeth^ to have rightfully defcended to King James.
Recognition, in the Drama. See Discovery.
RECOGNITIONS adnullanda per vim & duritiem facia, is a Writ to the Juftices of the Common-Bench, for fending a Re- cord touching a Recognizance, which the Recognizor fuggefts to have been acknowledged by Force and hard dealing ; that if it fo appear it may bedifanmilied- Sse Recognizance.
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