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the Complements of the Legs A B and A C, being confider'd as Legs themfelves, and in rectilinear Triangles, theSides them- felves being taken for the Sines and Tangents of the Sides) The whole Sine -with the Co-fine of the mean or middle 'Part is equal to the Sines of the di'ju.icl or feparate Parts, and the Co-tangents of the confitn&W-. contiguous 'Parts.
For an Illufiration and Application of this Rale, in the Solution of the various Ce'fes cf fpherical Triangles ; fee Triangle.
TRIPLING or Trichino, from the Saxon, Trihinga, an. Extent containing three or four Hundreds, or the third Part of a Shire or Province. See Tithing.
The Word is alfo ufed for a Court held within that Circuit, which was the fame with what we now CaUa Cburt-Zeet, which is above a Court Baron, and inferior to the County Court. See Court, Leet, i$c.
TRILLION orTRimoN, in Arithmetic, fheNumberof a Billion of Billions. See Numeration.
After 'Billions, we reckon by Trillions, which makes^ a Clafsof Numeration, and are divided, like the other Clafles, into three Places : Thus we fay Trillions; '(ens of Trillions ; Hundreds of Trillions, g?c.
TRIM, in the Sea Language. — To Trim a Seat, is to fet the Paflcngers ft as to keep the Boat even on both Sides.
Trim of a Ship, is her bell Pofture, Proportion of Ballaft, and hanging of her Mails for failing.
Hence, to rind the bell way of making a Ship fail fwiftly, is to find her TrJnf.
TRIMACRUS, Tp/j/azp©-, in the ancient Profody, a Foot in Verfe, confuting of three long Syllables. See Foot.
TRIMILCHI,' from the Saxon Trimilc, a Name by which the Englijh Saxons called the Month of May • becaufe they milked their Cattle three times a Day in that Month.
TRIMMERS, in Architeflure, Pieces of Timber, fram'd at right Angles to the Joints, again!! the Ways - 7 for Chimneys and Well-holes for Stairs.
TRINE Ttinsenfion, or Three-fold Tiinienfion, includes Length, Breadth and Thicknefs. See Dimension*
The Irine Dimenfion is peculiar to Bodies or Solids. See Bony, f£c.
Trine in Afirology, is the Afpect or Situation of one Star with regard to another, when they are diftant 120 Degrees, as the Arch A B (Tab. Aftronomy, Fig. 3. ) which is a Third of a Circle, and its fubtenfe A B, a Side of an equila- teral Triangle A B inferibed in the Sphere. See Aspect.
It is alfo called Trigon, and fignified by the Character A. See Tricon.
TRIjiGLE, in Architecture, a Name common to feveral little fquare Members, or Ornaments ; as Reglets, Liflels and Plat-bands. See Reglet, Listee, SiV.'
The Word is French, where it fignifies the fame thing.
Tringle is particularly ufed for a little Member fix'd ex- actly over every Triglyph, under the Plat-band of the Archi- trave ; from whence hang down the Guttie or Pendant Drops. See Trigi.yi'H and Guttje.
TRINITARIANS, a Term ufed very varioufly, and ar- bitrarily — Frequently it Hands as a common Name for all Hereticks, who have Sentiments on the Myftery of the Trinity, contrary to thofe of the Catholic Church. See Trinity.
Sometimes it is more immediately reftrain'd to feme one or other particular Clafs of Hereticks : Thus the Trinitarians are frequently confounded with the Unitarians. See Unita- rians.
Sometimes it is even applied to the Orthodox themfelves, in Contradiftincfion to the AntitrinitarianS, who deny or impujip.the Doctrine of the Trinity : Thus the Socinians and others us'd to call the Athanafians, Trinitarians,
Trinitarians are alfo an Order of Religious, inftituted in Honour of theTrinity, for the Redeeming of Chriftian Cap- tives from the Infidels 3 vulgarly call'd Mathllrins, and Bro- thersof the Redemption- SeeMATHuRiN.
They are cloath'd in White, and bear on the Stomach a Crofs, partly Red and partly Blue ; by which three Colours, White, Red and Blue, is fuppofed to be reprefenced, the Myftery of the Trinity.
The Trinitarians make it their Bufinefs to go and ranfom Chriftians held in Slavery in the Rcpublicks of Algiers, Tunis and Tripoly, and the States of Morocco. — They have a Rule peculiar to themfelves ; though feveral Hiftorians rank them aoonf theOMervers of the Rule of St. Augufiin.
Tlie Order had its Rife in 11 98, under the Pontificate of Innocent III. The Founders were John de Matha and Felix ieVaieis: The firft of Fauccn in Provence ; the fecond, not of the Royal Family of the yahis's, as fome have imagin'd ; but thus call'd, in all probability, as being a Native of the Country Valois.
Gavthier of Chatillon was the firft who gave them a Place in his Lands to build a Convent ; which afterwards became the Chief of the whole Order : Honorius III. confirm'd their Rule. Urtc.n IV. appoinwd the Bifbop of Paris and others,
to reform them : they did it ; and the Reform was approved in 1267, by Clement IV.
This Order poffefies about 2J0 Convents, divided into Thirteen Provinces ; whereof fix are in France, three in Spain, one in Italy, and one in Portugal. — Formerly, there was one in I-u s land, another in Scotland, and a third in Ireland.
In the general Chapters held in 157? and 1575, a Reform was order'd, and begun fome time afterwards by Julian de Nututonville, and Claude Altph, two Hermits of Sx. Michael, but now permitted by Pope Gregory to take the Habit of the Trinity ; u ; on which their Hermitage was converted into a Houfe of the Order.
In 1 609, Pope Paul allow'd them to build new Houfes, and to introduce the Reform into the old One. In 1635 Urban VUl by a Brief, appointed the Cardinal de Rochefou- cault to introduce the Reform into all the Houfes of the Order, which was done accordingly, by a Sentence contain- ing the Reform in Eight Articles, the Principal whereof were, That they fhould obferve the primitive Rule approved of by Clement IV. mould abftain from Flefli, ufe woollen Shirks, have Matins at Midnight, (Sc. In 1554 tllcr e was aifc a Reform made among thofe of Portugal.
The Habit of the Trinitarians is different in different Countries ; and that of the Rclorm'd different from the reft.
Sare-foot Trinitarians, are a Reform of this Order; made in Spain at a general Chapter, held in 1504, where it was refolved, That each Province fhaulil eftablilh two or three Houfes, where the primitive Rule ftiould be obferv'd, and where the Religious mould live up to a greater Aufterity, ufecoarfer Cloaths, gfc. and yet fhould have the Liberty of returning to their ancient Convents when they thought fit.
'JJom. Alvares Sajdn, intending to found a Monaftery at ValdepgnaSi and deiiring to have it held by bare-foot Religi- ous ; it was agreed to add Nudity of Feet to the Reform ; that theTrinitarians might have the Benefitof thatEftablim- ment. The Reform afterwards grew into three Provinces and was at length introduced into Poland and Rujfia, and thence into Germany and Italy.
There are alfo bare-fooled Trinitarians in France, efta- blifh'd by F. ferom Hallies, who being fent to Rome to fol- licit the firft Reform mentioned above ; not content therewith, he carried it further, and obtain'd a Permilfion of Pope Gregory, to add a coarfe Habit, and Nudity of Feet thereto. He began with the Convent of St. <Dcms at Rome, and thofe of Aix in Provence.
In 1670 there were Houfes enough of this Reform to make a Province ; and accordingly they held their firft general Chapter the fame Year. See Province.
There are alfo Nuns of the Trinitarian Order, eftabliffi'd in Spain by St. John de Matha himfelf, who built them a Convent in 1201. — Thofe who firft took the Habit were only Oblati, and made no Vows ; but in 120 1 the Monafte- ry was fill'd with real Religious, under the Direflion of the Infanta Cmfiantix, Daughter of Peter II. King of Arragon, who was the firft Religious, and the firft Superior of the Order.
There are alfo Sare-foot Nuns of this Order, eftablilh'd at Madrid about the Year 1612, by Frances de Romero, Daughter of Julian de Romero, LieutenantGeoeral in the Spanifll Army. Her Defign being to found a Monaftery of Sare-foot Augufiines, fhe affembled a Number of Maids for that End, lodging them, for the Time, in a Koufe be- longing to the Monaftery ox~ Sare-foot Trinitarians in the Neighbourhood.
Here, attending at the Church of thole Fathers, and be- ing under the Direction of F. John Safitifi of the Concep- tion, their Founder 5 the Knowledge of that Father, and the Services he did them, m.ide them change their Refolu- tion of becoming Augufiines, and demand of their Director the Habit of his Order ; which he gave them.
But the Order oppofing their Defign, and refufing to take them under its Jurifdiction, they addrefs'd themfelves to the Archbifhopof Toledo, who allow'd them to live accord- ing to the Rule of that Order ; fb that they took the Habit anew in .1612, and began their Noviciate.
Laftly, there is a third Order of Trinitarians. See Thirtj Order.
TRINITY, Trinitas, Trias, Triad, in Theology, the ineffable Myftery of three Perlons in one God ; Father, Son, and Holy Spirit. See Person and Mystery.
'Tis an Article in the Chriftian Faith, that there is one God ; an Unity in Nature and EfTence, and a Trinity of Perfons. — TheTerm Trinity implies the Unity of three, the Unity of three divine Perfons really different, and the Identity of an indivifible Nature : The Trinity is a Ternary of divine Perfons of the fame EfTence, Nature, and Sub- ftance.
Theology teaches, that there is in God one Effence two ProeeHions, three Perfons, four Relations, five Notions, and
the
