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ExtraB firft the Cube Root of the firft Term a', w. a, and fet it down in the Quotient: Then Subtracting its Cube a% fay, How many Times is its triple Square, or 3 a a, contained in the next Term of the Remainder 3 a a b ? and there comes out b ; wherefore write b in the Quotient, and fubrraaing the Cube of the Quotient, there will remain o ; therefore a + b is the Root. After the fame Manner, if the Cube Root is to be extraBed out of z s + 6 z s — 40 z' -f- 96 z — 4, it will come out m + z z "~ 4- And fo likewise in higher Roots.
EXTRACTS, in Law. See Estreats.
EXTRAORDINARY, fomething rare and uncommon.
Extraordinary Cour iers, are thofe fent exprefs on fome urgent Occafion. See Courier.
An Embaffador, or Envoy Extraordinary, is fuch a one as is fent to treat, or negotiate fome fpecial and important Affair, as a Marriage, a'Treaty, Confederacy, iHc. or even on Occafion of fome Ceremony, as Condolance, Congratula- tion, Q$c. See Embassador and Ordinary.
A Gazette, Journal, or other News-paper Extraordi- nary, is that publifh'd after fome great and notable Event, containing the Detail, or Particulars thereof, which were not found in the ordinary Papers. — Our News Writers generally ufe Poft-fcripts, inftead of Extraordinaries.
EXTRA VAGANTES, a Part of the Canon Law, containing divers Constitutions of the Popes, not contain'd in the Body of the Canon Law; whence the Denomination of Extravagantes; J^iiafi extra corpus juris vagantes. See Canon La-iv.
They are divided into two Parts : The firfl contains XX Constitutions of %ybaXXII; and the fecond, other later Conftitutions of the faid John and his Succeffors. See Constitution.
EXTRAVASATION, in Medicine, the Aft, or Mo- tion, whereby the Blood extravafates it felf, i. e. breaks out of its ordinary Veffels, the Veins and Arteries, and gathers and Stagnates in fome Part of the Body: The Blood that flows out of the Body, or that is drawn from it in opening a Vein, is not properly faid to be Extravafated. See Blood.
Extravafated Blood always corrupts and turns into an lmpofthume. See Imposthume, Tumor, &c.
The ordinary Caules of Extravafations, are unnatural Repletions, and Distentions of the Veffels 5 or Lacerations, and Erofions thereof.
There is a Neceffity for bleeding, to prevent the Blood's growing to fuch a Head as to Extravafate. See Phle- botomy.
In Wounds of the Head, particularly, bleeding is neceffary, to prevent the Extravasation of the Blood in the Brain.
The Term is likewife ufed with Regard to other Humours befide the Blood, as the Lympha, Urine, (3c. See Drossy.
The Gardeners likewife ufe it, in fpeaking of Gums, Juices, iSc. oozing out of their Trees either Spontaneously, or at In- cisions. S^e Gum, Balm, c^c.
The Word is form'd of the Latin, extra, without, and vas, veffel.
EXTREME, orExTKEAM, is applied to the laft Part of any Thing ; or that which finiflves, and terminates it, and beyond which you cannot go.
There is no pafling out of one Extreme, into the other, without going thro" the middle. — Extreme Remedies muff only be fiad Recourfe to in Extreme Difeafes.
Some Anatomifts apply the Denomination Extreams, or Extremities, to the Arms and Legs.
The Arms, or upper Extremes, fnperiour Extremi- ties, confift of do Bones; thirty one in each, viz. the Omoplate, Humerus, Cubitus, Radius, eight in the Carpus, four in the Metacarpus, and fifteen in the Fingers. See each in its Place, Omoplate, &c.
The Lower Extremities, or Legs, confifl of fixty ; thirty in each, viz. Ae Femur,' Rotula, Tibia, fibula, feven in the farfns, five in the Metatarfus, and fourteen in the Eingers. See Leg, Femur, £?g.
Extremes, in Logic, are the two Extream Terms of the Conclufion of a Syllogifm, viz. the Predicate and Sub- ject. See Conclusion.
The Predicate, as being likewife had in the firft Proposition, is call'd the majus extremum, greater Ex- treme ; and the Subject, as being put in the feeond, or minor Propofition, is call'd the minus Extremum, leifcr Extreme. See Predicate and Subject.
They are both call'd Extremes, from their Relation to another Term, which is a Medium, or Mean between them. See Medium.
Thus, in the Syllogifm, Man is an Animal, 'Peter is a Many therefore 'Peter is an Animal: The Word Animal is the greater Extreme ; Peter the lefs Extreme ; and Man the Medium. See Syllogism.
Extreme and mean Proportion, in Geometry, is when a Line is fo divided, that the whole Line is to the greater Segment, as that Segment is to the other.
Or, as Euclid exprefleth it, when the Line is fo di- vided, that the Rectangle under the whole Line and the leffer Segment, Shall be equal to the Square of the greater Segment.
The Invention of this Division is thus : Let the given Line be A B = a, (fab. Geometry, Fig. 04.) and for the greater Segment put x, the leffer will be a — x. Then bj the Hypothesis, a : x : a — x —-. Therefore a a — a x = x x, confequently aa = x x -\-zx. And by adding I a a on each Side, to make x x -\- 3. x -^- * aa a com- pleat Square, the Equation will Stand thus |- aa = u -f- x a -\- % a a.
Now, Since the latter is exactly a Square, its Root x-\- i
a = •/ \ "aaT ant ^ ky Tranfpofition it will be y 7 i "aa t
a=#; which laft Equation is a Canon to find x.
For at the Foot of A B = a, fet at right Angles C B = i a : Then draw C A, the Square of which is equal, ABq-fCBq=4:aa. And therefore A C = / i 17; make C D = C A.
From whence C B = j a being taken, as the Cafe re- quires, there remains B D = x ; which transferr'd into A B, Shall give the Point E, where A B is cut according to Extreme and mean Proportion.
This cannot be exactly done in Numbers ; but if you would have it tolerably near, add together the Square of any Number, and the Square of its half, and extracf. as near as you can, the Square Root of the Sum ; from whence taking half, the Rema.nder is the greater Part.
EXTREME-UNCTION, one 'of the Sacraments of the Romifo Church, the fifth in Order, admir.iiler'd to People dangerously Tick, by anointing them with holy Oils, and performing feveral Prayers over them. Sec Unction and Sacrament.
This Sacrament is not only in Ufe in the Latin, but alfo in the Greek Church, and throughout the Eaft, tho' under another Name, and with fome Difference- in the Circumflances ; in that the Orientals don't wait till their Sick are come to Extremity, in Order to anoint them : But the Sick generally go to Church themfelves ; and it is adminifter'd to them as often as they are indifpofed. The Greeks taking that Direction of St. James, C. V. ver. 14. which is the Foundation of the Practice, in a general Senfe : Is any Sick among you ? let him call for the Elders of the Church, and let them J>my over him, anointing him with Oil.
Fa. Ulandini distinguishes two Kinds of UnBion among the Maronites: The one cali'd, UnBion with the Oil of the Lamp 5 but this, he fuggefts, is not the facramcntal UnBion, ordinarily adminifter'd to fuch as are in ex- treme SickneSs, for that the Oil is only Confectated by a Simple Prieft, and that it is given to all who are prefenr, not to the lick only, but alfo to the healthy, and even to the Prieft himielf who officiates. The other Kind of UnBion, according to that Father, is only for the Sick ; it is perform'd with Oil Confecrated by the Biihop alone, on Holy fhurfday. And this, it feems, is their facramental UnBion.
But that UnBion with Lamp Oil, is in USe not only among the Maronites, bur throughout all the Eaftern Church, who ufe it very religiously. The Truth is, they don't fcem to have any other Sacrament of Extreme UnBion befide this.
Fa. Goar obferves, that tho' it be only a Ceremony, with regard to thofe in Health, it is a real Sacrament to thole that are Sick.
In their great Churches they have a Lamp, wherein this Oil for the Sick is preferved : This Lamp they call, Kap/iiAa tb svysKtut, that is, the Lamp of Oil join'd with Prayer ; For what the Latins call Extreme UnBion, the Greeks call, iM^Kcuoy, or aj«p sao/op, that is, Oil with Prayer, or Holy Oil.
'Tis call'd Extreme UnBion, as being only given to Perfons in Extremity. — In the XHIrfi Century, it was call'd the UnBion of the Sick, and not Extreme UnBion. For in the earlier Ages, it was given before the Viaticum. Which Practice, according to Fa. Mabillon, was not changed till the X1U th Century. See Viaticum.
The Reafons he affigns for the Change arc, that in that Ase there arofe divers miftaken Opinions, feveral of which wlfind mention'd aid condemn'd in the Englijh Coun- cils. Among t> reft, 'twas held, that fuch as had received this Sacrament, in cafe they recover d, might not ufe the Rites of Marriage, nor eat Meat, nor go bare-footed: Whence, they chofe to forbear ufing it till the laft Extremity, which Practice prevail d. See the Councils of mrcepr and Exeter, in the Year 1287 5 that
