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the roots of elecampane, gentian, black hellebore, of the leaves of rue and favine, 2. Extract of liquorice. 3. Of logwood. 4. Of peruvian bark, both foft and hard. Of lignum vitæ, both foft and hard. 6. Of jalap. And, 7. The cathartic extract which is prepared from proof spirit poured upon a proper quantity of fuccotrine aloes, the pith of coloquintida, fcammony, and the leffer cardamom-feeds husked. The thebaic extract confifts only of opium diffolved in water, ftrained and evaporated to a confiftence. Let it be remarked, that all watery extracts fhould be moistened or fprinkled with a little spirit of wine, to prevent their growing mouldy. EXTRACT, in matters of literature, is fomething copied or collected from a book or paper.

EXTRACTS of writings or records, are notes upon them. See ESTREAT. EXTRACTA CURIE, are the iffues or profits of holding a court arifing from the customary dues, fees and amercements. EXTRACTION, in chemistry and pharmacy, the operation by which effences, tinctures, &c. are drawn from natural bodies. See the article EXTRACT. EXTRACTION, in furgery, is the drawing any foreign matter out of the body by the hand, or by the help of inftruments. In extracting arrows and fuch like bearded weapons ufed by barbarous nations, the whole bufinefs confifts in drawing out the head, fo as that its protuberant beards or hooks may not wound and lacerate the contiguous parts. If it appears to be lodged but fuperficially under the integuments, it will be beft to draw it out the fame way it entered, provided the wound be firft fufficiently dilated by incifion, in order to prevent the laceration of the adjacent parts: otherwise it must be thrust forwards, and drawn out in the direction of its point in the oppofite fide, if poffible, an incifion being first made to meet it. This laft method is moft eligible, when the weapon has defcended very deep; fo that there is much lefs fpace for it to pafs onward, than to be drawn back again; and also when it has paffed beyond any large bloody-veffels or nerves, fo that it would induce a laceration of them to draw it back,

In extracting foreign bodies from the ear, you must first be informed by the account of the patient, and by fearching with a probe, of what nature the offending body is; and if it happen to be a lump of dried indurated wax, it will be proper VOL. II.

to inject fome warm milk, or oil of olives or almonds, ordering the patient to hold his head inclined on the contrary fide while you use the fyringe. If a small calculus, &c. be lodged in it, you must first of all relax and mollify the paffages of the ear, and then carefully extract the body with a probe or pliers. But if the foreign body fhould happen to be a peat bean, or other grain, which is too much fwelled by the humours to be discharged intire by the probe, er other inftrument, you must break it with pliers, or cut it with fmall fciffars, and extract it bit by bit. Sometimes an infect gets into the ear, and by struggling to get loose fro a the glutinous ear-wax, excites an int lerable pruritus and tickling, which in time turns to acute pain. When the infect can be perceived, it may be drawn out by a probe, &c. but if that fails, you must inject warm oil, of fpirit of wine, which will quickly kill the infect, and then you may wash it out with the fame or fome other liquor, and afterwards cleanse the cavity of the ear with a bit of cotton or lint upon the end of your probe. To extract bodies fallen into the eyes, the firft and moft eafy method is by agitating and extending the eye lids with one's fingers, holding the head down at the fame time, by which means the increafed flux of tears excited by the vellicating body, very often washes it out of the eye without much difficulty. But if this method does not fucceed, the next remedy is to blow fome levigated pearl or crab claws through a quill under the eyelid, that as thefe are washed out by tears, they may also take the foreign body with them, otherwife the furgeon must take the fmall round head of a flender probe, or the end of a tooth-pick, and extending the eye lids gently from the eye, carefully extract the offending body. Lime or any acrid falt may be washed from the eyes by a pencil bruth of foft feathers, or a bit of fine fponge foftened in a quill, dipped in warm water.

The method of extracting fmall bones of fish, needles, pins, &c. fticking in the fauces or gula, is as follows. When the offending body cannot be removed by taking a large draught of fome liquor, or fwallowing a large mouthful of bread, &c. recourse must be had to fome inftrument. The tongue is firft to be depressed with a fpatula, in order to obferve whether the obstacle can be feen; and if it appears near the upper part of the oefor 7 M phagus,

phagus, it should be cautiously extracted with a pair of pliers, or fome fuch inftrument. But if it is lodged deep in the oefophagus, the furgeon may then give the patient a piece of sponge to swallow, that has first been dipt in oil, and well faftened to a strong cord, by which it is to be pulled up again, after it has been fwallowed by the patient as far as it will go; by which means the body sticking in the oefophagus, will be either forced down into the stomach, or elfe drawn up into the mouth.

For the extraction of bullets, &c. from wounds. See GUN-SHOT WOUNDS. EXTRACTION, in genealogy, implies the ftock or family from which a person is defcended.

EXTRACTION of roots, in algebra and arithmetic, the method of finding the root of any power or number.

See the

articles, Roor, SQUARE, CUBE, &c. The reader will perceive by the articles involution and power, that the extraction of roots, or the refolving of powers into their roots, is the reverse of involution, and consequently that the roots of fingle quantities are easily extracted by dividing their exponents by the number that denominates the root required; for the powers of any root are found by multiplying its exponent by the index that denominates the power; and therefore, when any power is given, the root must be found by dividing the exponent of the given power by the number that denominates the kind of root that is required. Thus the fquare root of a is • &=a*; and the square root of a + b c2, is a2 b+c. The cube root of a 6 b 3, is ab3a2b; and the cube root of x y z12, is x3 y2 24. It will also appear from what we fhall fay of involu tion, that any power that has a pofitive fign, may have either a pofitive or negative root, if the root is denominated by an even number. Thus the fquare root of a may be + a ora, because +axta or -axa gives + a2 for the product. But if a power have a negative fign, no root of it denominated by an even number can be affigned, fince there is no quantity that multiplied into itself an even number of times can give a negative product. Thus the fquare root of a cannot be affigned, and is what we call an impoffible or imaginary quantity. See the article Rooт.

2

But if the root to be extracted is denominated by an odd number, then shall

12

the fign of the root be the fame as the fign of the given number whole root is required. Thus the cube root of➡s 3 is -a, and the cube root of-ab3, is -ab. If the number that denomi nates the root required is a divifor of the exponent of the given power, then fall the root be only a lower power of the fame quantity. As the cube root of a12 is a 4, the number 3 that denominates the cube root being a divifor of 12. Butt the number that denominates what t of root is required is not a divifor of the exponent of the given power, then the root required fhall have a fraction for its exponent: thus the fquare root of a1s a 2, the cube root of a 5 is a, and the fquare root of a itself is a. Thele powers that have fractional exponents, a called imperfect powers or furds, and are multiplied and divided, involved and evolved, after the fame manner as per powers. Thus the fquare of is a3; and the cube of a} is a3*5

fect

a2 x 3

a. The fquare root of a is a = a; and the cube root of a is a!. See the article SURD.

The fquare root of any compound quantity, as a 2+2 a b+b2, is discovered atter this manner. First take care to di.pofe the terms according to the dimen fions of the alphabet, as in divifion; then find the fquare root of the first term a 4, which gives a for the first member of the root. Then fubtract the fquare from the propofed quantity, and divide the fir term of the remainder 2 ab+b2, by the double of that member, viz. 2 a, and the quotient is the fecond member of the root. Add this fecond member to the double of the first, and multiply their fum 2 a+b by the fecond member b, and fubtract the product 2 a b + b2 from the forefaid remainder 2ab+b2, and if nothing remains, then the fquare root is obtained. The manner of the operation is thus: a2+2ab+b2

a 2

2a+b,zab+b2 xb/2ab+b2

0. 0.

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But if there had been a remainder, you must have divided it by the double of the fum of the two parts already found, the quotient would have given the thad member of the root. Thus if the qua tity propofed had been a2+2ab+

root; annex the quotient to that double, and multiply the number thence arifing by the faid quotient; and if the product is lefs than your dividend, or equal to it, that quotient fhall be the fecond figure of But if the product is greater

+ b2+2bc+c2, after proceeding as above you would have found the remainder 2 ac+2bcte 2, which divided by za+2b, gives e to be annexed to a+b, as the third member of the root. Then adding to 2a + 2b, and multiplying their fun 2 at 2 b+c by c, fubtract the produk zac+2bctc from the forefaid remainder; and fince nothing now remains, you conclude that a+b+c is the fquare root required. The operation is thus:

2

a2+2ab+2ac+b2+2bc+c" (a+b+c

a 2

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But if it is a number above 100, then its fquare root will confift of two or more figures, which will be found by different operations by the following rule. Place a point above the number that is in the place of units; pafs the place of tens, and place again a point over that of hundreds; and go on towards the left hand, placing a point over every fecond figure, and by thefe points the number will be diftinguished into as many parts as there are figures in the root. Then find the fquare root of the first part, and i will give the firft figure of the root, fubtract its square from that part, and annex the second part of the given number to the remainder. Then divide this new number (neglecting its laft figure) by the double of the first figure of the

the root.

9,

than the dividend, you must take a lefs number for the fecond figure of the root than that number. Much after the fame manner may the other figures of the quotient be found, if there are more points than two placed over the given number. To find the fquare root of 99856, I first point it thus, 99856, then I find the Square root of which therefore 9 to be 3, is the first figure of the root. I fubtract 9 the fquare of and to the refrom 3 mainder I annex the fecond part 98, and I divide (neglecting the laft figure 8) by the double of 3 or 6, and 1 place the quotient after 6, and then multiply 61 by I, and fubtract the product 61 from 98. Then to the remainder 37, I annex the last part of the proposed number (56) and by dividing 3756 (neglecting the Jaft figure 6) by the double of 31, that is by 62, I place the quotient after, and multiplying 626 by the quotient 6, I find the product to be 3756, which fubtracted from the dividend, and leaving no re. mainder, the exact root must be 316.

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raifing a+b to the fifth power and fabtracting it, there being no remainder, I conclude that a + b is the root required. If the root has three members, the third is found after the fame manner from the first two confidered as one member, as the second member was found from the firit, which may easily be underflood from what was faid of extracting the íquart

In general, to extract any reot out of any given quantity: first range that quantity according to the dimentions of its letters, and extract the faid root out of the first term, and that shall be the first member of the root required. Then raise this root to a dimenfion lower by unit than the number that denominates the root required and multiply the power that arises by that number itself; divide the second term of the given quantity by the product, and the quotient fhall give the fecond member of the root required. Thus to extract the root of the fifth power out of 5+ 5a4b+10a3 b2 + 10 a 2 b3 + 5 a b+ + b3, I find that the root of the fifth power out of a3, gives a ; which I raise to the fourth power, and multiplying by 5, the product is 5 a; then dividing the second term of the given quantity 5 a 4 b by 5 a 4, I find b to be the fecond member; and

2

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of a3 + x3 will be found to be at ICX12 243a11+ &c.

gast

5x9

81 aǎ

x3

3a2

The reader will find a general theorem for extracting the root of any binomial under the article BINOMIAL.

The roots of numbers are to be extracted as thofe of algebraic quantities. Place a point over the units, and then place points over every third, fourth, or fifth figure towards the left hand, according as it is the root of the cube, of the fourth or fifth power that is required; and if there be any decimals annexed to the number, point them after the fame manner, proceeding from the place of units towards the right hand. By this means the number will be divided into fo

8a4

64a, &c. St.

many periods, as there are figures in the root required. Then enquire which is the greateft cube, biquadrate, or fifth power in the first period, and the root of that power will give the first figure of the root required. Subtract the greateft cube, biquadrate, or fifth power from the fir period, and to the remainder annex the first figure of your fecond period, which fhall give your dividend. Raife the firft figure already found to a power lefs by unit than the power whofe foot is fought, that is, to the fecond, third, or fourth power, according as it is the cube root, the root of the fourth, or the root of the fifth power that is required, and multiply that power by the index of the cube, fourth or fifth power, and divide the divi dend by this product, and the quotient will be the fecond figure of the root re quired. Rait

Raife the part already found of the root, o the power whofe root is required, and if that power be found lefs than the two irt periods of the given number, the econd figure of the root is right; but if t be found greater, you must diminish he, fecond figure of the root, till that Dower be found equal to or less than those Subtract eriods of the given number.

t, and to the remainder annex the next eriod, and proceed till you have gone hrough the whole given number; findng the third figure by means of the two irst, as you found the fecond by the first, nd, afterwards finding the fourth figure if there be a fourth period) after the ame manner from the three first.

Thus to find the. cube root of 13824,

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oint it 13824 find the greatest cube in 5, viz. 8, whose cube root 2 is the first igure of the root required. Subtract 8 rom 13, and to the remainder 3 annex 8, he first figure of the second period; diide 58 by triple the fquare of 2, viz. 2, and the quotient is 4, which is the econd figure of the root required, fince he cube of 24 gives 13824, the number propofed.

Operation.

13824(24

8=2X2X2

3X4=12)<8(4

Subtra& 24X24×2413824

Rem.

After the fame manner the cube root of 3312053, is found to be 237.

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n extracting of roots, after you have one through the number proposed, if here is a remainder, you may continue ce operation by adding periods of cyhers to that remainder, and find the ue root in decimals to any degree of actness required.

or the method of extracting the root of by affected equation. See, the article uadratic EQUATION, &c. TRACTOR, in midwifery, an inftru

ment, or forceps, for extracting children by the head. See DELIVERY. EXTRAORDINARII, in roman antiquity, a body of forces confifting of a third part of the horse and a fifth part of the foot, which was feparated from the reft, with great policy and caution, to prevent any defign that they might poffibly entertain against the natural forces. A felect body of foldiers, chofen from the extraordinarii, were those calamong led ablecti. See the article ABLECTI, EXTRAVAGANTES, those decretal epiftles, which were published after the clementines.

They were fo called because, at first, they were not digefted, or ranged, with the other papal conftitutions, but seemed to be, as it were, detached from the canon law. They continued to be called by, the fame name when they were afterwards inferted in the body of the canon law. The firft extravagantes are thofe of John XXII. fucceffor of Clement V. the last collection was brought down to the year 1483, and was called the common extravagantes, notwithstanding that they were likewife incorporated with the reft of the canon law. See the article DECRETAL. EXTRAVASATION, in contufions, fiffures, depreffions, fractures, and other accidents of the cranium, is when one or more of the blood-veffels that are diftributed on the dura mater, is broke or divided, whereby there is such a difcharge of blood as greatly oppreffes the brain, and disturbs its offices; frequently bringing on violent pains, and other mifchiefs; and at length, death itself, unless the patient is timely relieved. See the articles CONTUSION, FISSURE, and FRACTURE.

If the extravafated quantity of blood be ever so small, it will certainly corrupt, and affect the meninges, and the brain itself, with the fame disorder: from hence will proceed violent inflammations, deliriums, ulcers, &c. and even death itself, fooner or later. And this will frequently be the cafe, after a violent blow upon the cranium, though the bone should escape without any injury. In this cafe the blood is fpilt either between the cranium, and dura mater, or between the dura mater and pia mater, or between the pia mater and the brain, or laftly, between the finules of the brain. Each of these cafes are attended with great danger, but the deeper the extravasation happens,

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