Page:Cyclopaedia, Chambers - Supplement, Volume 1.djvu/148

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Wiies fevcral others that occur in Apollonius Pergaws, and Pappus Alexandrinus. Staid. Hift. Philof. P. 5- P- 26 3- The order of the Sjnthtfts is contrary to that of the Analyfis, one beginning where the other ends. The two methods cannot always be ufcd indifferently ; the Analyfis is molt pro- per for the difcovery of truth, and fynthefis for teaching and explaining it in a fyftcmatical way. Hence fome call Analyfis the method of invention.

Analysis may be divided into antient and modern, or new and old.

The modern Analyfis Is what is often called Algebra ; but they ought to be diftinguifhed, Algebra being only a part of the analytic art.

The moderns are at fome lofs concerning the antient Analyfis, i. e. concerning the art or method whereby the antients re- folved problems and invented theorems. Some traces of their method are extant in Pappus », Apollonius b, and Euclid = ; and Dr. Hook fufpeds, that their Analyfis went backwards thro' almoft all the fame fteps, by which their demoftrations went forwards'— [• Prsef. ad L. 7. Vid. Fabric. Bibl. Grace. 1. 5. c. 22. * De Seflione Rationis. V. Mem. de Trev. an. 1706. p. 702. 'Elan. 1. 13. Vid. Stanl. Hift. Philof. P. 5. p. 263. d Pofthum. Work. p. 68.]

That this might often be the cafe, feems evident to any one •who has (ludied Euclid with care. They have indeed left us no precepts of their art. This, like almo'ft all others, muft be acquired by imitation of the excellent examples left us by the Greeks. But may we not fay alfo, that the moderns have given lis no precepts of their art, and that it cannot be acquired other- wife than by imitation ? The precepts of invention we meet with in algebraical writers are very general and vague; and the principal point,the invention of the diagram, by which a pro- blem is to be folved, or a propofition demonftrated, is com- monly left untouched ; fo that, altho' we have very good obfervations in Newton's algebra and in fome others, yet all thefe go hut a little way towards the art of invention, which is a habit to be acquired in modern analytics, as well as in 'antient, by imitation and ufc, and not by precept. Men of genius among the moderns, who have itudied the works of ■the antient geometers, have been thereby enabled to imitate them, and penetrate into their methods : the works of Hug- gens and Newton, and of late, the treatife of conic fecfions by Mr. Simfon, profeffor of mathematics in the univerfity of Glafgow ; as alfo fevcral parts of Mr. MacLaurin's treatife -of fluxions, are evident proofs of this. We have an attempt to reduce the geometrical Analyfis to an art, "by Hugo de Omeriquc, a Spaniard. This work has been ap- plauded by good judges; fho' fome modern analyfts pretend, that he has done nothing but what may be performed much more eafily by algebra.

Weigelius has endeavoured to retrieve the antient Analyfis of Ariftotle, from Euclid, and other antient geometricians. Vid. XVeigel. Analyfis Ariftotelica ex Euclide rcftituta.

Analysis is divided by fome authors into fimple and com- pound.

Simple Analysis it that employed 'in folvrng problems redu- cible to fimple equations. Reynatt, Anal. Demonftr. Praf. p. 4.

Compound, or Complex Analysis, that which gives the ex- preffions or folutions of problems in compounded equations. -Analysis of Powers denotes the refolving them into their roots. V. Jones Synopf. Palmar. Mathef. p. 51. In this fenfe Analyfis amounts to the fame with what we other- wife call evolution. See Evolution, Cycl. We find divers other kinds of Analyfis treated of by mafhe- 'matical writers, as the Analyfis of indivifibles, &c e. M. Leibnitz fpoke of an Analyfis ftius, different from the Analyfis of magnitudes'.—^ Aft. Erud. Lipf. an. 1686. p. 292. ' V. Wolf. Elem. Anal. inPrarf.

The Analyfis of' geometrical curves fhews their properties and internal conftitution, their curvature, points of inflexion, fta- 'tion, retrogradation, variation, &c. — In this Analyfis, curves are ufually confidered as polygons compofed of an infinite number of infinitely little fides ; but this fuppofition is neither accu- rate nor neceffarv, tho' it fometimes affords convenient hints for invention. V. MacLauyinh Fluxions paflim. F. Reynau of the oratory has given a large fyftem of alge- bra under the title of Analyfis s. F. Cartel cenfures it as not fufficiently methodical or fyftematical h. The great divifions and members are drowned in the multitude of particular rules and methods. — [ s Analyfe Demontree. P. 1708. 4°. 2 Vol. V. Mem. de Trev. 1708. p. 1493- feqq- h Cajtel Mathem. Univ. p. 666.]

Analysis, in chemiftry — The Analyfs of metals andmetallic minerals confrfts in what they call the mercurification of them : The Analyfs of other bodies is performed by diftillation, lixi- viation, &c. V. Mem. Acad. Scienc. art. 1702. p. 46. The order of matters which arife in analyfing vegetable and animal bodies is different, according as thofe bodies have been fermented or not ; if they have, the fpirits and volatile falts ' arife firlr, then aqueous liquors, then foetid oil, after which a caput mortuum, which by calcination and lixiviation, is re- duced to a fixed fait and infipid earth, in bodies unfermented, the aqueous parts rife firft, afterwards the reft fuccecd in the fame order as above.

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The zeai for cmalizing plants and other matters belonging tb the materia medica, in order to a more precife difcovery of their internal qualities, is much abated of late years, as having been proved in great meafure ufelefs. The Analyfs gives the chief principles feparately ; from the qualities of which no conclufion can be drawn concerning the plant Hfelf, wherein thefe principles are united. Befides that, the fire alters the ftruclure of much the greater part of plants'. Fourteen hundred plants underwent this examination in the royal aca- demy of fciences at Paris ; from all of which, however dif- ferent in virtues, the fame matters were procured. The decompofition feems to reduce all to the fame fluff. Plants in this ftate may be confidered like houfes in ruins ; whatever different forms or difpofitions they had before, the rubbifh is much the fame in all. M. Lemery fuggefts a new fort of Analyfts. According to this author, to learn the nature of a mixt, we are not to analyfe it exactly, but only bring it down one pitch lower, refolve it not into its principles, but into other mixts a degree Ampler than the former j the chief of which are'faline and fulphureous or fatty parts k. — [* Jour, des Scav. T. 68. p. 16. k V. Hilt. Acad. Scienc. an 1719.P. 63. Mem. ibid. p. 227.

Mr. Hales has given an attempt towards analyfing the air by chymico-ftatical experiments, which fhew in how great pro- portion air is wrought into the compofition of animal, ve- getable, and mineral bodies. Hales, Veget. Stat, in fine. But it may be obferved, the ingenious author here ufes the word in a fenfe fomewhat different from what a reader at firft fight would imagine. The tendency of this author's experi- ments is not to makewhatwe cv\\ an Analyfs of the air, to fhew its ingredients and principles, but to feparate or difingage it from the bodies it happens to be mixed with, or inclofed in. — ■ So that analyfing in his fenfe amounts to the fame with what we ordinarily call extricating. See Air.

ANALYST, a perfon who analyzes a thing, or makes ufe of the analytical method. See Analysis, and Analytic. Cycl. and Suppl.

Some reftrain the word more peculiarly to denote a mathema- tician, who makes great ufe of the algebraic method or calculus in geometry, inexclufion of the fynthetic or Uriel geometrical method.

In which fenfe Analyfl amounts to much the fame with Com- putijl or Calculator.

In a Ccn^e not unlike this, a late ingenious writer gives the title Analyjl to a book againft the modern geometry, or doctrine of fluxions. See Fluxion, Cycl. and Suppl.

ANALYTIC Chemiftry, the art of analyfing vegetable, animal, and mineral fubftances,' and refolving them into their differ- ent parts or principles. The whole of chemiftry may be com- prehended under the art of refolving bodies into their princi- ples, and of compofing new compounds from thefe principles, this laft part of it is called fynthetic Chemiftry. Sbaw y % Lectures, p. 145.

ANALYTICS, {Cycl.) in literaryhiftory, is particularly ufcd to denote certain writings of Ariifotle under this title. Ariftotle's Analytics confift of four books, two under the de- nomination of former, Avzav\\xw wgokgiw, and as many under that of latter, wrt%m. — They belong to the clafs of his acroa- matic works. Galen fuggefts, that the antient and genuine title of the two former books, was vt^i evKKoyiapa, concerning fyllogifm, which is confirmed by Boethius : The title of the two latter, according to the fame Galen, was tti^i awAi^s . on demonftration. Petit maintains, that the Analytics, men- tioned by Ariftotle to Nicomachus, were different from thofe now extant. In effect, Laertius fpeaks of eight, or according to other copies, of nine or ten books of the former Ana- lytics, befides two of the latter. Add, that Ammonius aflures us, that in the time of Ptolemy Philadelphus* there were no lefs than forty books of Ariftofle's Analytics in the Alexan- drian library^

Proclus cenfures Ariftotle's Analytics^ for being too plain and intelligible to every body : Ramus* perhaps with more jufHee, frequently complains of their being obfeure and incomprehen- fible.

However it muft be owned, that Ariftotle in this work has fhewn, that he thoroughly underftood reafoning and demon- ftration ; a compliment which cannot with juiHce be paid to many modern writers on the human uuderfianding and logic* We have various commentators on Ariftotle's Analytics ; for which we refer to Fabric. Bibl. Grac. \. 3. c. 6.

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ANAMNESEISj Ava^^uv, in antient writers, denote enco- niums of perfons who had behaved well in war or elfcwhere, rehearfed before the emperors of Conftantinople* to put them in mind of bellowing fuitable rewards. Meurs. Glofs. Graec. Barbar. in voc.

AKAMNE CSj in medicine, are ufed by fome writers to denote thofe figns which help to difcover the paft ftate of a patient's body. Thefe are otberwife called Rertumoratives. Cajl. Lex. in voc

Anamnestic t3 alfo applied by Blancard to remedies pro- per for reftoring or ftrengtheningthe memory. Such according to this author are all fpirituous things. Vid. Blancard, Lex. in. voc,

ANANAS.