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ANALYTIC, Analytical, Something that belongs to, or partakes of the Nature of Analyfis. See Analysis.
Thus, we fay, an Analytical Demonstration ; Analytical Enquiry ; Analytical Table, or Scheme 5 Analytic Method, &fe. See Method.
The Analytic Method fiands oppofed to the Synthetic— % As in Mathematicks, fays Sir I. Newton, fo in Natural ' Philorophy, the Invclligation of difficult Things by the ' Analytic Method, ought to precede the Method of Com-
- pofition. This Analysis confifls in making Experiments,
- and Obfervations, and in drawing general Conclusions
' therefrom by Induaion, and admitting of no Objections ' againfl the Conclusions, but fuch as are drawn from Expe- ' riments and other certain Truths. And tho the arguing ' from Experiments and Obfervations by Induction, be no ' Demonstration of general Conclusions ; yet it is the bell ' way of arguing which the Nature of the Things admits of; ' and may be eileem'd fo much the Stronger, as the Induc- ' tion is more general. And if no Exception occur from ' Phenomena, the Conclusion may be pronounced generally. ' By this way of Analyfis, we may proceed from Compounds
- to Ingredienrs ; and from Motions to the Forces producing
' them ; and in general, from Efftas to their Caufcs, and ' from particular Caufes to more general ones, till the Argu-
' ment end in the moll general. This is the Analytic
' Method.
' The Synthetic confifls in aSSuming the Caufes difcovered, 1 and eftab'liShed as Principles ; and by them explaining the ' Phtenomena proceeding from them, and proving the Ex- ' planations.' See Synthesis.
ANALYTICS, Analytica, the Doarine, and Ufe of Analyfes. See Analysis.
The great Advantage of the prefent Mathematicks above the antient, is chiefly in Point of Aualyticks.
The Authors on the antient Anatyticks, are enumerated by 'Pappus, in the Preface to his 7th Book of Mathematical Colkaions ; being, Euclid, in his Data, and 'Porifmata ; Apollonius, dc ScBione Rationis ; Apollonius, in his Conicks, Inclinations, and Tailions ; Arifttsus, dc Zocis Solidis, and Eratofihenes, de mediis proportionalibus. But the antient Anatyticks were very different from the modern.
To the modern Anatyticks, principally, belong Algebra ; the Hirtory of which, with the feveral Authors thereon, fee under the Article Algebra.
The chief Writers upon the Analyfis of Infinites, are its Inventors, Sir Jfaac Ne-Mon, in his Analyfis per gHiantita- tum Series, Fluxiones iy Differentia*, cum cnumeratione Limanim 3" ordinis ; and de Quadratttra Curvarnm : and M. Leibnitz, in AS. Eruditor. An. 1684 : The Marquis dc I'Hopital, in his Analyfe des Infiniment fetites, iSoS : Carre, in his Methods "pour la mefitre des Surfaces, la di- menfion des Solides, &c. par C application dtt calcul integral, 1700 : G. Manfredius, in a poflhumous Piece, de Conjlruc- tione Equationum differentiiatium primi gradus, 1707 : Nicb. Mercator, in Lcgitrithmotechnia, 166$; Cheyne, in Metbodo Fiuxionum inverfa, 1703 ; Craig, in Metbodo figu- rarttm lineis reSis C? curvis comprebenfarum Qiiadraturas dclcrminandi, i«8> ; and de Quadraturis figurarmn curvi- linearwn t£ has, &c. 1S93 : Dav. Gregory, in Exercita- tione Geometrica de dimenficne figurarum, 1684; and Niu- entiit, in Confiderationibus circa Analyfeos ad quantitates
infinite parvas applicatc?, principia, 1605. The Sum of
what, is found in I'Hopital, Carre, Cheyne, Gregory, and Craig ; is colleaed into one Volume, and very well explain'd by C. Hayes, under the Title of, A Treatife of Fluxions, ckc. 1704.
Analytick, in Logick, is a Part of that Science, teach- ing to decline and conllrue Reafon, as Grammar doth Words.
ANAMORPHOSIS, in Perfpeaive and Painting, a mm- flrous \Proje£Iion ; or a Representation of fome Image, ei- ther on a plane or curve Surface, deformed ; which at a cer- tain distance Shall appear regular, and in proportion. See Projection.
The Word is Greek ; compounded of ctvz, and f-fo^aovs, formatio, of y.o^n, form.
To make an Anamorpbofis, or monStrous Projeaion on a
Plane. Draw the Square ABCD, (Tab. 'Perfpe3tve,
Fig. 18.) of a bignefs at pleafure, and Subdivide it into a Number of Areolas, or letter Squares. — In this Square, or Reticle, called the Craticular Prototype, let the Image to be diflorted be drawn. — Then draw the Line tf£ = AB; and divide it into the lame Number of equal Parts, as the Side of the Prototype A B ; and in E, the middle thereof, erect the Perpendicular E V, fo much the longer ; and draw VS perpendicular to E V, fo much the Shorter, as the Image is defir'd to be diflorted. From each Point of Divi- sion 'dra* right Lines to V, and join the Points a and S; as alfo the right Line a S. Thro' the Points defg, draw Lines parallel to ji; then will abed be the Space that the Monftrous Projeflion is to bo delineated in ; called the Cratieiilar Etlyfe,
Laflly, in every Areola, or fmall Trapezium of the Space abed, dtaw what appears delineated in the correfpondent Areola of the Square ABCD: by this means you will ob- tain a deformed Image, which yet will appear in juSt P ra . portion to an Eye diftant from it the length F V, and rai- led above its height, VS. See Designing.
It will be diverting to manage it fo, that the deformed Image do not repreScnt a mere Chaos ; but fome other Image : Thus, we have feen a River with Soldiers, Wag. gons, £5?c. marching along the fide of it ; fo drawn, that when viewed by an Eye in the Point S, it appears to be the fa- tyrical Face of a Man.
An Image alio may be diflorted mechanically, by perfo- rating it here and there with a Needle, and pbcing it a - gainft a Candle, or Lamp ; and obferving where the Fay s which pafs thro' thefe little Holes fall on a plane, u -<. ve Superficies; for they will give the correfpondent f
the Image deformed : by means whereof the Deformation may be compleated.
to drain the Anamorphosis, or Deformation of an Image upon the convex Surface of a Cone.
It is manifeft from the former Cafe, that all here requi- red, is to make a Craticular Ecrype on the Superficies of the Cone, which Shall appear to an Eye duly placed over its Vertex, equal to the Craticular Prototype.
Let the Bale ABCD, therefore, of the Cone, (Fig. 19.) be divided by Diametets into any Number of equal Parts, that is, the Periphery thereof: And let fome one Radius be likewife divided into equal Parts, and thro' each Point of Division draw concentrick Circles : thus will the Craticular Prototype be made.— — -With double the Dia- meter AB, as a Radius, defcribe the Quadrant EFG, (Fig. 20.) fo as the Arch EG be equal to the whole Pe- riphery : then this Quadrant folded duly up, will form the Superficies of a Cone, whofe Bafe is the Circle ABCD. — Divide the Arch AB into the fame Number of equal Parts as the Craticular Prototype is divided into, and draw Radii from each of the Points of Divifion. Produce GB to I, fo that FI = FG, and from the Centre I, with the Radius I F, draw the Quadrant F K H, and from I to E draw the right Line IE. Divide the Arch KF into the fame Number of equal Parts, as the Radius of the Craticu- lar Prototype is divided into; and draw Radii thro' each of the Points of Division, from the Centre I meeting E F, in 1, 2, 3, %$c. Laflly, from the Centre F, with the Radii, F 1, E2, F3, tic. defcribe the concentrick Arches. — Thus will the Craticular Eaype be form'd, each Areola whereof will appear equal to other.
Hence, what is delineated in every Areola of the Crati- cular Prototype ; being transferred into the Areolas of the Craticular Eaype: the Image will be diflorted or deformed: yet an Eye being duly raifed over the Vertex of the Cone, will perceive it in jufl proportion.
If the Chords of the Quadrants be drawn in the Craticu- lar Prototype, and Chords of their fourth Part in the Crati- cular Eaype, all things elfe remaining the fame ; you will have the Craticular Eaype on a quadrangular Pyramid.
And hence it will be eafy to deform any Image, in any other Pyramid, whofe Bafe is any regular Polygon.
Becaufe the Eye will be more deceived, if from contiguous Objeas it cannot judge of the distance of the P^rts of the deformed Image ; therefore, thefe kinds of deformed Images are to be view'd thro' a fmall Hole.
ANANAS, in Natural Hiflory, by fome called Nanas, by others Jayama, and by us popularly the 'Pine-Apple on account of the refemblance it bears to the Cones of Pines or Firs ; is a fine Indian Fruit, which grows on a Plant like the Fig-tree, and of the Size of an Artichoke.
The Fruit is adorned on the Top with a little Crown, and a bunch of red Leaves refembling Fire. The Flefh. is fi- brous, but diflblves in the Mouth ; having the delicious Tafte of the Peach, the Quince, and the Miifcadine Grape, all together. — M. du 1"ertre defcribes three Kinds of Ana- nas. They make a Wine from the Juice, which is almoft equal to Malmfey Sack, and will intoxicate as foon.
It is good to Strengthen the Heart and Nerves, againfl naufeating, to refrefh. the Spirits, and excites Urine power- fully; but is apt to occafion Abortion in Women. — They make a Confection of the Ananas on the Spot, which they bring hither whole ; and is found of good Service to reftore a decay'd, or aged Conftitution.
The Anana, or Wejl-India Pine-Apple, is generally al- low'd, both for its rich and delicious Flavour, and its beau- tiful Colour, for the King of Fruits. Great Endeavouts
have of late been ufed to cultivate the Plant in Europe ; in which they have Succeeded, zvi there are now produced de- licious Fruits of this kind, in fome of the fine Gardens in England.— They are ufually about the Size of a Tennis-Bail.
ANAPEST, Anapestos, a Foot in the Greek and Latia Poetry, confining of two Short, and one long Syllable. See Foot.
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