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Chambers, Ephraim, 1680 (ca.)-1740 / Cyclopædia, or, An universal dictionary of arts and sciences : containing the definitions of the terms, and accounts of the things signify'd thereby, in the several arts, both liberal and mechanical, and the several sciences, human and divine : the figures, kinds, properties, productions, preparations, and uses, of things natural and artificial : the rise, progress, and state of things ecclesiastical, civil, military, and commercial : with the several systems, sects, opinions, &c : among philosophers, divines, mathematicians, physicians, antiquaries, criticks, &c : the whole intended as a course of antient and modern learning

Analecta - antimony,   pp. 83-109 PDF (20.2 MB)

Page 84

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ANALYTIC, AIAtYYTICAL, fomething that belongs to,
,r partakes of the Nature of Analy/is. See ANALYSIS.
Thus, we fay, an Analytical Demonflration; Analytical
inquiry; AnabDctical Table, or Scheme 5 Analytic Method,
fèc. See METH1IOD.
The Analytic Method flands oppofed to the Syntbetic.-
t As in Mathematicks, fays Sir 1. Newton, fo in Natural
Philofophy, the Inveiligation of difficult Things by the
A4alytic Method, ought to precede the Method of Coin-
'pofition. This Aalyfis confifis in making Experiments,
£ and Obfervations, and in drawing general Conclufions
' therefrom by Inducaion, and admitting of no Objeclions
againfl the Conclufions, but fuch as are drawn from Expe-
' rimnents and other certain Truths. And tho the arguing
' from Experiments and Obfervations by Indukleion, be no
Demonftration of general Conclufions; yet it is the bell
way of arguing which the Nature of the Things admits of;
and may be eileem'd fo much the fironger, as the Induc-
' tion is more general. And if no Exception occur from
' Phxnomena, the Conclufion may be pronounced generally.
' By this way of Aaalyfis, we may proceed from Compounds
' to Ingredients ; and from Motions to the Forces producing
' them; and in general, from Effeas to their Caufes, and
' from particular Caufes to more general ones, till the Argu-
ment end in the moil general.-This is the Analytic
' Method.
' The Synthetic confifis in afruming the Caufes discovered,
and eflablifhed as Principles; and by them explaining the
Phatnomena proceeding from them, and proving the Ex-
' planations.' See SYNYTHESIS.
ANALYTICS, ANALYTICA, the Doarine, and Ufe of
Analyfes. I See ANALYSIS.
The great Advantage of the prefent Mathematicks above
the antient, is chiefly in Point of Awalyticks.
The Authors on the antient Analyticks, are enumerated
by Pappus, in the Preface to his 7th Book of Mathematical
Colleaions; being, Euclid, in his Data, and Porifmata;
A~pollowius, de Scaiizne Rationzs; Aptolloifius, in his Conicks,
Inclinations, and 7adizons ; Arinf/us, dc Locis Solidis, and
Eratcfihenes, de wedlis proportionalibus. But the antient
Anzal3yticks were very different from the modern.
To the modern Analyticks, principally, belong Algebra;
the Hiflory of which, with the fevcral Authors thereon, fee
under the Article ALGEBRA.
The chief Writers upon the A4nalyfs of Infinites, are its
Inventors, Sir faac NTewton, in his Analyfis per 2tantita-
turm Series, Fluxiones L Difforentias, cum enurneratione
Linearum 3ii ordinis; and de Quadratura Curvarum: and
M. leibnitz, in AFI. Eruditor. An. 1684: The Marquis de
l'fopital, in his Analyfe des Infiniment petites, 1696:
Carre, in his Methode pour la zefure des Surfaces, la di-
wenf/on des Solides, &c. par I' application dii calcul integral,
17Co : G. Mlanfredius, in a pofihumous Piece, de Confi ruc-
tione Equationurn differentiali urn primi grades, 1707:
Nich. Mercator, in Lsgarithmotechmia, i668 5 Cbeyne, in
Alethodo f7mxionurn inveifa, 1 703; Craig, in Methodo figfi-
raruim lincis reals & curvis comprehenfafruvm  Qadraturas
d.terminaandi, i685 ; and de guadraturis figurarum curvi-
linearum U  locis, &C. i693 : Dav. Gregory, in Exercita-
tione Geometrica de dirneafione fgurartim, 1684 ; and Niu.
entiit, in Con.f/derationibus circa Analyfeos ad quantitates
infinitL parvas applicatoe, principia, I 69 5.--The Sum of
what is found in l'Hopital, Carre, LCheyne, Gregory, and
Craig ; is colleced into one Volume, and very well explain'd
by C. Hayes, under the Title of, A  1reatife of .Fluxions,
&t. 1704.
ANALYTICIx, in Logick, is a Part of that Science, teach-
ing to decline and confirue Reafon, as Grammar doth
ANAMORPHOSIS, in Perfpeaive and Painting, a mon-
ft ronus Projeftion ; or a Reprefentation of fome Image, ei-
ther on a plane or curve Surface, deformed ; which at a cer-
tain diflance fhall appear regular, and in proportion. See
The Word is Greek; compounded of area, and pofpo,
formatio, of tLo,,;, form.
To make an naamorphojfis, or monftrous Projcrtion on a
Plane. --Draw the Square A B C D, (Tab. Perfpetive,
Fig. i8.) of a bignefs at pleafure, and Subdivide it into a
Number of Areolas, or lefter Squares.-In this Square, or
Reticle, called the Crat'cular Prototype, let the Image to
be diflorted be drawn.-Then draw the Line a b ==AB ;
and divide it into the fame Number of equal Parts, as the
Side of the Prototype A B; and in E, the middle thereof,
cevtc the Perpendicular E V, fo much the longer; and
draw XI S perpendicular to E V, fo much the fhorter, as the
Inage is defir'd to be diflorted. From each Point of Divi-
fona draw right Lines to V, and join the Points a and 5;
,is alfo the right Line a S. Thro' the Points d efg, draw
Lines parallel to a D ; then will abed be the Space that
the Monfirous Projcedion is to be delineated in i called the
(,;Iaticalar EOtie.
Laflly, in every Areola, or fmall Trapezium of th
a bcd, draw what appears delineated in the correfil
Areola of the Square A B CD: by this means you
tain a deformed Image, which yet will appear in j
portion to an Eye diflant from it the length F V,
red above its height, VS. See DESIGNING.
It will be diverting to manage it fo, that the de
Image do not reprefent a mere Chaos; but fotn
Image: Thus, we have feen a River with Soldiers
gons, Qec. marching along the fide of it, fo drawn, thi
viewed by an Eye in the Point S, it appears to be
tyrical race or a ivian.
An Image alfo may be diftorted mechanicall
rating it here and there with a Needle, and p
gain" a Candle, or Lamp; and observing wher
which pafs thro' thefe little Holes fall on a plan
Superlicies; for they will give the correfponden
the Image deformed  by means whereof the I
may be compleated.
To draw the Anamorphofis, or fDeformation of an Imige
upon the convex Surface of a Cone.
It is manifefi from the former Cafe, that all here requi..
red, is to make a Craticular Ecype on the Superficies of
the Cone, which fhall appear to an Eye duly placed over
its Vertex, equal to the Craticular Prototype.
Let the Ba~e A B C D, therefore, of the Cone, (Fig. i9.)
be divided by Diameters 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 Divifion draw concentrick Circles: thus will the
Craticular Prototype be made. -With double the Dia-
meter AB, as a Radius, defcribe the Quadrant EFG,
(Fig. to.) 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 A B CD.-
Divide the Arch A B 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 GE
to 1, fo that F I = F G, 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 I E. Divide the Arch K F 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 Divifion, from the Centre I meeting E F, in
x, ±, 3, Cc. Lafily, from the Centre F, with the Radii,
F i, F Pt F3, Fc. defcribe the concentrick Arches.-Thus
will the Craticular E61ype 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 Ectype: the Image will be diflorted or deformed:
yet an Eye being duly raifed over the Vertex of the Cone,
will perceive it in jufi proportion.
If the Chords of the Quadrants be drawn in the Craticu-
lar Prototype, and Chords of their fourth Part in the Crati-
cular EcLype, all things elfe remaining the fame; you will
have the Craticular E&ype 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
Objects it cannot judge of the diflance of the Parts of the
deformed Image; therefore, thefe kinds of deformed Images
are to be view'd thro' a fmall Hole.
ANANAS, in Natural Hiffory, by fome called Nanas,
by others 7ayama, and by us popularly the Pine-,pple 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 Flelh is fi-
brous, but diffolves in the Mouth; having the delicious
Taile of the Peach, the Quince, and the Mufcadine Grape,
all together.-M. du 7'ertre defcribes three Kinds of Ana-
nas. They make a Wine from the Juice, which is almodt
equal to Malmfiey Sack, and will intoxicate as foon.
It is good to flrengthen the Heart and Nerves, againft
naufeating, to refrelh the Spirits, and excites Urine power-
fully; but is apt to occafion Abortion in Women.-They
make a Confed~ion of the Ananaas on the Spot, which they
bring hither whole ; and is found of good fervice to reflore
a decay'd, or aged Conflitution.
The Anana, or Wefl-Izdia 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 Endeavours
have of late been ufed to cultivate the Plant in Europe; in
which they have fucceeded, and there are now produced de-
licious Fruits of this kind, in fome of the fine Gardens in
Etzgland.-They are ufually about the Size of a Tennis-Ball.
ANAPEST, ANAPrsTus, a Foot in the Greek and Latih
Poetry, confifling of two r.ort, and one long Syllable. See
4_ ;W-7 3
I Qj  I 
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