CUB                          (3B
demonftrated, that the Figure of the leafi Particles, is en-
tirely different from that which appears in the CryJfzl. See
PARTICLE.
CRYSTALOIDES, the Cryflalline Coat of the Eye;
a Coat, or Tunic, immediately encomrafling, and containing
the Cryflalline Humour; and fuppoled to ferve, by con-
firinging or dilating that Humour, to vary the Place of its
Focus. See CRYSTALLINE.
Anatomi~ls are divided about the Reality of fuch Tunic,
which is alfo, from its fine Texture, called Adranea 71unica,
or Arachnoides. See ARACHNOIDES.
CRYSTALOMANCY, the Art of divining, or foretel-
ling future Events, bv means of a Mirror; wherein the
Things requir'd are reprefented. See MIRROR.
It is alfo call'd Catoptromancy: The firfk from nidsaAt,
congeal'd Water, or Cryflal; and the fecond from *6wrejiV,
Mirror, and ptv7elcr, Divination.
CUBATURE, or CUBATION, the Cubing of a Solid;
or the meafuring of the Space comprehended in a Solid;
as in a Cone, Pyramid, Cylinder, &c. See CONE, PYR AMID,
CYLINDER, SC.
The Cubature regards the Content of a Solid, as the
Quadrature does the Superficies of a Figure; fo that the
Cubature of the Sphere turns on the fame thing as the Qua-
drature of the Circle. See SOLIDITY, and QUADRATURE.
CUBE, in Geometry, a regular or folid Body, confiflingof
fix fquare and equal Faces, or Sides; and its Angles all
right, and therefore equal. See SOLID, and REGULAR
Body.
The CGube is alfo call'd Hexaedron, becaufe of its fix Sides.
The Word comes from the Greek xvea, re/Jara, Die.
The Cube is fuppos'd to be generated by the Motion of
a fquare Plane, a ong a Line equal to one of its Sides, and
at right Angles thereto: whence it follows, that the Planes
of all Sedtions parallel to the Bafe, are Squares equal there-
to, and confequently to one another.
IVo defcribe a Rete, or Net, -whence any given Cube may
be c'yiflruded, or wherewith it may be cover'd.  On the
right Line AB, (Tab. Geometry, Fig. 49.) fet off the
Side of the Cvbe, four times ; on A erect a Perpendicular,
A C, equal to the Side of the Cube AI, and compleat the
Parallelogram A C B D. With the Interval of the Side of
the Cube, in the Line C D; determine the Points K,M and
0 : Lafilv, draw the right Lines I K, L M, NO, and
B D; produce 1K and LM, each way to E and F, and to
G andH tillEL=IK=KF, and GL=L-M=MH,
and draw the right Lines E G, F H.
T'o determine the Surface and Solidity of a Cube: As the
Surface of a Cube confifis of fix equal Squares, a Side mul-
tiply'd by it felf, and the Product by fix, will give the Su-
perficies; and the fame Producl, again, multiply'd by the
Side, the Solidity.  See SURFACE, and SOLIDITY.
Coroll. Hence, If the Side of a Cube be Io, the Solidity
will be xOOo; if that be I1, this will be 1728 : Where-
fore, the Geometrical Perch being io Foot, and the Geome-
trical Foot to Digits, Uic. the Cubic Perch is 0ooo Cubic
Feet, and a Cubic Foot iooo Cubic Digits, Fec.
Hence, alfo, Cubes are in a triplicate Ratio of their Sides;
and are equal, if their Sides be fo.
CUBE, or CUBIC Number, in Arithmetick, is a Number
arifing from the Multiplication of a fquare Number by its
Root. See NUMBER.
Thus, if the fquare Number 4, be multiplied by its Root,
2, the Faflum 8 is a Cube or Cubic Number; and the Num-
ber 2, with refpecd thereto, a Cube-Root. See ROOT.
Hence, fince, as Unity is to the Root, fo is the Root to
the Square ; and as Unity is to the Root, fo is the Square to
the Cube; the Root will, alfo, be to the Square as the
Square to the Cube: that is, Unity, the Root, the Square,
and the Cube, are in continual Proportion ; and the Cube-
Root is the firfl of two Numbers that are Mean Proportio-
nals between Unity and the Cube. See POWER.
For the Compofition of CUBIC Numbers.  Every Cubic
Number of a Binominal Root, is compos'd of the Cubic
Numbers of the two Parts, of the Fadfum of thrice the
Square of the firfi Part into the fecond, and of the FTaum
of thrice the Square of the fecond Part into the firfm.
Dernonfl. For a Cubic Number is produced by multi-
plying the Square by the Root: But the Square of a Bi-
nomial Root, is compos'd of the Squares of the Parts, and
the double Fatlum of one Part into the other. See SoUARE.
Wherefore, the Cube is compos'd of the Cube of the firfi
Part, of the triple Fat um of the Square of the firfi Part
into the fecond, and of the triple Faaum of the Square of
the fecond Part into the firfi, and of the Cube of the fecond
Part. See RooT.
An ocular Demonfiration of this we have in the follow-
ing Example, where Multiplication alone is ufed. Suppofe,
v. Z. the Root 24, or  + 4. Here,


24-


f# TY I


20' +  . 4. 20+4'
0+ 4X
+4.  +0 2. 42. 20+41
10 +2. 4. 20'+    42, 10


24' 1C3 +3. 202. 4+3. 4 ao+4'
203 =8ooo
3- 20' 4 =48o0
3, 42 20 -960
43   64


14. = 13814


Coroll. Hence, as the Part on the right Hand is plac


among Units, and that on the left among Tens; ti
Number of the right hand Part mufi be put in the rigl
the Faiam of its triple Square into the left, in th
Place; and the Fadam of the triple Square of the
the right, in the third: latcly, tie Cube of the I
Part falls in the fourth Place.
If the Root be a Multinomial, two or more C
on the right mutt be efieem'd as one; that it m
the form of a Binomial.
'Tis obvious, that any Cube is compos'd of the
the feveral Parts of the Root, and oP the Fa5fuja
triple Square of any of the left-hand Charaoers
nevt n" th- chiit .  n ,-4 n I 4 .A1 ru.sts DC .-f U


Square of the right-hand Chara&ers into all the left.
pofe, v. g. the Root 243: Take 240 for one Part o
Root, 3 will be the other Part; Confequently,
240'  I53824000
3. 240.3 =   518400
3. 240.3'=     6480
3 =         7-
243' = 14348907
The Places of the feveral Faafums, are determin'd
what was obferv'd above: for regard mufl here, too, be
to the Ciphers to be added to the Numbers multiplic
each other, if they be placed alone.
This Compofition of Cubic Numbers once well conc
the Extra&ion of Cubic Roots will be cafy. See EXT
TION.
CUBE Root, or CUBIC Root, the Origin of a Cube I
*ber; or a Number by whofe Multiplication into it felf
again into the Produ&, any given Number is form'd.
,CUBE Number.
The Extra lion of the Cube Root, is the fame thiu
the finding any Number, v. g.. 2; by whofe Multiplic
into it felf three times, a given Number, v.g. 8, is
duced: The Procefs whereof, fee under the Article
TRACTION.
CUBEBS, in Pharmacy, a Fruit brought from the I
of lava, in Grains refembling Pepper, both in form
fize ; whence fome call it Wild 'Pepper.
'Tis faid, the Natives of the Place boil it ere they,
it to be exported, to prevent its being fown in other Coun


Cubebs fortify the Stomacb, Brain, and other Vifc
and enter as an Ingredient in feveral Officinal Compofiti
CUBIC Equation, is an Equation wherein the unki
Quantity is of three Dimenfions, as x I _ a 3  b-  , &c.
EQV ATION.
For the ConfdruFlion of Cubic Equations, fee CoNsT]
UNION.  For their Refolution, fee RESOLUTION.  Fo


hlennft see KttAr


CUBICAL Parabolois. a Term      u'A     mom  Wrfter f 4


a Parabola of the higher Kind, v. g. where a' x =y I
See CURVE; fee alfo PARABOLA.
CUBIT, a long Meafure, us'd by the Antients, efpeci
the Hebrews; taken from the ordinary length of a M
A He 4Ad- .,  An. V I _L- - .L -  p_ o- ta-  In _1 e_ J.


SURE, ARM, and HAND.
In the Scripture, we find Cubits of two lengths, the
equal, according to Dr. fIrbuthbot, to l Foot, 9 Inches,
of an Inch, our Meafure being the fourth Part of a
thorn, double the Span, and triple the Palm: The 4
equal to i-' Foot, or the four hundredth Partofa Stad
A aI_ LVf-. ._1    U _  a_7 :.  _ |  I _  ata


4fo-6 of an Inch.
F. Merfenne makes the Hebrew Cubit I Foot, 4 Di
and 5 Lines, with regard to the Foot of the Capitol.
cording to Hero, the Geometrical Cubit is 14 Digits;
according to Vitravius, the Foot is 2 of the Roman CZ
i. i6Digits. See FXnnY n    o  v?,


CUBITMEUS Externus, or Ulnaris, in Anatomy, the
firfi of the Extenfor Mufcles of the Fingers.
It has its Name, as being placed along the Cubitu5, ex-
ternally.: It rifes from the external Extuberance of the .tbk
merus, and palfing its Tendon under the Ligamentum A
mulare, is iftedrinto the fourth Bone of the Metacar,"S.
that fuflains the little Finger.                  _


(VUBIT&V


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