CUB
C 354)
demonstrated, that the Figure of the leaft Particles, is en- tirely different from that which appears in the Cryfial. See Particle.
CRYSTALOIDES, the Cryfialline Coat of the Eye ; a Coat, or Tunic, immediately encompaffing, and containing the Cryfialline Humour 5 and fuppoled to ferve, by con- ftringing or dilating that Humour, to vary the Place of its Focus. See Crystalline.
Anatomifts are divided about the Reality of fuch Tunic, which is alfo, from its fine Texture, called Aranea Tunica, or Arachnoides. See Arachnoides.
CRYSTALOMANCY, the Art of divining, or foretel- ling future Events, by means of a Mirror ; wherein the Things requir'd are reprefented. See Mirror.
It is alfo call'd Catopromancy ; The firft from xpfociftA®*, congeal* d Water, or Cryflal $ and the fecond from n&rbxfl&v, Mirror, and futvrefa, Dim-nation.
CUBATURE, or CUBATION, the Cubing of a Solid 5 or the meafuring of the Space comprehended in a Solid 5 as in a Cone, pyramid, Cylinder, &c. See Cone, Pyramid, Cylinder, £$jV.
The Cnbature 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. Sec Solidity, and Quadrature. CUBE, in Geometry, a regular or folid Body, confittingof fix fquare and equal Faces, or Sides 5 and its Angles all right, and therefore equal. See Solid, and Regular Body.
The Cube is alfo call'd Kexaedron, becaufe of its fix Sides. The Word comes from the Greek Jtu/2©-, Tejfjhra, 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 Sections parallel to the Bafe, are Squares equal there- to, and confequently to one another.
To defcribe a Rete, or Net, -whence any given Cube may be onjh'itclt'd, or -wherewith it may be covered. On the right Line AB, (Tab. Geometry, Fig. 4.9.) fet off the Side of the Cube, four times ; on A ereft a Perpendicular, A C, equal to the Side of the Cube A I, and compleat the Parallelogram ACBD. With the Interval of the Side of the Cube, in the Line C D 5 determine the Points K,M and O : Laftly, draw the right Lines IK, L M, NO, and B D ; produce I K and L M, each way to E and F, and to GandH; tMEL=IK = KF, and GL = LM = MH, and draw the right Lines EG, FH.
1*o determine the Surface and Solidity of a Cube : As the Surface of a Cube confifts of fix equal Squares, a Side mul- tiply'd by it felf, and the Product by fix, will give the Superficies 5 and the fame Product, again, multiply'd by the Side, the Solidity. See Surface, and Solidity.
Coroll. Hence, If the Side of a Cube be 10, the Solidity will be ioco ; if that be 12, this will be 1728 : Where- fore, the Geometrical Perch being 10 Foot, and the Geome- trical Foot 10 Digits, &c. the Cubic Perch is 1000 Cubic Feet, and a Cubic Foot 1000 Cubic Digits, &c.
Hence, alfo, Cubes are in a triplicate Ratio of their Sidess 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, it the fquare Number 4, be multiplied by its Root,
- , the Fail-urn 8 is a Cube or Cubic Number 5 and the Num-
ber z, with refpecl thereto, a Cube-Bjiot. 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 firft of two Numbers that are Mean Proportio- nals between Unity and the Cube. See Power.
For the Composition of Cubic Numbers. Every Cubic Number of a Binominal Root, is compos'd of the Cubic Numbers of the two Parts, of the Faclum of thrice the Square of the firft Part into the fecond, and of the Faclum of thrice the Square of the fecond Part into the firft.
Demonfi. 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 Fa&um of one Part into the other. See Square. Wherefore, the Cube is compos'd of the Cube of the firft Part, of the triple FaBum of the Square of the firft Part into the fecond, and of the triple Factum of the Square of the fecond Part into the firft, and of the Cube of the fecond Part, See Root.
An ocular Demonftration of this we have in the following Example, where Multiplication alone is ufed. Suppofe && the Root 24, or 20 -j- 4* Here,
CUB
Zl'=i 20*4-2. 4. 20 + 4."
- ° + 4'
+ 4. 10-V4-2. 4'. *o+4* 20* + 2. 4. 20*-(- 4*. 2
i4* = ao! + 3. so*. 4 + 3- 4' 204-4"
20* =8000 3- 20 1 4 =4800
3. 4* 20 =950 4'=d 4
24* = I3824
Coroll. Hence, as the Part on the right Hand is placed among Units, and that on the left among Tens ; the Cubic Number of the right hand Part mufl be put in the right Place - the Factum of its triple Square into the left, in the feLond Place ; and the Factum of the triple Square of the left into the right, in the third : laftly, the Cube of the left-hand Part falls in the fourth Place.
If the Root be a Multinomial, two or more Characters on the right mufl be efteem'd as one 5 that it may have the form of a Binomial.
'Tis obvious, that any Cube is compos'd of the Cubes of the feveral Parts of the Root, and of the FaSums of the triple Square of any of the left-hand Characters into the next on the right ; and alfo of the FaSums of the triple Square of the right-hand Characters into all the left. Sup. pofe, v. g. the Root 243 : Take 240 for one Part of the Root, 3 will be the other Part ; Confequently, 240' = 13824000
3. 240'. 3 = 518400
3. 240. 3 s = #480 3^= 27.
243 ' = 14348907
The Places of the feveral FaSums, are determin'd from what was obferv'd above : for regard muff here, too, be had to the Ciphers to be added to the Numbers multiplied by each other, if they be placed alone.
This Compofition of Cubic Numbers once well conceiv'd, the Extraction of Cubic Roots will be eafy. See Extrac- tion.
Cube Root, or Cubic Root, the Origin of a Cube Num- ber ; or a Number by whofe Multiplication into it felf, and again into the Product, any given Number is form'd. See Cube Number.
The ExtraSion of the Cube Root, is the fame thing as the finding any Number, v. g. 2; by whofe Multiplication into it felf three times, a given Number, v.g. 8, is pro- duced : The Procefs whereof, fee under the Article Ex- traction.
CUBEBS, in Pharmacy, a Fruit brought from the Ifland of Java, in Grains refembling Pepper, both in form and fize ; whence lome call it Wild 'Fepper.
'Tis faid, the Natives of the Place boil it ere they allow it to be exported, to prevent its being fown in other Countries. Cllbebs fortify the Stomach, Brain, and other Vifcera; and enter as an Ingredient in feveral Officinal Compofitions. CUBIC Equation, is an Equation wherein the unknown Quantity is of three Dimenfions, as;l^*=<^ , — b*,l$c. See Equation.
For the ConflruSion of Cubic Equations, fee Construc- tion. For their Refolution, fee Resolution. For its Root, fee Root.
CUBICAL farabolois, a Term us'd by fome Writers for a Parabola of the higher Kind, v.g. where a' x=y\ iSc. See Curve; fee alfo Parabola.
CUBIT, a long Meafure, us'd by the Antients, efpecially the Hebrews ; taken from the ordinary length of a Man's Arm, from the Elbow to the Tip of the Hand. See Mea- sure, Arm, and Hand.
In the Scripture, we find Cubits of two lengths, the one equal, according to Dr. Arbuthnot, to 1 Foot, 9 Inches, f"-.- of an Inch, our Meafure ; being the fourth Part of a Fa- thom, double the Span, and triple the Palm : The other equal to i.\^ks Foot, or the four hundredth Part of a Stadium. The Romans, too, had a Cubit, equal to 1 Foot, 5 Inches, T-svo- °f an Inch.
F. Merfenne makes the Hebrew Cubit 1 Foot, 4 Digits, and 5 Lines, with regard to the Foot of the Capitol. Ac- cording to Hero, the Geometrical Cubit is 24 Digits ; and according to Vitruvius, the Foot is i of the Roman Cubit, i.e. 16 Digits. See Foot, Digit, iSc.
CUBIT^iUS Externus, or Ulnaris, in Anatomy, the firft of the Extenfor Mufcles of the Fingers.
It has its Name, as being placed along the Cubitus, ex- ternally. It rifes from the external Extuberance of the Hu- merus, and pafling its Tendon under the Ligamentum An- nulare, is inferted into the fourth Bone of the Metacarpus, that fuitains the little Finger.
CUBITJEUS
