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CYLINDER, in Geometry, (from the Greek™™**, a round long Stone ■) a folid Body, contain d under three Surfaces ; luppos'd to be generated by the Rotation ot a Parallelogram, as CBEF, (Tab. Geometry, Fig. J*0 about one of its Sides, CF. See Solid. ^tjet.
If the generating Parallelogram be Reflangular, as C B £ F , the O/iH/fer it produces will be a r«W Cylinder, Under whofe Axis is perpendicular to its Bale
If the Parallelogram be a Rhombus, or Rhomboides, Cylinder will be oW/yae, otfiatenous.
The Surface of a Wgi't t>/r»ier, exclufive of its Bales, is demonflrated to be equal to a Reftangle contain d under the Periphery, and the Altitude of the Cylinder.
The Periphery, therefore, of the Bafe, and thence the Bafe it felf, being found, and multiply'd by two, and the Produft added to the Reflangle of the Height, and peri- phery of the Cylinder ; the Sum will be the Area or Super- ficies of the Winder: multiply this by the Area of the Bafe ; and the" Product will be the Solidity of the Cylinder.^
For it is demonflrated, that a Circle is equal to a Tri- angle, whofe Bafe is equal to the Periphery, and Height, to the Radius 5 and alfo, that a Cylinder is equal toalri- anoular Prifm, having the fame Bafe and Altitude with it felf: Its Solidity, therefore, muft be had by multiplying the Superficies into the Bafe. See Prism.
A»ain, fince a Cone may be efteem'd an infinite-angular Pyramid ; and a Cylinder an infinite-angular Prifm : a Cone is one third Part of a Cylinder, upon an equal Bale, and of the fame height. See Cone.
Further, a Cylinder is to a Sphere of the fame Bale and Altitude as 3 to 1. See Sphere.
Laftly, It being demonflrated in Mechanicks, that every Figure, 'whether Superficial or Solid, generated, either by the Motion of a Line, or of a Figure; is equal to the FaBum of the generative Magnitude into the Way or its Centre of Gravity, or the Line its Centre of Gravity de- fcribes : Hence, if the ReBangle A B C D, (Tab. Mecha- nicks Fig. 43.) revolve about its Axis AD, it will delcribe a Cylinder, and its Side B C the Surface of the Cylinder. But the Centre of Gravity of rhe right Line B C, is in the Middle F j and the Centre of Gravity of the generating Plane in the Middle G, of the right Line E F. The Way of this, therefore, is the Periphery of a Circle defcrib'd by the Ra- dius E G ; and of that, the Periphery of a Circle de- fcrib'd by EF. The Superficies, therefore, of the Cylinder, is the Faltam of the Altitude B C, into the Periphery of the Circle defcrib'd by the Radius EF, 7'. e. into the Bafe : But the Solidity of the Cylinder, is the FaBnm of the ge- nerating Reftangle ABCD, into the Periphery of the Cir- cle defcrib'd by the Radius E G ; which is Subduple of EF, or the Semidiameter of the Cylinder.
Suppofe, v. g. the Altitude of the defcribing Plane, and therefore of the Cylinder, BC = «, the Semidiameter of the Bale D C = r ; then will E G = i r ; and fuppofing the Ra- tio of the Semidiameter to the Periphery, = 1 : m ; the Periphery defcrib'd by the Radius, \ r will be equal to m r. Therefore, multiplying ~mr into the Area of the Rectangle jVC = «i" ; the Solidity of the Cylinder =lmar' : But 1 m a r'=" r.mr.a, and J r.mr, the Area of the Circle defcrib'd by the Radius D G. The Solidity of the Cylinder, there- fore, is equal to the Fallum of the Bafe, and the Altitude.
For the Ratio of Cylinders ; as the Radii of all Cylin- ders Cones, tSa. are in a Ratio compos'd of their Bafes, and Altitudes : Hence, if their Bafes be equal, they will be in the Ratio of their Heights ; if their Altitudes be equal, in the Ratio of their Bafes.
Hence, alfo, the Bafes of Cylinders and Cones being Cir- cles ; and Circles being in a duplicate Ratio of their Dia- meters ; all Cylinders and Cones are in a Ratio compound- ed of the dire£l Ratio of the Altitudes, and the duplicate one of their Diameters : and, if they be equally high, as the Squares of the Diameters.
Hence, again, if in Cylinders the Altitude be equal to the Diameter of the Bafes, they will be in a triplicate Ra- tio of the Diameters of the Bafe. All Cylinders, Cones, &c. are in a triplicate Ratio of their homologous Sides 5 as alio of their Altitudes.
A°ain, equal Cylinders, Cones, &c. reciprocate their Ba- les and Altitudes.
Laflly, a Cylinder whofe Altitude is equal to the Dia- meter of the Bafe, is to the Cube of its Diameter, as 785
to 1000.
To find s Circle equal to the Surface of a given Cylin- m we have this Theorem : The Surface of a Cylinder is to a Circle, whofe Radius is a Mean Proportional be- 1 the Diameter and Height of the Cylinder. See So-
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r-ERFlCIES. .
The 'Diameter of a Sphere, and Altitude of a Cylinder. equal thereto, being given ; to find the Diameter of the Cylinder : The Theorem is ; The Square of the Diameter
Under, equal to it, nearly, as triple the Altitude of the Cylinder, to duple the Diameter of the Sphere. See Sphere.
2l> find a Rete, or Net, whence a Cylinder may beform'd or ivbereidth any Cylinder may be emier'd. With the Diameter of the Bafe, defcribe two Circles ; find their Pe- ripheries : and upon a Line equal to the Altitude of the Cy- linder, form a Rectangle, whole other Dimenfion is equal to the found Periphery. Thus may the Cylinder rcquir'd be form'd, or cover'd.
Cylinder charged, in Gunnery, is the Chamber of a great Gun. See Ordnance.
Cylinder concave, in Gunnery, is all the Chace, or hol- low length of a Piece of Ordnance. See Ortnance.
Cylinder vacant, in Gunnery, is that P*rt of the Hol- low that remains empty, after the Gun is charg'd. See Canon.
CYLINDROID, in Geometry, a folid Body, approaching the Figure of a Cylinder ; having, v.g. its Bafes el- liptical, parallel, and equal.
The Word comes from the Greek •ulurJ'i©-, Cylinder, and eidV, Form.
CYMA, in Botany, a Term fignifying the Top of any Plant, or Herb.
Cyma, in Architecture. See Cima, Sima, and Cyma- tium.
CYMATIUM, CIMATIUM, or CIMA, in Architeflure, (from the Greek mfiimt, undula ;) a Member, or Moulding of the Cornice, whofe Profile is waved, ;'. e. concave atop, and convex at bottom ; frequently alfo call'd Doucine, Gorge, or Gula Retla ; efpecially by the French : by the Italians Go- letta, i. e. parva Gula ; but more ul'ually, Cymatium, a- mong us ; as being the laft, or uppermoft Member, q. d, the Cyma, or Summet of the Corniche. See Corniche.
Some write it Simaife, from Simits, Camus, flat-nos'd ; but this Etymology is unlucky : the Beauty of the Mould-
ing
confiding in its having
Projecfure equal to its Height.
"M. Fellbien, indeed, will not allow this Etymology ; con- tending, that the Moulding is not fo denominated from its being the uppeimofl Member of the Corniche ; but, according to the Sentiment of Vitruvius, from its being waved.
This is certain, that Vitruvius fometimes ufes the Word Unda for Cymatium, and fometimes Lyfis, i.e. Solution, Se- paratist 5 in regard, Corniches, where rhe Cymaifes are found, feparate one piece of Archirecfure from another ; as the Pedeftal from the Column, and the Frieze from tha Corniche.
But, withal, it muft be obferved, that he does not confine Cymatium to the Corniche ; but ufes it indifierently for any fimilar Moulding, wheree'er he meets with it : in which he differs from the moft accurate among the Moderns.
Felibien makes rwo Kinds of Cymatiums ; the one right, the other inverted : In the firit, that Part which projects the furtheft is concave, and is othcrwife call'd alfo Gula Retla, and Doucine. See Doucine.
In the other, the Part that projects furtheft is convex, called Gula Inverfa, or Talon. See Talon.
Our Architects don't ufe to give the Name Cymatium to thefe Mouldings, except when found on the Tops ot Cor- nices ; but the Workmen apply the Name indifferently, wherever they find 'cm.
'Palladia diflinguiflies the Cymatium of the Corniche by the Name Intavolatum.
Tufcan Cymatium, confifts of an Ovolo, or Quarter- Round. 'Philander makes two Doric Cymatiums, whereof this is one : Saldus calls this the Lesbian Afiragal.
Doric Cymatium, is a Cavetto, or a Cavity lefs than a Semicircle, having its Projecfure fubduple its Height.
Lesbian Cymatium, according to Vitruvius, is what we otherwife call Talon, viz. a concavo-convex Member, having its Projecfure fubduple its Height. See Talon.
'CYMBAI/, a Mufical Inftrument, ufed among the An- tients ; call'd by the Greeks r-o^Cnt.©-, and by the Latins urn.
It was of Brafs, like our Kettle-Drums ; and fome think in their Form, but fmaller, and its Ufe different.
Cafftodorus, and Ifidore, call it Acetabulum, the Name of a Cup or Cavity of a Bone wherein another is articulated ; and Xenophon compares it to a Horfe's Hoof : whence it muft have been hollow 5 which appears, too, from the Figure of feveral other Things, denominated from it, as a Bafon, Cal- dron, Goblet, Caique ; and even a Shoe, fuch as thofe of Empcdocles, which were of Brafs.
In effect, the antient Cymbals appear to have been very different from our Kettle-Drums, and their Ufe of another Kind : To their exterior Cavity was faften'd a Handle ; whence 'Pliny takes occafion to compare 'em to the upper Part of the Thigh, Coxendicibus ; and Rabban to Phiols.
They were ftruck againft one another, in Cadence, and made a very acute Sound.
ot
Their Invention was attributed the Sphere, is to the Square of the Diameter of the Cy-^o Cybele 5 whence their ufe in Feafts and Sacrifices: Set-
