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# Title: Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences (shelfmarks Leibn. Marg. 71; ZEN Leibn. Marg. 71)
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Caus, ir d a sete Realon ot, itich vort ae UN. ) Cor. 1. From hence have ve che DiHAHBS O
che Sphiere and Cylinder, borh a5. 10 Solidiey and
Surtace; tor let d be che Diamerer ot rhe Spherc
and Cylinder, and rd the. Circumterence ot ehe
Base oFrhe Cylinder, chen will the whole Ba(e b.
=r d d (itrich also is che Area ot a grear Cirele ot
cheSphere;) andchis Bale mulciplr d by d che AI.
cirude, siresrd dd tor chesolidier ot che Cylin-
der; and cheretore by chis Prop. Z Oi chac gives
Ehe Sphere (1. c.) Erddd Solidir ot rhe Sptiere:
andchai las Ouanciey divided by ? d (one sixch ot
and in che orher D, che Solidies e eer (che Diamerer) giresrdd rhe Surtace ot chie Sphere.
2. Which Surtace rdd is manilesttus Ouadruxe
Ot :rd due the Area oF a prear Circle oF rhc Sphere,
char is, che Cylinders are as the Cubes ot cheir or che Bale ot che Cylinder.
Diameters. L F. D.
portion os sonds.
3. Wheretore, by mulcipixine r d (= 20 etic
Periphery of che Base of che Crtinder by d che AI
cirude, vou have rd d for ehe Curre Surtace et
the Cylinder; itich cheretore is equat. (raken
withour is proxer Bales) ro the Surtace ot the
Sphere; and conlequenely, addins in the Bases
(cach et nhich is =r d d) che wrhole Surtace ot che
Cylinder, Bales and all, will be 1. = r d d; chac 15,
coche Surtace oF the Sphere a5 3102.
à Phe Square ot che Diamerer (d d) eoche
Area oF the Circle =r d d, 15 a5 d.  r d. (For d d
rdd:: d. =r d) chac i5, a5 the Diameter 10 =
Olche Circumterence.
5. Decause ihe Solidiry oF che estinder is. =r d dd.
cheretore che Conc ot the lame Bale and Fleiptir
Will be r.r d d d; which is plainsy che difference
betveen =r d d d and. r d d d, che Solidiey oF che
Cylinder and Sphere, (0 chac the Conc is equal t0
the excess of the Cylinder above the Spbere: And
he Conc, Sphere and Cylinder arc a5 3, 2, and +)
(0 chac che Sphere is ruvo chirds ot che Cylinder.
sec this proved much Morrer under che word
Indivisibles.
IL vou consider. a Colinder as compoled oF an in-
tinire number oF Cylindrical Surfaces decreasine
(a5 che Circles ot che Base on which chey Randi
in Arichmerical Progrestion. IF rou call che ourer
most or prearest Surtace S, and che Radius of rhe
Baser, the Solidier ot the Cylinder will Be exprel
sed by =rS. And ic will be diverrine co meature
a Cylinder by borh oFrhele disterent mays, in order
ro sec hon nearly chey will agree.
EVETNDROTD, is a Solid Fixure, ich Ellip-
rical Bases, parallel, and alikee siruarec
CXLIHDROS, is a Plaitter made oblons:
vohich some Phylicians call Masdaleo. Blans
chard.
EFLEOSIS: Sec C yllum.
CXLLOM, senities a L es pur ouc oF joyne
ourmaraly. Alsoone Lame and Crooked
CTMA amone che Bocanists, sixnities thC cOP
CXMATIOM, a Member ol Archirecture
called Doucires Or Rixht Cula, che most advancee
Pare ot which is Cencave; and rhe orher Palon Or
Reversed Cula, whrich hach irs most advanced parr
Convex, buc is hollon below, a5 che tirM is a
bove.
CTIBITORHEO: Sec O. Naviculare.
CTMACHE
des Circle:) And rhen il che Alcicude oF che Cylin
der be called b (1. c. is heiptic) ehe Solidicy of rhe
Cylinder will be expressed chus,  r dd h.
2. HF heretore che Aleirudes ot any rvo CMm
aers be cescalro ihe Diamerers ot cheir BalCo, 
Cylinders must be to onc anoret as iBe Cades s lseit
Diameters or Alcitudes. et metes io nan
beins che lame wich d, theDiameters ot  CMes
oF che Balc. IE in one Cylinder ic be called a
will be 2Y dd d, and ot che lallet +r  ;
bur doubelels er beins a common FHicienE Or
Mulciplier: 2r dd d. =rDDD:: ddd: D DD.
3. Lvery Cytinder is Priple ot a Cone of che
tame Base and Heiphr; utich sec proved in ero
4. Every Cylinder i5 r0 a Sphere inceribed an.
et ine same Bale and Fleiphe a5 3102.
IF che Square and Ouadrane wich chie Diagona
a d be supvoled ro revolve round che Axis b d.
phe Square Will generare a Cylinder. ihe Oudata
AH Hlehisphere and che Trianele a a. Cont
l C ul hame Bale and Heiptic.
And Cince Circles are a5 the Squares oF thei
Diameters, and phar the Square oF e h(== VOF df)
=Iha) F E Bf. by 47. cr. There
fore the Circle delcribed by ch or is =c d, must
be equal eo civo Circles described by sh and by
bf. Takre awar chen the common Circle deleri-
bed by hs trom boch, and ehere will remain che
Circle delcribed by ch- to the Rins described by
ef. And rhus ic vill alvays bc, chac (V. gr) che
Circle described by Lm vill be equal eo the An
nulus or Rino made by the Morion OF i l; Where-
Fore all the Rines made by the Rerolurion ot ef
ih, ecc. must be equal ro all che Circles delerib d
by the Norion oF GB, m k, _cc. thac i5, aIl che
Solid, compoled ot the Rings made by che Mori
on oE ihe Parrs oC che Trilinear Fisure cflb a
MaII be equai to all the Circles generared by che ot any Plane er Ilerb
Elements ot che Friangle a d b: Wheretore Ance
Heiphr, and chat che Solid made by che Frilinear cave: TherC arE EVO COrES OE Cymariums, viz. One
cf1b a is allo anocher chird parr, as beins equat
roche Cone. The FTemilphere mukbe Z oF che
Cylinder, and consequentlr, it che Bale and Alri-
rude ot che Cylinder vere equal to the Diameter of
ede dplere, ihie wtiole sxtiere nould be, Ot e
the Cone is : OF the Cylinder on che same Bale and Whereot onc halt is Convex, and che orher Con
Cortinder.