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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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DDD. Thacis, Spheres are eo cach orter as che
Cubes oF rheit DIaMeTETS. D. L. D
2. The Coliditz oF a Sphere is equal ro che Sur-
Face mulriplied inFO  OF Ehe RaciuS; 25 is proved
FrOM COr, L. OF PTOP. 4. in thc Word Cylin
der.
3. A Sphere is equal t0 = oF a Cylinder, havine
the Diamerer oFus Base and is Axis equal r0 thar
OEche Sphere, 1. c. 2 Sphere is = OF ihe Cplindet
circumseribed: And che Surtace os the SpHere and
the curred one of the Cylinder circumsetibins it
isthe latme in Ouantity; a5 is proved in Cylinder
Prop. 4. atid Corollaries; 2s also very brieAts under
the Word indivisibles.
4. The Surtace DF che Sphere is equal EO FOUF
rimes che Area OC a oreat Circle. Sec Cylinder
Prop. 4. Coroll. WVhetetore add ro the Curve and
Surtace OF che Cxlinder ies aro circular Bales, and
chac Willmalce six great Cireles of the Sphere: S0
thac che Surtace OF che Sphere is buE Z oF chc
erhole Surtace oF the Crtinder. Sec allo Cylin-
dor,
anentire Sphere os Glass ill unite the Parallet
Rays oF any Object ac che Distance oF near iES
Semidiamerer Behind it. Molyneux Dioptr. P. 93
SPFTERE of Activity, Ot anv Body, is chac de
terminare Space or Excene all round abour il, 10
extrich, and no Farcher, the Fstuviums continualls
emicted trom chac Body do reach, and where they
opetate accordins co their Nature. Thus ve sec
Ehc Magneticat Fstuvia have cerrain Bounds and
Limics, berond Wvtrich chez will have no InAuence
Eo turn or to attract ehe Necale: Bur Where erer
a Acedle be placed, (0 25 thac ic can be moved by
a Lodd. Aonc, it may be Caid ro be wichin ehe
Sphereos Activity oF the Stone.
SPHERTCK Geometry, Or Projection, is ChC AEE
oF Delcribing on a Plane che Circles of rhe Sphere.
Or any Parrs of them in cheir just Policion atid Pro
Porrion. and of Meaturins cheir Arks and Anples
Wvhen Projected.
A5 an mcroduction co ivhich, rou must under-
Atand.
For let L BC i LCacC OL IC Cteulat Dale
then ist A L BC The Axis; and it che Cone be cul
by che Aris, the Section AB C will be 2 Frian
SIC. Lec c5, che Diamerer oF che Section, bc
drawn, curtins che Axis in i, Wheretore e f che
Diamerer ofthe Section Will be parallel 10B C, HC
Diamerer oF che Bale.
And consegueneis,
Whetctore, by Inverse Proportion, and ex aequo, 25
C: FB: : 18: ic.
ard A B and A C must De Rixtr Fines, because
che Surtace ofche Cone will be described br cirtier
otchem; Wheretore che Section AB C is a Fri
atisle. 2. F. Id.
II. Y a Cone as A B C be eut by a Piane Parallet
10 ies Base. the Section ese h will be a Cirt
ta L a C 1. 5 18, 3 2C: a
25 AF: FC :: A 1: 15.
BucBF = F C, chercloree ; = 18.
S: her place) cali ic V. lHCTCIOTC = radd. Z rDDV.
rydda =ryDDD. BAE = ryddd. 1).. aua
ANa CC Tae COMLCGUEHCE WI aIHC I VOU Tate
o and K, any evo ocher Poines in che Bale ana M
the Section; FOF K i being parallel t0 0F, and
a o F beins a Frianglc. AF: 0F :: A I: B i
buE 25 A F: F B :: Ai: I e. Wheretore ex
aquo dF: + D.. 1 1. 1c. Andcheretore R I
and i’e are equal also, and consequener che Se.
ction is a Circle: For i is a Point trom whence
more chan evo Righr Lines deawn co the Curve
e h8 Fare equal; Wheretore char Curve must bc
 Cirele. L.L. .
P R O POSITIONS.
1.  a Cone, as AB C, be eut by a Pla
eichet by the Axis, or ehiroush the Vertex, et
Sectior Well be a Triansle.
For the Point R is the Verrex ot thie Conc, and
quist De CooEche Trianple, and B C is a Riphe Linc
because tis he Diameter otche Circle or ite Base