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# Title: Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences (shelfmarks Leibn. Marg. 71; ZEN Leibn. Marg. 71)
# Folio - , page id 806933011:0763
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RC
T0 Project a lesser Cirele, nohen ils Poles are no
the Plane os che Projection. 
P R O P. XIII.
Al Great Circles of ihe Sphere, passins throuch ans
Point 2, in the Diameter of the Projection, sate
Sall have their C’entres in the Line 8F, which is
perpendicular tothe Diameter 8 b, and their C en-
ters will be distane fromthe Point 5, the Centre 0)
the Cirele A C D, by the Pansent os the Ansle os
cheir Intersection wich the Savet    .
Pet OF be the Diamerer oF such a Circle, a
Ruter From che Poined, Wrhere chie Fye is suppoled
to bc placed, to O, Will project the Point a; and
Fromt d to L, will proicet che Point b: Pheretore
a b, 25 the projected Diamerer, and consequen
ies midale Point e, will Bethe Cenere oF chac Cir-
cte in che Projection.
The Demonstration sou hare univertally in
Prop. 4.
Or, since b7 (Prob. L.) C a, and Cb, Will Beche
haIF Langens oF che AEHS AO, and R L, (For che
Primitire Circle is righr to che PyC ac d:) There.
Fore ro proicet such a Fesser Oblique Circle, vou
necd oniy calce chehale l’angenes ot the Distance oF
each end of theDiameter oF luch alesser Circle From
che Point A, oppotce ro the Fre, Cupposed acd;
and set ehem from the Centre C, and ther wrill find
che Poines a and b, che ends of the projected Dia-
mecex; and a b bissected, will sive he C’en
Ere c.
 dits 311s
st is plain from what hath been proved in PrODOSI
tion 10, chac che Ansle oFthe Radii os any evo Cir-
eles is equal io rhe Angle ofthe incersection oF cheir
Peripheries.: And cheretore il it vere required 10
draw a great Circle chro the Poine a wetrich
Mali mate ans siren Ansle wich che Circle
A a d.
Set the FaHGENE OF Etat AMPIC, Trom C the CeH-
Ter oF the Circle A a D, Found by chemakino a
Cirele palschro chechree PointS A, a and D, and
chac Mall End che Poinc s, ihie Cetitre oF ihe Ciccte
required.
COROLL ARY.
Fence, it a Be supposed eo be the Polar Poine
OFthe Worid projected, and it vere required thro
iE, to project all the FTour Circles: A a L, will be
the FTour Circle of siX, Whose Center is in s; and
by Terrins che Tangents oF 15, 30, 45, 60, (9c.
boch mars Erom ecorards fandh, (agreable tothe
Radius a 5) all che ocher FTour Circles maybe de-
scribed on the Plane ot the Projection; trom cheir
Cencers in che Line f B.
Which is the Foundation oE all Dyalline, Or thC
True Projection OF che Four Circles of the Sphere On
any siven PlanC.
itie sie regis Oti 
R OP. XNV.