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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 806933011:0761
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dra chrouph K the Center ot the Sphere, 2 rigHE
Line 25 9 d, perpendicular 1oB C, wtrich chere-
fore will be che Axis ol che obque Circle; ihen a
Rulex laid From A chrouch O and S, che Pole ot
chac Axis MaII Project he Polar FOII  L
and Z.
F0 Project the Poles oF the oblique Circle BC, j...  1
P ROP. VIII.
lies oblique ro the Primirire (in the Projection)
is so far discant tom C, the Center of the Pri-
P. (12o 01 l
Problem 2.
To Project a Lesser, or Parallet Circle l L, Whose
Poles are in the Line of Measures, C, r: repre
Senns che Plane of the Projection.
Lult, Project the Diamerer oF the Lesser Cirele
P L, intothac oF the Projection in che POIs a ahl,
and deam a Line from P coN; eo which erea
P C ac Righe Angles; (0 Mall, C be the true C M-
rex oF che plosclted CixClE.
The Center (P) of every Preat Circle (BG) whicb
rion of its Plan, abodee lan of the Pri-
mitive.
micire, as is the Tansent of the ArK OE Plera-
Make thC ArK B u = C I, che Complemene oF
che Angle et tlerarion, and draw u A, Wilch vil
tind che Poinc P, che Cenrer ot ihe Ltojecle
Cirele.
.2
i 100
DE MONSFR AYFON.
The AngIC N A P, is equal to che Angle O Pr;
because A N is parallel 10 P O: AIIO che Arele
A e P, is equal EO THC AIFerNaTO AnGIC C PL: BUF
the Angle c AP, added to the Anslec, is equalto
a RighE one. Wheretore che Anole O P r-
Pr O, = a RighE AnelC: THaE is, The ATOlC
d Pr, is a Rishe Angle. Wheretore dr, is thc
Diameter oF a Circle.
Because the Anole B A u = Anele C A C, (25 NTon NPC, Beins righeby Construction, cakC FTONL
Beins on equal ArChes) and e AnSle A B C equal ) those ro RighE AnGles, che common one dPC.
Eo rhe AnBleS A d e, (BY THC SUBCOMEFAEY POMTION)
cheretore che Triangles B A S and AC d are Simi-
lar, and consequenely che Anese D Cirtich is
equal cothe Anole A C a) IS d FISHC Onc.
Deam B L perpendicular 10 B C, Wherefore.
the Priangles B L C and AP C are Similat; FOF
Ansle L B C = Anele P C A, 25 beins bochrist
ones, and the Angle AP C = B L C, because
BL and AP, are Parallels; Wheretore che Ansle
BCL = Anole P AC.
Buc P C is che Tangent olthe AHSIC P AC, and
ThCTEFOR OF IES egual che Anole BC L, OF OF the
ArK BK, Which is equal co the obligue Circlés
Eleration abore the Plane oF e d; Wheretore Pthe
Lenter OF the obsique CIrClC IS aIITANE FrOm C bY
che Tangent of ies Fleratton avore  Lca C
3
and che Angle NP a (= L e) must remain equal
10 che Anele C Pr, and che Ansler, is = co che
Angle es because che Triangles NI d e, and P dr.
are smilar: Wheretore che Trianales P Cr, and
NP e, are similar; and consequenty, c N: NY P
:: PC: Cr; butCN = N P; ThCretOre PC = CY.
Theretore bochare Radii ot a Circle. 8. F. D.
and +0 prove PC = dC, and consequently that
they also are Radii.
FCay, The Friansle d P C, is an TCosceles, Be-
cause cheAnsle P a C, is equalto che Ansle d PC;
Wrtich Lchus prOvC.
The Anele P d 0 - 1 - L d P0 = RighE AnBIC,
==La P C -) LCPY, BUECPN = L e = d P0;
Thecetore cakins avar che common Ansle aP0,
(Or its equal C Pr) d P C must remain equal 10
P d C: TVhereFOre P C (= C r) = C d. Wrtere
Pore cisthe crue Cenrre os rheprojected Circle.
GOROLL ARZ I.
F. Denec Tis plain, Phar makine N D ehe Ra-
dius ot a Circle, whole Cenrre is NI, The proie-
Ated Circles Cenere C, is distane From N, the C en-
Pb, Or oF chat lesser Circles Diltance Erom iis
Pole b.
2. Lhc
D E M ONS Y R A X LB N.
E Do
COKOL.
AIIO, because the Friangles e P A and A C C
are Similar, (a5 having Ansle C = Angle C, by
SubContrarY POBtiOn) and the AnelC B A P = AN-
Ele C AC (as beins on equat ArKS) cheretore will
P: PA:: AC: C 6, thac 1S, e P =P A. But
LA is the SCCaHE OF the AnOle P AC, OF OF chc
et set trom e, Mall find P rhe Center 25 betore;
ArK BK; WHeretOre thC SCCANE OF the Fleration cer oF the Primitire, by NC, cheSecanc Of che ArK
PG, P A, or P d beins ies Radtius.