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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 806933011:0760
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But is
Provor
s.
ue 1o the Lye, the Parts
ction mill not be in the same
se in the Line it sels, but
it hich lic nearest to the Fye
u in the Projection appear longer thanth
WhteB lic more remote from it.
Ference, Which are sererally che halres oF the AN
Eles LE C, B E C, H E C, (90. ac the C CnErC: 0
ettch laccer Ansles, che Arks ot che Circle giren
C L, C B, and C HI, are che proper mealures
Wheretore MC LISHE LineS OL, DL LE, C9C
us thal CVery Diamerer ot a great Circle, OF IIS
Parts wichin or wichour che Primiere, 15 tO BC
meatured on the Scale oF FTaIF Pangenes; and thar
che Dirisions oF ic begin ac the Centre ot ille Frimi
are the Tangenes oF halt thole ArkS; which MewS
ure Circle.
Circle placed oblique to ihe Fye at A, will be a
true Circle in tho Projection; but ils true Cen
ter is different from ils apparent one-
Fet BC De che Diamerer oF an oblique CIr
cle, wtrich is eo be Projected from thc BBC S
A, On a Plane Represented by che Line F R, wrtict
Mr. Oushered calls the Line of Measures.
donser chan PF, che RepreleMCarion OL IHC OIHeF HAII
Wrtich lies remore trom cho lre; a5 is in a mannet
Telferident.
coincident ich, or parallel e0 us Axis, ic will b
Projected inco an intinire righe Line.
PROBL FMt L.
Lexthe Circle siven Bc A B CD; and lex it be
dirided into cighe equal ParrS, as in the Figure;
and lec che Ere be ac A. DraW FC ac ristie An
glesto AC, the Axis of che Lye, io represene rhe
Plane oF che Projection; and deam al(o From A
AF, AB, AI, A C, A H, AD, AO, chroue
che sererat Diritions oF the siren Circle; then wil
E B, BO, O E, F P, P D, and D C, bc cho
proxer Representarions ol che Pans  sr
Circleo
T.Tis plain ihe Diamerer B C ill be repre
Tented by che Line FP. Tis allo plain, char il ript
Lines vere drann from A ro all the ParrS OF cto
oblique Cirele, OF wrhich B C is the Diameter, thez
ould makre an oblique Cone oE RaYS, 25
ABC.
2. BuF P Cay thac the Ccalenous Conc OF RayS
A B C is cur by che PIanC F, R, subcontrarily EO it
Base, and consequentty the Section will be a Circle
(by che 34) Wheretore che siren oblique Circle
will alvars be represented by a Circle on the Plane
OFthe Projection.
Thac the Scalenons Cone A B C is cut SubcOn-
crarily eo ies Base, may be chus proved.
Dran AD chroush the Center OF the Sphere R,
and join BD and C D.
The Ansle A C D is a righeone, (beins in a Se-
micirele) and the Angle A H  is righe, by Suppo-
sirion and Construction; and the Angle D AC is
common roche rwo Triangles AH F and AD C
Wheretore cheyare Similar, and consequenty che
Ansle ADC is equal rothe Angle AFK
But che Angle AD C is equal to the AnSIC ABC
as beins in the same Segmene; and the Angle ADC
ras betoreproved =ro the Angle A PK; Wvheretore
the Angle A B C = Angle AF K; and since the
Angle ABC is common co boch, cheretore the
Ansle F must be equal ro che Angle C, and Con
seguentiy the Conc A B C is cur subcontrarily, and
cheretore LP is the Diameter ot a crue Circle
wtose real Centre wilt be in Pche midale Poinr;
buc che apparent Centre of the Circle will be aE L.
ertiere the Poine O (tich is che midele Poine ot
BC) is projected.
There are several otter ays oF cndins P che
Cenere ot che Projected Cirele; buc chis is AS expe-
70
TMS, IE the Eye BC AE A, FCayE
CLir
eBC
Iying oblique eo ic, will be projected into che L inc
D F; and its halF B F, Which lies nearer co che
Ere, Mall De represenced by Line D F, wrtich i
IF a Circle be righe tothe Fre, Or hath irs Plane
L1OP. O. Forepresent on the Plane of che Projectio
Rishe Circle, and to distinsuist there sue
Parts and Ordisions as salt truly corresporutn
those osue   sto.
di
And is on A as a Center vich che Distance A F
another Circle be described, tis plain, chat O F
E B and F F, (3C. Wwill bC Tangenrs oF the An
Bles O A F, BAF, FAF, 8C. ac ihC CC dirious aS arY.