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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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2. The Semidiamerer of this projected Cilele
C d) is equal+o (C P) Whic
eticT.
Laid Ark P B, or oF char Cireles Distance from irs
All Angles made by Circles on the Supersicies of the
Sphere, are equal vo chose made by cheir Represen-
racives on che elino os che Projection.
Polc.
OP. Z
The Angle of the intersection of any tuo Cireles on a
Plain, is equal to the angle made by their Radi
drann from their Centers ro the Point of Inter
section.
TCaY, IHe Kectilineal Ansle cTn; made by
thervo RadiicT, and Fn, is equal toche Curri
lincal Anele oTC, made by che Arks oT, and
eT; Wwhich is equal also coche Currilineal Ansle
n Y an made by che Arksn Y, and L a.
Deav o F, and P a, Fangenes co che imersect.
Ing Circles.
Thenthe Angles oF Contact, o FC, and n I a-
Wvhich are made by che Tangenes and che Curres
being less chan any Acure ones, and indecd no
Ouantiry; che Pangenco T0, and d T a, will Fal
in wich che Circles, and makre etre same Angles
wich onc anocher, a5 the Acks ot those Circles do:
Wheretore che Currilineal Ansleo TC, is equal 10
the Rectilineat ore o J d; andi on the ortier side
che Currilineal Auslen Pa, is equal rothe Recti
lincal one a P c.
Wheretore since che Rishr lin d Angles d TC,
and o T n, are boch Riphe Angles, and equal: IH
rou cate avay che common Angle oTC, the AN-
Ele d To, must be equalco che Anslec Pn; and
consequeney che Anele cTn, is equal to che AN
fle oF Incersection oY c. 8: H. D.
Texthere be ruo Circles, C and F, interlectine
cach orher ac d.
TCaY, TheAnele Od T, made By che PIaneS OF
these Circles, is equal ro che Angle osh, made by
their Tangenrs od, and d h, Wvhen projected.
Lerrhe Fye be ac A, and che poinc ot incerlecti-
on d; chendraw dh, a Tangene cothe outer C ir-
cle d F, and d o, a Fangent r0 che Inner Circle
de
Then snce che Plane oF che Projection e ∞, 25 al
(0 chat made by the Tangenes a h, and do, (Whick
are in che lame Plane) are boch perpendicular 10
the Plane oF che Circle cT d R; FheIE COIIOI
Incersection oh, must be a Rishe Line, and al(o
Perpendicular 10e 8.
Dran all che Lines, as in theFigure; then will
the Anole A d m, (made by the Tangent and Se-
Cant) be equal coche Anele q. (in he oppolite Ses-
menc) wrhichis equal 10 q d A, becaule the Tri-
ansle q A d, is ani Isosceles; bur che Anole 9 d A
L h8d, becaule q d is parallelro cg: There.
Fore the Anole he d = l Ad m Verrical AN-
ele hd g: Wrheretore che Priane lc h d 5, i5 a1t 1so-
sceles, and consequenes d h = B 8.
Fence che Frianole od B, hach avo Sides,
oh, and ha, and the RighE Anole oh d, equal 10
evo Sides, and one Anssc, in che Trianele obs:
NVheretore all chinss are equal, and consequently
the Ansle osh, is equal co che Angle o d h, equal
co che Currilineal AnslC C dY. 8. F. B.
tR OP. XII.