# Leibniz Legible — https://leibnizlegible.com
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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 806933011:0759
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IIL. I a Scalenous Cone ABC DE Cut B  LEuta
in a subcontrary Position to its Base, the Sectu
DEH nou be a C irelem
Ra75.
4. An Olique Circle, votiose Plane lies osde le
3. A Rixht Circle, vohose Plare is coincidete
Axis oE  23 et WM EnC VIUa
che AXis oF che Fre, P0 chac ic makes unequal An-
8les wich ir
Fo Project the Sphere truly in Plano, is a PAFF OF
Perspective; Whereot chere are several kinds; bui
the most usual is what is proxerty called the Stereo:
graphicte, Ox Solid Projection of the Sphere; aud the
Orthorraphick, or che analemma: The Lallet Ot
ertrich, sec in analemma.
Inche Former, che Circles ot thelo atc arabon
ex reprelenced on a Plane, erhich passes cibuph
irs Center, and hach the Fye, supporec ro be in
che Pole or 900 distant from ic; Poechine the lere
ral Circles or Arks oF Circles on char Planc, Ox on
any one parallel to it.
In ehis Projection, it a Line pals Mouph che
Fiye, or be coincident or Palatus d C XIS, ir wil
be represented by a Point.
IV. Is a Line be direct 1o the Ereq it ill be pro–
i
1. The Section A BC made chroust che Axis,
is a Friangle.
2. The Friangle A F D is Similar E0 A B C,
tho placed a contrary ray, (by che Supposion)
(Whichis called Subcontrary Posicion.))
3. F D beins the mutual Intersection OF EO
Planes wilt be a Riphr Linc, on Which cake any
PoinE, 25 (i) and chroueh ic deaw F i C parallel 10
BC, and ehere ler the Cone be cur al(o, etien the
Plane chac curs ic beins parallel 1o che Bale oF the
Section, P HIC must be a Circle, and F C a Dia-
meter.
Nou, because boch chele Interlectine Planes
arc Righero che Plane ot che Triangle AB C theix
common Incersection IFI, Will allo be a Righe
Linc, and perpendicular co the Plane oF che Fri
anele, and eo the rvo Lines P D and FC. And
then, because che Triansles ABC, A B D and
A F C arc all Similar, che Angles at C and P must
be equal; and che Verrical ones at i beins (0r00,
che Triansse F P I must be Similar e0 ID.
Wheretore D I: IG : : F I: T F. theretore
IDIE = () FIG5 bur because F C is the
Diameter oF a Cirele, and I FI perpendicular ro it,
and cerminared ac che Circumterenco, twill be a
midole Proportional berreen the Segments of the
Diameter, and hare ies Square equal ro the Rect.
angle FIG, (a5 aI(0 eO iEs Bqual F ID) where-
Fore che Poine II is in the Circumterence of a Cir-
cle, wohose Diameter is D F. 8. F. D.
DEFENETIONT
ACirole of the Sphere, as eo its Projection on any
Plane, is oF tour Kincs.
I. The Primitive Circlo, or Limb ehich bounds
ehe Projection, and wichin wrtich ris alvars
made.
2. A Direct Circle, whole Plane is directiy oppo-
sirero che Fyc, or iotien che Ere is in chc Axis ot
The Plane.
merer ot a larallel Circle) is luppolea cone lalal
telto D F, and is projected into ir from the Lye at
A, il rou deaw rhe LineS AD, A F, and AF, che
Triangles ABC and AD F will be Similar; 25
also will A CFC and A F F; Wheretore aS AB
AD:: BC: D F. and as AB: AD:: AC3
(+ L.  dd L 5 2L~:: BC: DP :: C
L F. Trasct ad CHC. Wose BC Wo che Wvhole
F  116 L at BL.. 6C.
sected into a t LMe, nisse lals be in
the same Proporrion to one another, as those os
the Primitive Line, os which it is the Repre-
sentation.
Fo, Since The Line B C (WIIICM LLIA) DE LHCBIa-
PRO