# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/806933011:0346
# Permalink to this reading: https://leibnizlegible.com/page/806933011:0346?run=74
# Title: Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences (shelfmarks Leibn. Marg. 71; ZEN Leibn. Marg. 71)
# Folio - , page id 806933011:0346
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=806933011&page=346
# Source image: https://digitale-sammlungen.gwlb.de/content/806933011/jpgs/default/00000346.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 121 lines, status machine
# Lines: 121 recognised, mean confidence 0.89
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

2. In PlanoConcave Classes, when the Ray.
Fall Parallel to che Aris, che Virtuat Pocus iS de
stane from the Clals che Diamerer oF the Conca
vits.
3. In Plano. Concare Clases ; A5 107: 193:
Sorhe Radius of the Concarity:
Toche Distance oF ehe Virtual FOEUS.
4. In double Concares oF the Came Sphere, Pa
Fallel Rays hare cheir Virrual Focus ac che Dictance
oF che Radius of che Concarier.
Bur Whecher the Concariries be equal or une
qual, ehe Virruat Focus, er Point of Divergency 
the Parallel Rays, is decermined by this Rule:
AS theSum. oF the Radii oF boch Concariries:
Isro rhe Radius ot cither Concavier: :
S0 is che double Radius of cother Concarity:
T0 che Distance oF che Virrual Focus.
5. In Concave Clattes, il ihe Poine co which che
incident Ray Converges, be distant trom the Glass
Carcher than che Virtual Focus oF Parallel Ray
The Rule findins che Virtual Focus oE chis RaY,
this:
A5 the Diserence berween che Distance oF chi
Poine trom ihe Otals, and the Distance oF the Vir.
tual Locus From che Class:
Is ro rhe Distance oF rhe Vircual Foeus:
S0 he Distance oF chis POInE OF COnVersenCC
Fromthe Glass:
Fo che Distance oF che Virtual Foeus oF chis
Convergins Ray.
S. In Concave Classes, is che Poine r0 which
che Incidene Ray Converses, be nigher c0 che
Clals chan che Vircual Focus of Parallel R ays: Th
Rule co find where it crosses the Aris is tMIS.
ASthe Fxce(S OF the Virrual Focus morechanchii
Poine OF Conversenc):
Torhe Vircual Focus:
So che Distance oF ehis Point OF ConVergenC)
From the GlaIS:
Foihe Distance os che Poine Where chis Ra)
croresche Anis.
7. Fotind che Focus oF a Meniscus GlasS; sec
under the Word Menisens.
Practicat Rules for findins the FOci of Cilasses.
For Convex Spherick Classes.
IFit be a Plano Convex Class, makce it resect che
Sun against a WVall; Wve Mall on the. Wall perceire
CD IOLIS OL LISHL:, one more brieht wichin ano
Wal eill rhe brisht LIMasC IS aE iS Imallest, che
Cla(S is then distant trom the W all abOnEThC FOULH
abouc hass ee Ldaus d he Conrerier curna
trom the Sun: And che sccond Dittance is about
half che Radius of c’ocher Convexies litewile
As the Sum ot the Hac et Borh Converirs:
Toche Radius ot cirher Convexity
Soisthe double Radius oF che other Conrexs,
Toche Distance OF chC FOCUS.
ThC Foci os Concares ave obcairid by Reslecti
On; FOr aS a Concave Mirror, Ox Speculum, burrS
ac the Distance oF abBBE halF the Radius OF Mhe
Concarier; (0 a Concave Glass, beine supposed, a
Restectine Speculum, MaII unite che Rays OF che
Sun ac che Distance ot abour halt ehe Radius ot
the Caritr.
MP. HallesSDoctrine oF che Foci oE Spherical
Classes oF aHI Porrs, expoled cither 10 Di
vergins, Conrergins, or Parallel Rays, is ad
Follos. Sec Appendix 10 Molyneuxs Diop
ricte.
PROPOSTTION
Zo find he Fccus os any Pareet es Rays Divereine
trom, or Convergins ro a siven Point in the Aris
os a Spherical Lens, and inclined therero under
the same Anele, ihe Rario of, the Sines in Refra
ction dme onu.
Cthe Cenret et che Sphiere, Whereot it 15 2
Oche Object or Poine in che Axis, 10 Or FCOMC
Wtrich che Rays do procced.
OP a sivel tas.
Lex che Rario oF Retraction be 25 r 20s: Make
CRIOC O aSSTOr, FOF che Immersion O( 2 R aY;
OF aSr tO sFor the Fmersion: (that is, 25 che Sines
I. FOr Clases oF Imall SphereS, (thac is, OF OFche Aneles in che Medium which c’e Rayenters
deep Converities) applr chem cocheend ol a Scale eo cheir correspondins Sines in the Medium out ot
ot Tnches and Decimal Parrs, and expole chem be-
Fore che Sun; and upon the Scale we all find che
brighe Intersection ot the Rars exactr measured
ont; or expolechem in the LTole oE a dark Cham
ber, and phere a WVhice P’aper receires the distinct
Representarion oE distant Objects. there is the FO-
cus oF chis Clals. Thisis an unirerlal and cerrain
Wvaz For all Converes.
Whichic comes.)
And lavins C R Crom C comards O, che Poine
Rs Mall BC che Canic Cor all che Rays ot e
PoincO.
Then deaw che Radius P C il necd be, conti-
nued, and wichche Cenere R, and Distance O P
Crcep a touch of an Arch incerlecting P C in C.
the Line QR being deawn, Mall BC Parallel coche
refracted Rar; and P F beins made parallel there.
For a Clato ot a prels sonB Locuo, erde co Mall incerseet che Axis in che Poine F, wohich is
fome distane Objects chro ic, and recede from the FOCUS TOUGHE.
he OlaIS, tillthe Fre perceires all in C’onfusion, Or
rill che Objects besinco axpeas inverced; liere Ese
Eye is in che Focus.
Or matie iE a5 CO: CP:: CR: CF, ane
CF Mall be the Distance os ehie Focus seom ihe
Demonstration.
FHCL MMOTC obscure, WIC a MC Cales Fromthe
Pa OF is Focal L. enBch.
TFic be a double Loc exPole each side r0 che
ces ofrheClals trom the all. LIC SI BManceis
Sun in like manner, and oblerre boch the liltan-
Whence che Locus is Found by chis Rule.
Thus we hare che Radii ot the rmo Conrexicies;
Let  L Bethe Lens.
P any Pone n is Surtace.
Vile Polechereot.
Scoiment.
Ceriter ot the Sphere.