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# Title: Leibniz-Handschriften zur Optik und Dioptrik LH 37, 2
# Folio 95v, page id 00068531:0190
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 91 lines, status machine
# Lines: 91 recognised, mean confidence 0.82
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vale est autem B perpendiclaris
expahuc melius si langentem alite
cuenlationem circu centrum B vocemus
. Sc. dtp:
Data curo. Ft invenire curvam ZG talem, ut omnes radus
qui paralleli incidunt in FF, ut DF inde n refringantur
in punctum datum  B.
: Est : to N. 9 ∞: : 2cd: IdB: (B
Ergo _ BB eB +c. Ergo
Quod motabile i B+to AEBEC
sit  Per punctum B ducatur recta radiis parusleta
nempe BG ett ex puncto curvae F ad eam ducatur ordinata 
cumcmora sit erit BG abscissa, FG ordinata, illa appelletur
X haec y. et cumdetur curva natura dabitur et relatio
inter X et y. sit FP. perpendicularis ad curvam
axi occurrens in P. dabitur et GP. nempe u (per
methodum inveniendi tangentes curvae datae. nempe FG: GP::
=: x: dy. tam radius DF ipsi BG parallelus non perget
versus H in linea recta sed intrans in vituum refringetur
ad perpendicularem in FM versus perpendicularem  P.
ita ut si centro F radio FH aequ. c. describatur circulus secans
FM in M, et ex punctis H. M. in FP ducantur perpendiculares
HL. MN. data sit ratu HL: MN:: d. e. secundum
quantitatem refractionis vitri. Quia PH paralleta G,P
erit trianus. FL H simile triangulo pGF et quium
fiet ponmus PG: GF: PF:: ty: dx: da. (posito du p Sdx ad). FL. Ht.
et FH aqu. C. fiet: FLH Cdqe HL C dx iam Ma HL, e
et
ego MNB ce  et FN  M M  N E . eo 11 S tB. C2
Porro FM radius refraetus contrnnatusque occuvrat, curvae gq un puncto que
Habetur in porro ex d punctis R. Q. calculo habetur FQ
fit enim est enim FK + HQ A FQ et FK  GA 
enim BR H Z. RZ B V. jam FK +KZ B FQ
sit
et
FKH GRA BG - BR p X - Z. etKQY, GF - RQA  7 L B
fiet FQB 1) X - Z + 14g. . Ex puncto Q in ipsam F
ducatur perpendicularis GV. eritque FM: AV:. FQ: EV.:: ddod: C d
Ergo 2) ,A  F. 2 + C qu vl edi.
d duo
y
1
jam 2): 2d. ek. PB: : FG. BF.: dy: u
hoo 2dp 1 a  C D etu.
Porro FD. FK:: FB: PR.:  deo: de
Ergo FB C FK X -3 de
rursus FBp (CKN A Z + XxA in Cto ruvu S . 
aedus
Quos duos valores aequando et pro dco ponendo dxadu fiet:
1al X Z d rdtu
u  A ()  Z + (2)7 B  12 C a
Cn 2 , B C a2 e t
de’dus
(2) X27 dx  16  B () g. v C1 + C tu f
Hac rel aquatio n dificile. ntom
BE V,  +  quod notibile
unus nempe Z B vocaddo 1. et
V dc fier
eF
a
est
a dio
item inter dy et x erc tolli possunt dx. tu. item alterat in
harum duarum X et y. igitur acua ad huc aequatione opus est
qua tollatur et altera, ut scilicet tantum restent Z et v
Hanc novam ita porro pergendo inveniemus. Radius FG ipsi
curvae occurrens inde refringitur non pergit in es diae recta linea
sad ibi ex vitro in aerem egreditur adeoque refringitur a perpendiatum
5Z in QB occuriens tandem puncto dato B.
ponntu
sumatur q5aequ. 9B. et ex punctis S. B. in ipsam perpendicularem curvae
nempe sique  T ducuntur perpendiculare, Bcd. 5F. Et quidem
BC  bis inveniri potest primum ex eo quod semper in curva
supposita ut data perpendicularis ex puncto dato ad curvae perpen
seu langenti curvae parallela) duci potest.  sed eadem BC et
ex eo habetur quod ratio ejus ad 5  data est. Primum itaque Bad
Equaeramus exurore communi methodo ex curva
datur anta
ducatur B perpendicularis ad GB. et (ipsi 4 A9 productae necurre
in a poter  faciamus: dip 1 dz + do.
AR. RE. AZ: do: du: L i AB BS. Aa :. A :D B: AB. datur anter
seu dep 42 + d0
Z+ du  dc + du C  EV ABr AR +RB. ARH _ v tBA Z fier AB, n
et .B5 1, + d0 ∞ C   v, de + an
dix
tarodr sere
part
140
vel
bax
vit pet