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# Title: Leibniz-Handschriften zur Optik und Dioptrik LH 37, 2
# Folio 75r, page id 00068531:0149
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 76v); this page is its right half.
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 106 lines, status machine
# Lines: 106 recognised, mean confidence 0.80
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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eulemus an per meras  superficies
circulares radii  inter se paralleli in unum
punctum cogi possint. Id quoniam constat
uno vitro fieri non posse, tentemus an praestari
possit duobus. Inspiciatur huc fignua quae
est ascripta problemati. data una superficie
lentis invenire aliam ita ut radii paralleli
priorem incidentes in uniam punctum
aatc t et eC
 ea tantum erit
Sa p AX. RA pt eiit recta constans.
AA erit recta conslans B  Ast BL  C- Z.
n2- XC
vic+ Cx Z- 7F- 2 3C S9b- 5
3X - vx CyD +Z)
ie vier ais -9.  p. 8b - 5.
64 yZ- XV,
Dioptricum generalem, et posito
primis radio incidere paralt circulo paralle 
ejus diam etro ejus inter se adeoque diametr
qY +X B∞. et Gerit constans
Aa L Z. eAt  erit recta constans.
esfeet: 
hp n’X + YC
ya 
 et rie nosetrsomvereie
9653 C -  2dgu S b(F 2X3  v5  , X~ 9B xvyC
528+ XvO=  292 ro  (D unar
q. EpE
B. I 5 . V.5 = 2V 5 1XZ
Et ABea  L. fC VV 30 - l. Z
l. Or
de
refringi in punct data
ut radius refractus primus dirigatur
versus punctum axis (H). Setmus a
a  idem a secuma superficie refract
diigatur versus punctum axis (H) idem
Si A 5 p av 9. 1v9 (2 
d
a tertia superficie refractus dirigatur
versus punctum axis (H)adem
deniq quarta superficie re fractu
irigatur versus punctum Axis ((HB
sitque sumtoque puncto fixo in axe
nempe dtro circul primi, quod sit s
sit AF AH) aequ (h) ACHph
A(H ) h) A B(
positisque radiis circulorum
 primi s, seu
tertii 17).  quar 
at ((a)) aequel ADB. ete
fiat ateng. quid a et e. datae,
92D V+ 8Ov 29. 11D0, 1. p 3= 212BO quaea quatio efficienda ine expliaatione in determinatarum
uX
L On fo rap. lanc f me 
1mB eet eg- eo  2) ( (Y B + vd
Recurr 
Ch) tan 
Bs- cy p Ysuc + nc XC B
Bes ex sip YA YSC X
(h) (i l
s imit
punctum
Nlig + 2xH 6((7 - (h3 be sy) - 16) (X) b
ahD (SD ceti
Y 1s ( CXx q 25p 5C +250∞ (1Y F
umanstsib
Ah1)
D(y rch + uxto b(5) ct D C = chD ∞HC
153) byht
2) (h t(B C((12) - (h NBY) Z ( X
Itaque in valore posterioris h. semper inserendus valor prioris
Praeterea quia in quo incipiendum ab ultimo ht nempest
eique inserendus valor penultimi, et lumc
alor ante penultimi, usque ad primum.  quod melius
est quam si incipiamus a secundo et huic inseramus
Hine si hnon est quantitas constaas
primum et tertio secundum hc. quia primum h
Rutrus cur potius regrediendum quam  prab ultimo si eti qu
quam a primo progrediendum haec est quodue primum
est roterogeneum nonnihit unde culcillum statim
ab intio turbat al piendur ab ultimo semper
tua somileter compositi valores inseruntur, et ita
 quodam ordinie procedis, uscad prmum epclusive
in e ves tertio sconum, asses
Recurratur ideo ad calculum meum
o citenti
et y. vel (y) vel (ys etc. ordinata a
et y ordita a
noto sin circuli ad axem  abscisse
inde a centro usque ad ordinatam
defractiones metiente.
a aequ A(A). (a) aeqo (A) A).
a
inde et X. (X) ((X)) etc. abscissa in
e e et b ratione b.  ad c
Et Ae
ex qua patet no
Hetori 9 er
S6. 5-cEyt - XC
compendi
si
9
(5)l
) ac 2) 51.) - by - (2 b