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# Title: Leibniz-Handschriften zur Optik und Dioptrik LH 37, 2
# Folio 121r, page id 00068531:0241
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068531&page=241
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 71 lines, status machine
# Lines: 71 recognised, mean confidence 0.91
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=si punc Lucidum L
 per supficiem
s ad eu redu
sis in refracte
etiam L5. V5) adeoque
Calentus Refractionum ad superficiem circularem
perspicuum refringens)
Da
N Lucidum L in superficiem AR, cujus axis,  projicit
radium LR, qui sine refuctione contumatus fuisset versas
reliactu Radique sine re fractione continuatus foret RC
radius refractus seu verus RV axi occurrens in V.
quaeritur longitudo ipsius AV ex data natura curvae AR
AD superficies tangens in
ordinata AN.
sit
aremlemad quam perpondicularis PR axi occurcat in P
in S
sit SR e tangens curvam AR in R, sexans axem in 5
et ex R angulo SR P recto educta R Paxi occurm p
ex et in SR agantur no sinq seu normales LT in medio
tenniore, VD in medio d
jam sinus angulova LT et VD sinus angulorum inci
dentiae et refractionis sunt in composita ratione
diametrorum et rationis refractionem metientis
quae sit +: d, fiet LT: VD.. t. LR: d. RVR
e
porro datur LA item AP. datur ergo, item AP ex Hypothest
puncti R, et AP ex natu
et ob angu trvangula LFS (et PX R similia fiet
LT: LS:: PX: PR, et C VD. VS:: PX: PR
 +. LR: d. VR
2
D:: S: V
jam LR  LX = IX VR - VX = XR seu Et (S,VS lndux
L
T.
unde LT. VD  et
R+ LX itaque fiet LR: YR:: IXR+ LC
2.+xB + VX = dL5: tV5
et fiet X R + L X. Hoc est Notabile autem theorema est
rad ios incidetem et refractum t R et LS LS: VS:: t. LR: d. VK
seu axem seu distant LV distantoum puncti emissentes et recipientis
radium a superficie refringente fecoriuasR ecari in ratione compo–
sita radiorum incidentis et recracti et resistentiae superficieru
ecar
LA, V R. et resstenti resistentrae mediorum t, et d
vel qua quod eodem redit radios LR incidentem et RV refactum
esse in ratione composita ex cortionis viam radii in uno medio esse
perm in Tradiare
itellinau
s
2
punet tantam et proinde
utrumque punctum emitens
da ad viam in alio medio in ratione directa in composita
ex is rectes portionibus
LS: VS :: t. LR: d. VR seu LR. RV.: d. LB. t. 5)
ex puncto L unius medii radius perveniat.
in punctum  alterius medii et media per superfiliem planam
si Lcidum  si
cet superficies separatrix sR plana intelligatur erit via
radii in uno medio ad viam ejusdem in alio media seu LR ad RV
et recipiens aeque a super
eR ar seu secantes copsto in composita ratione ex ratione dipta viarum brevissimarum
seu ratio
ficie re fringente abesse
intelligantur erunt radi
ocus in reci procabademedion
medtorum.  seu ratione d ad +. Quod ti LF. 10 poneiteitur a pales ue
tam