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# Title: Leibniz-Handschriften zur Optik und Dioptrik LH 37, 2
# Folio 49r, page id 00068531:0097
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 44v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068531&page=97
# Source image: https://digitale-sammlungen.gwlb.de/content/00068531/jpgs/default/00000097.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 36 lines, status machine
# Lines: 36 recognised, mean confidence 0.91
# 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.

quam, sngemab incento excogdtauit ople sut quoo demonstaari
posset; est etq it ne deincps dethrni geomelnie o postet
quo prause loco radu sncurrant pt refractionem in quocumque
vitro passam cuiuacumquo tondem figura sil sulud, iem it ex
figans oibus ellgi possent illa quae ad hunc gctum cont
aplissima, alie de quibas consturet illas o tam perteces radios
alligere respuerentur. quare nesuio anriolior onguam ad porticiendam
visconem, et ad eam artem certe demceps sundamento Aabiliendam
excogttata sit, aut excogchari in potucit. demonstratur à hoc modo
primum in elxpse, in qua sactu porte diametri h2 ad totum
diametrum d k, et sinces ongule resracto de figura supenons
ad sinum b f anguli smadentia, desoriptlag Alypsi eo modo quo pgulo.
ante datum e, crigitur in ca qddam ex arbetrio panctum b: sum
vero ad slud punctum duutur recta a b parallola diametro
ellypsis d h tantae langitadinis, quantae longstadinis e ipsa b 2
qua intra ellopsim a pancte b duutor ad soum entenorem 1.
demde duotâ bh ad fouum intorcorem h, auitur per b tangens
eC, quae cum bh et b1 de more faccat angulos utrinqu aequeles.
denique ad b ducitur  pependicularis l9, qua bidariam secat
angulum h b 2, ad samqh ex 1 in 9 et ex a n l ducuntar
perpendiculares, quae eum sint attora quidem a l semus sinues
angali smudentiae radii a d, alia vero GL semus anguli resraationis,
ostenduntur ce aB smuicem in ea raoe quam het d k ad 1 li
ae proinde servare praecise intor se rationem quam ex sigura
sapenine Constat ine debere iner radium seu angulum mudentia
et angulum retractionis, sequidem in eaderatione sunt d het
Ih, in praetenti sigura.
Sie à ostonditur d raiem candem treant inter se a l’et GL, quam
raoem tient inter se d k et h I. nam 1 a le ad g2 t 02
ad si 2, et mox domonstrabitur e n a lad 92 Et a b ad
_ 2 ppter simildudinem trangulerum A lb 29n: imo cum ab
sit aequalio ipsi b2 et a l ad 91 ut b 2 ad n 1: e à b2
ad n 1 ut or ad hi ut patet: 90 a l, e ad 9 L ut or ad
nV. gd Si iam 2 loco ostendipt quor sit aequalio mae
diametro b H, a pmimo ad ultsimum concludetur qd al
Se