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# Title: LBr. 57, 2 · Bernoulli, Joh.
# Folio 153r, page id DE-611-HS-3653099:0305
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 152v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-3653099&page=305
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-3653099/jpgs/default/00000305.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 38 lines, status machine
# Lines: 38 recognised, mean confidence 0.94
# 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.

sillum attendere velles, videres statium speculum spha
ricum non minus utile posse  esse quam onne aliud
elliplicum; fateo cassua posce ocurrere quo s speculum
spharicum eadem curva redeat, sed idem etiam contia
gere posse  speculum nioci ellipdicum jam ea prae
cedeatibus monur, ad quod respondisti eum casum
posse evitari mutata tantum ellipsi, idem nunc dico
fieri posse mutata tantum sphara, id est, majoro mino
rive sphara adhibita; curvas autem per specula
spharica ordinarie diversas esse a daris, vel hine
patet quod aliquando curva ca se rediens pro cata
caustica sua habere possit curvam aspntoticam ad est
in infinitum abeuntem, quod idem etiam in speculis elli
imoin quavis curva
plicis contiagere posse facile perspicio; sit enim steculum
spharicum AGD; clerva aliqua CNB radiaas se
cundum tangentes NG; ejus catacanrtica LKD
quae ainaum forpatur per interscitiones
radiorum reflexorum Gk; pro Lujus forma
tione duo sumerdam esse GL = NGXGF; et ge
 RG: NBE FG: NGquaterCC. jam ocum, cir ANG GFicissim
Tesit radians et ABcata caxstica, sid SN=KG. GF: AFGA5, sed quia GH = GF, redit aequadio prior
Et ge heraliter si speculum sit concavum qualemna
VGX; at quaratur longitudo radim reflexi: descir
bendus eet circulus orculator in G, qui secet
radium cacideatem NG(i opus est) prolongatum
in F, erit semper GK = NG~GF
4NG-GF
quod no
vum ea theorema horteaus nondum cognitum, un
de apparet, quelecunque sit speculum sive spharim
sive aliud, et qualiscuaque curva data CNB eliaasi
ia se redieas, modo eo propiaguitatis acedat ad speculius
ut NG tandem aequetur LFG; fore tuac Gk infiait.
id est catacaupicam LAP habituram ospatoton SR, et
portea evadente NG miavre qua GF, mutai calacaulicaa LAP
s
se