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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 274, page id 175905688X:0296
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=296
# Source image: https://digitale-sammlungen.gwlb.de/content/175905688X/jpgs/default/00000296.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 34 lines, status machine
# Lines: 34 recognised, mean confidence 0.86
# 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.

274
DK X
1a
FR AN CISCE, d SCHOOFFN
ad EEpatet DK ad HI Tesse, ut a d ad ae, hoc estr
ut d ad c. Ouod iplum, cum de quoris radio A B ip (i D K paral-
delo similicer incellioendum sE, Hos docet, ope ritri Flliprici
DBK, in quo DK ad FT Leandem habet rationem, quam d’ade,
hoc es, candem quam inter le serrant linex, qua hujus vitrire-
Fractionem metiuntur, radios, qui in aere existentes diametro
DE sune paralleli, omnes ita decorqueri, uc, postquam superti.
eiem ejus conrexam D B K tranlierume, collisancur sumul in
puncto I.
Denique Si Fuerie vierum, habens Figuram TEyperbolae DB,
cujusaxis (IED K: ad investigandum, quo pacto radius AB, qui
in ritro existens ip(i DR est parallelus, se infectere debcat, polt.
quam superticiem ejus conrexam D B cric egresus, supponendo
ejuldem rieri refractionem esse eam, qua est inter lineas dex e, ta
cioTID vel RI∞A, HI∞Z, _ DF∞V: ericque F HI ∞ y = 1
vela -7, de FI∞Z. Fy -a. Ouibus politis, (i Fsyporbola DB
descripta intelligatur beneticio tili, quemadmodum Capite 8ro
Dioperices ab Authore tuit indicacum, vel etiam a nobis libro q
Exercitationum nostrarum Machematicarum, erie, Fact a B I∞H,
BFI∞∞ =Z-F 2 a. EInde jam Facile est invenire quantitatem y.
supponendo quippe quantitates x e Z eRe cognicae. Si enim à
quadrato BFI. X X -  Z ∞ + 2Z. + 4 a X = = a Z  + a a Cubduca
cur quadracum FFI. yy =  ay- F aa, rectabiex x -  Z ∞ L L
Yy. F ay. F3 aa F + a ∞ = = aZ. PrO quadrato F B. Similiter, si
a quadrato BI. x x auteratur quadratum FI.
aZ = ay + a a, relINGUCEUY QUOqUC X X = Z
2Z y + yy-
y - yy +
aZ. F ay = aa, prO quadrato FB. Flinc, cum habeatur a quatio
inter