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# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 291, page id 175906937X:0315
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=315
# Source image: https://digitale-sammlungen.gwlb.de/content/175906937X/jpgs/default/00000315.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 48 lines, status machine
# Lines: 48 recognised, mean confidence 0.83
# 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.

ri
p
I F B. II. C A P. TII.
Sulum FIMO ∞ CCZZ eea
au b: hinc cum ex natura Lyperboles
Sic utlatus rectum ad tranlverlum, sire ut bb ad ee, ita M F qua-
dracum, id est, vr, ad praedictum rectangulum HIM O: erir
ecvV CCZZ eeat
bb3
qb4 e multiplicatis omnibus terminis per aa
Factoque per cedirilo,
aa00
vy
a0
bb ∞2 p Dein restitutoy
in locum ipluIs Z, exurset
YV V
BB ∞yy - 243y
60; adeoque, multi-
plicatis omnibus per b b, Factoque diriso per aa, habebieur
VV∞
2 a
== 2 ay. Denique restituto x -- in locum ipliuSV,
expunctisque iis qua se inricem destruune, atque omnibus rite
Ordinatis, tet W N L 2 ay ∞=
. Ouodtuit propolicum.
P R O B L E M A IL
Propositio 16.
Datis duobus punctis certium invenire, a 9uo 2d
bina data ductx rectae lincae dato differant intcrrallo,
locumque decerminare ac describere, quem quaesitum.
punctum contingat.
Sint data duo puncta A e B, oporteatque invenire tertium, ut-
Duca C, Uanempeuc duex rectae C A, C B differant datointer-
raliloFC (eu AD.
Ouoniam in quaectione angulus datus non est, quo Facilior (IE
operatio, assumatur rectus, ideoque a puncto C in rectam A B,
qua data puncta conjunsit, productam, siopus fuerie, intellisa-
cur demicsa perpendicularis, uc C F; cum, suppolitis, juxta Re-
sulam, AF X F. C incognitis atque indeterminatis, assumpeum
angulum A F. C comprehendentibus, tanquam cognitis ac deter-
inatiS, CaTUM PTIOF, NIIIFUI AF, VOCCtUE X, ac PolterIOE,
nempe EC, nominetury, ipsa autem AB, seu datorum puncto-
rum coenita distantia, rocetura, _e data FC sive A D exprima-
tuT Per b. FIinc cum BF sive (si punctum B CadAEINEOF A _ F.)
AF = AB, auc ((i punCtu P inter A e B cad at) AB - AP (IE
C
∞ X