# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/175905688X:0032
# Permalink to this reading: https://leibnizlegible.com/page/175905688X:0032?run=74
# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 10, page id 175905688X:0032
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=32
# Source image: https://digitale-sammlungen.gwlb.de/content/175905688X/jpgs/default/00000032.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 43 lines, status machine
# Lines: 43 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.

CF E O ML E Y R I A
lineis; quaeritur primo punctum, a quo totidem alixre
etx lincae, lingula ad lingulas dacarum duci postine, qux
cum ipsis dacos efficiant angulos, e quarum rectanou-
lum, sub duabus contentum, datam habeat rationem
ad quadratum certixe, si linttres; vel ad rectangulum ic-
liguarum duarum, si sIE quatuOr; Aut li quinque (IME,
ut parallelepipedum, quod sub tribus ex illis compre-
henditur, datam habeat rationem ad parallelepipedum,
quod sub duabus reliquis comprehenditur e alia qua-
dam data; Aut si sex line, ut parallelepipedum sub eri-
bus contentum datam habeat rationem ad parallelepi-
pedum lub tribus reliquis comprehenluu; Aut E Cint lep-
tem, uchioc, quodproducitur ex mulciplicatione qua-
tuor ductarum in se invicem, datam hrabeat iationem ad
illud, quod ex mutua mulciplicatione reliquarum trium
 alia quadam data producitur; Auclisint octo, ut id,
quod ex quatuor ductis inter se mulciplicatis produci-
tur, datam habeat rationem ad productum ex reliquis
quatuor. Acque ita porro quastionem hanc, ad ommem.
alium lincarum numerum, extendere licet.
Deinde, quia semper intinnica sunc puncta, dux latista-
cere postunt iis, jua huc quaeruntur, requiritur inlupei,
ut coonoscatur atque delcribatur linea, in qua illa omnia
reperiantur.
Dicit autem Pappus, Sitantum 3 aut a lincae dentur,
lineam illam tunc aliquam ex sectionibus Conicis exi-
Aere. Verum non suscipit iplam decerminare neque de
Ecribere, non magis quam explicare lineas illas, in qui-
bus quaelica puncta inveniri debent, quando quaeltio pro-
polica est in pluribus lincis. Pantum addie, quod Vetc-
eesunam ex illis libi imaginati tucrint, quam ibidem u
eilem esse monstrarune, sed qua manitestissima videie.
cur, nec tamen prima existeret.. Duod occalionemmi-
hiPFa-
C
re
At
pa
1
c
nC
qulo