# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1041163592:0122
# Permalink to this reading: https://leibnizlegible.com/page/1041163592:0122?run=74
# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 88, page id 1041163592:0122
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1041163592&page=122
# Source image: https://digitale-sammlungen.gwlb.de/content/1041163592/jpgs/default/00000122.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 41 lines, status machine
# Lines: 41 recognised, mean confidence 0.92
# 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.

8.8
PTTTLOSODMTLE NATDRALIS
De Moro dum Frajectoria describebatur, demitre normalem O FI Circulo oc-
EORFONOM CUIEECnEeM in RL eE L. FC ubi crura illa alEerA CK, BR CONCUT-
runc ad punctum illud E quod Resulae propius est, crura prima
CF, BP Parallela crune axi majori, e perpendicularia minori;
e contrarium evenict s crura eadem concurrunt ad punctum remo-
tius L. Onde li decur Frajectoriae cenerum, dabuntur axes. Hisce
aucem datis, umbilici sunE in prOmpeu.
Arium vero quadrata sune ad invicem uE R EL ad L. FI, ec inde
Facile est Prajectoriam
specie datam per data
quatuor puncta deseri-
berc. Nam (I duo Cx
punctis datis constitu.
antur poli C, B, tertium
dabit angulos mobiles
PCK, Y BK; his au-
tem datis delcribi porest
Circulus YBKG C.
Tum ob datam specie
Prajectoriam, dabitur
ratio OFI ad OK, ad-
eoque ipsa OII. Cen-
tro O de interralloOH
describe alium circulum,
ex recta quae tangit hunc circulum, al clansit per concurlum crurunt
C.K, BK, ubi crura prima C P, B F concurrunt ad quartum da-
cum punctum erit Regula illa M N cujus opc Prajectoria descri
Betur. Inde etiam vicissim Prapezium specie dacum (si casus qui-
dam impossibiles excipianeur) in daca quaris Sectione Conica in-
scribi potect.
Sunt ec alia Lemmata quorum opc Prajectoria specie date,
datis punctis ex tangentibus, describi portunt. ljus generis
eA quod, s recta linca per punctum quodris positione datum
ducatur, guae datam Conifectionem in punctis duobus interse-
cet, e interfectionum incerrallum bisccetur, punctum bisectionis
tanset aliam Coniseetionem ejusdem speciei cum priore, aeque
axes habencem prioris axibus parallelos. Sed propero ad magis
veilia.
VLMLAA