# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1041163592:0168
# Permalink to this reading: https://leibnizlegible.com/page/1041163592:0168?run=74
# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 134, page id 1041163592:0168
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1041163592&page=168
# Source image: https://digitale-sammlungen.gwlb.de/content/1041163592/jpgs/default/00000168.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 32 lines, status machine
# Lines: 32 recognised, mean confidence 0.95
# 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.

134
DHTILOSOPHILLE NATDRALIS
Moro aequalibus, rel describene FIipses in plano illo circa centrum C.
Conxonvn vel periodos morendi ulero cieroque in lineis rectis per centrum C
in plano illo ductis, complcbunt. 8. F. D.
Scholium.
FIis attines Cune ascensus ac descensus corporum in superfciebus
curvis. Concipe lineas curras in plano delcribi, dein circa dres
quolris dacos per centrum Virium transcuntes revolvi, ec ca revo-
lutione superficies curras describere; tum corpora ita moveri ut
eorum centra in his superAciebus PerPCTUO rEPCRiIaNEUr. Si COr-
pora illa oblique ascendendo ec descendendo currant ulero cirroque
peragentur corum motus in planis per axem transcuntibus, atque
adeo in lineis curvis quarum revolutione curre illae supertcies sc-
nIEx TUnE. Ictis igicur in casibus sufficit motum in his lineis cur-
vis considerare.
PROPOSITIO ZIVIII TMEOREMA XVI
Si Rota Globo extrinsecus ad anculos rectos insistat, e more ro-
tarum revolvendo proerediatur in circulo maximo; loncitudo
Trineris curvilinei, quod punctum quodvis in Rotae perimetro da
tum, ex quo Clobum tetioit, confecit, (quodque Cycloidem vel
Fpicycloidem nominare licet) erit ad duplicatum sinum versum
arcus dimidii qui Clobum ex eo tempore inter eundum tetioit,
ut summa diametrorum Clobi e Rotae ad semidiametrum Clobi.
PROPOSITIOZIIZ. TTIEOREMA XVII
Si Rota Clobo concavo ad rectos angulos intrinsecus insistat es re-
volvendo proerediatur in circulo maximo: loncitudo Ttineris
curvilinei quod punctum quodvis in Rotae perimetro datum, ex
quo Globum retieit, confecit, erit ad duplicatum sinum versum
arcus dimidii qui Clobum 1oto hoc tempore inter eundum reti-
sit, ut differentia diametrorum Clobi e Rotae ad semidiame-
trum Clobi.