# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1041163592:0195
# Permalink to this reading: https://leibnizlegible.com/page/1041163592:0195?run=74
# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 161, page id 1041163592:0195
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1041163592&page=195
# Source image: https://digitale-sammlungen.gwlb.de/content/1041163592/jpgs/default/00000195.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 47 lines, status machine
# Lines: 47 recognised, mean confidence 0.89
# 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.

PRIHCIDLA MATTEMATICA.
L
ris periodici inverse: Patet hanc rationem compositam diminui per
Lt ∞ 6. X
actionem vis PL, adeoque cempus periodicum, si maneae Orbis Pumos.
radius Y P, augeri, idque in subduplicata ratione qua ris illa cen-
cripeta diminuitur: auctoque adco vel diminuto hoc Radio, tem-
Dus periodicum augeri magis, vel diminui minus quam in Radii hu-
sus ratione sesquiplicata, per Corol. 6. Prop. IV. Si ris illa COrpOrIS
cencralis paulatim lansuesceret, corpus P minus semper ee minus
actractum perpetuo recederet lonsius a centro Z; ec contra, si vis
illa auseretur, accederet propius. Ergo si actio corporis longin.
qui S qua vis illa diminuitur, augeatur ac diminuatur per vices:
augebitur simul ac diminuetur Radius P P per riceS, e tempus De-
riodicum augebitur ac diminuetur in ratione composita ex ratione
selquiplicata Radii ec rarione subduplicata qua ris illa CenEFIDCEL
corporis centralis T, per incrementum vel decrementum actionis
corporis longinqui S, diminuitur vel augetur.
Corol. 7. F.X praemisis consequitur etiam quod Elliplcos a COr-
Pore P descriptae Axis, seu Aplidum linca, quoad mocum angula-
rem progreditur de regreditur per rices, sed magis tamen progre-
ditur, et in singulis corporis rerolutionibus per exceltum progrei-
sionis Fertur in consequentia. Nam vis qua Corpus P urgetur in
CorpuS T in Ouadraturis, ubi vis M N cranuie, Componitur ex vi
L. M et ri centripeta qua corpus P crahit corpus P. Vis prior L. M
si aureacur distantia P F, augetur in eadem fere ratione cum hac
distantia, ec vis posterior decreseit in duplicata illa ratione, 2deo-
que summa harum virium decrescit in minore quam duplicata ra-
cione distantia PT, _E PrOPFerCA (per C OrOL. T. PFOD. ZLV) eHicit
uE Aux, seu Apsis Cumma, regrediatur. In Conjunetione vero et
Opposicione, vis qua corpus P urgetur in corpus P disterentia eAt
incer vim qua COrpus T trahie corpus F ec vim KF; ec differen
eia illas propcerea quod ris RL ausetur quamproxime in rarione
distantix F F, decrescit in majore quam duplicata ratione distan-
tiae F FT, adeoque (per COrOL. L. PEOD. XL V) CHICIE UE AuX Progre.
diatur. In locis incer S72y gias ec Ouadraturas pendet morus Au-
sis ex causa veraque conjunctim adeo ue pro hujus vel alterius
excessu progrediatur ipsa vel regrediatur. Onde cum vis KL in
Syzygiis sic quasi duplo major quam ris L. M in Guadraturis, ex-
cessus in toca revolutione erie penes vim R L, transferecque AU
dem singulis revolutionibus in consequencia. Veritas aurem hujus
de praecedentis Corollarii Facilius intelligetur concipiendo Systema
corporum duorum Z, P corporibus pluribus 5, 5, 5, ecc. in Or-
BC F SF. consistentibus, undique cinsi. Namque horum actioni-
buS
HIIIHMIIIIHIII
ATTHTETHEAIHEIIIEEHTEIHEI HIETBIHTPTENTTINTETEITHTTHHNETHHINTIHIHEINTIBIIIIIIIII