# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/1041163592:0164 # Permalink to this reading: https://leibnizlegible.com/page/1041163592:0164?run=74 # Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166) # Folio 130, page id 1041163592:0164 # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1041163592&page=164 # Source image: https://digitale-sammlungen.gwlb.de/content/1041163592/jpgs/default/00000164.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 45 lines, status machine # Lines: 45 recognised, mean confidence 0.87 # 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. n PMIILOSOPHISE NATVRALIS kronvI dCx CA m = 3. Id quod per Exempla sccunda manifettum cst. Unde liguet rim illam in majore quam criplicata alticudinisratione, in recessu à centro, decrescere non posse: C. Orpus tali vi revolvens seque APSide discedens, si caeperit descendere nunquam perreniet ad apsidem imam scu alticudinem minimam, sed descendetusque ad centrum, describens Curram illam lineam de qua egimus in C Or. 3. PrOP. XLI. Sin caeperit illud, de Apside discedens, vel minimum alcendere; alcender in intinitum, neque unquam perveniet ad AP. sidem summam. Delcribec enim Curram illam lineam de qua ac rum est in codem Corol. ec in Corol. 6, Prop. ZLIV. Sic et ubi zis. iprecessu a centro, decrescit in majore quam triplicata ratione alcitudinis, corpus de Apside discedens, perinde ut caeperit descen- dere vel ascendere, vel descendet ad centrum ulque vel ascendet in infinitum. Ac s vis, in recessu a centro, vel decrelcat in minore quam criplicata ratione alcitudinis, vel creleat in alcieudinis ratione quacunque; corpus nunquam descendet ad centrum usque, (ed act Apsidem imam aliquando pervenict: de contra, si corpus de ApSi- de 2d Apsidem alternis vicibus descendens et ascendens nunquam appellac ad centrum; vis in recessu a centro aut augebitur, aut in minore quam triplicaca altitudinis ratione decrelcet: ex quo ci- eius corpus de Apside ad apsidem redierie, eo longius ratio virium receder a ratione illa criplicata. VF S corpus revolutionibus 8 vel 4 vel 2 vel 12 de ApCide Cumma ad apsidem Cummam alterno de- Ecensu e ascensu redierit; hoc CA, Si FuCrIE m ad n uE 8 vel 4 vel nn 2 vel 2= ad 1, ad eoque inm = 3 raleat 5+= 3vel 16 = 3 vel + = 3 rel 3 = 3: CriE viS UE A64 3 vel A 16 3 vel A += 3 ve) A8- id CA, rCCIPROCC UE A3= 64 vel A3 = 16 vel A3= 4 vel A3-3 Si corpus sinsulis rerolucionibus redierit ad Apsidem candem immo- tam; erit m ad n uE ad T, adeoque Amm 3 aqualis A = 2 seu A ec propterca decrementum virium in ratione duplicata alcicudinis, ut in praecedentibus demonstratum cAt. Si corpus partibus revo- lutionis unius vel tribus quartis, vel duabus tertiis, rel una ter tias vel una quarta, ad Apsidem candem redierit; crie m 2d n ue B vel 5 vel 3 vel à ad F, adeoque Amm 3 aequalis A 4 - vel 3 vel A3= 3 vel A16 -3; et proprerea ris AUE reciproce u A9 DE MOTV