[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 45
Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.83.
Original at the GWLB · Page image · Annotations (IIIF) · Download text
The machine reads it as
- M
- N
- M
- est
- LACIAOCLTA MAETTEMATICA
- Scholium.
- Ec simili argumento corpus morebitur in Ellipsi vel etiam in
- Arperbola vel Parabola, vi centripeta qux SIE RCCIPROCC UE CU-
- bus ordinacim applicaca ad centrum virium maxime longinquum
- cendentis.
- PROEOSITIO IX. PROBLEMA WV.
- Oyretur corpus in Spirali P OS secante radios omnes SP, SC, C.
- in angulo dato: requiritur L. ex
- vis centripetae tendentis ad
- centrum Spiralis.
- Detur angulus indehnite par-
- rus FS∞ ec ob datos omnes
- angulos dabitur specie AOuTASP ZRT. Ergo datur rario
- eT quad
- eAtque
- R Ut Q T, hOc CsFUES. P. Mutetur jam utcunque angulus P5B
- ec recta e R angulum contactus _ P R subtendens mutabitur (PCF
- Lemma XI.) in duplicaca ratione iphus P R vel 9T. Ersomanebit
- DT quad.
- X
- eadem quae prius, hoc est ut SP. Ouare
- l9. 25F9
- 3
- CA uE SP cub. adeoque (per Corol. L _E5 PFOP. VL.) vis centripeta eA
- reciproce uc cubus distantia SP. 8. F. I.
- Idem aliter.
- Perpendiculum SY in tangentem demissum; ec circuli Spiralem
- cansentis chorda P V sune ad alcicudinem SF in datis rationibus;
- ideoque SP cub. eA ucSZgX P V, hoc eA (per C orol. 3ec 5 PrOP. VI. )
- reciproce ut ris centripeta.
- L E MIMI A ZII.
- Paralleloeramma omnia, circa datae F. lipseos vel Fyperbolae diametros
- quasvis conjuratas descripta, esse inter se aequalia.
- Constat ex Conieis.
- L.tBF
- PRLMDS
- LRC
Cite
[Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica, fol. 45. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1041163592:0079?run=74