Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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1revolutionis quam proxime. Conjungantur hæ rationes cum ratio­
nibus Corollarii 14, & in quolibet corporum T, P, SSyſtemate,
ubi Pcircum Tſibi propinquum, & Tcircum Slonginquum re­
volvitur, errores angulares corporis P,de centro Tapparentes,
erunt, in ſingulis revolutionibus corporis illius P,ut quadratum
temporis periodici corporis Pdirecte & quadratum temporis pe­
riodici corporis Tinverſe. Et inde motus medius Augis erit in da­
ta ratione ad motum medium Nodorum; & motus uterque erit ut tempus periodicum corporis &c.
quadratum temporis periodici corporis Pdirecte & quadratum
temporis periodici corporis Tinverſe. Augendo vel minuendo
Excentricitatem & Inclinationem Orbis PABnon mutantur mo­
tus Augis & Nodorum ſenſibiliter, niſi ubi eædem ſunt nimis
magnæ.
DE MOTU
CORPORUM
Corol.17. Cum autem linea LMnunc major ſit nunc minor
quam radius PT,exponatur vis mediocris LMper radium il­
lum PT; & erit hæc ad
112[Figure 112]
vim mediocrem SK
vel SN(quam expo­
nere licet per ST) ut
longitudo PTad lon­
gitudinem ST.Eſt au­
tem vis mediocris SN
vel ST,qua corpus T
retinetur in Orbe ſuo
circum S,ad vim qua
corpus Pretinetur in Orbe ſuo circum T,in ratione compoſita ex
ratione radii STad radium PT,& ratione duplicata temporis pe­
riodici corporis Pcircum Tad tempus periodicum corporis T
circum S.Et ex æquo, vis mediocris LM,ad vim qua corpus
Pretinetur in Orbe ſuo circum T(quave corpus idem P,eo­
dem tempore periodico, circum punctum quodvis immobile Tad
diſtantiam PTrevolvi poſſet) eſt in ratione illa duplicata periodi­
eorum temporum. Datis igitur temporibus periodicis una cum di­
ſtantia PT,datur vis mediocris LM; & ea data, datur etiam vis
MNquamproxime per analogiam linearum PT, MN.
Corol.18. Iiſdem legibus quibus corpus Pcircum corpus Tre­
volvitur, fingamus corpora plura fluida circum idem Tad æqua­
les ab ipſo diſtantias moveri; deinde ex his contiguis factis confla­
ri Annulum fluidum, rotundum ac corpori Tconcentricum; &
ſingulæ Annuli partes, motus ſuos omnes ad legem corporis Pper-

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