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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 409, page id 1041163592:0443
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PRINCIDTA MATHEMATICA.
409
in f, conveniant autem hx tangentes in aXC ZG ad Y; _ A LIBEN
ML. designet spacium quod Luna in Circulo revolvens, interea ZEx VIVS.
dum describit arcum P M, urgente ee impellente vi praedieta
3TT, motu cransverio describere porter, et mi desionet spatium
quod Luna in Fllipsi revolvens eodem tempore, urgente etiam ri
3IE, delcribere ponet; et produeantur L. P et Ip donec occurrant
plano Rclipricae in G eC G; _E jUnGAnEuE FC eE fG, quarum FC
producta secet pf, p8 dc TQ in c, e e R respective, de f8 pro-
ducta secet T a in r: Ononiam vis 3TT seu ZFK in Circulo
eAt ad vim 3YY seu 2pR in EIIpA, uE P R ad pR, Pcu AF 20
aT; erit spatium M L. vi priore genitum, ad spacium mi vi Po-
ceriore genitum, ut FK ad pK, id eAt, ob similes Aguras
DYKP EE FYRC, AE FR adCK. FA autem MF ad FC (0b
similia triangula F L. NB, PGF) ut P L ad P C, hoc cA (Ob
Parallelas LR, F K, GR) ut pl ad pe, id est, (ob similia crian-
cula plm, cpC) uc im ad ce; e inverse ut L. M CA ad Im, seu
FR ad c R, ita CA FC ad cc. FF propterea si fe CNCE ad cC UE
FY ad cP, id est, ut fr ad cR (hoc CA, ut fr ad F R _ FR ad cR
conjunctim, id cst, ut fT ad FT e FC ad ce conjunctim,) quo-
niam ratio FCr ad ce uerinque ablata relinquie rationes fe 2d FC
_ fY ad FT, Foret fe ad FG uc fY ad FT; acque adeo anguli,
quos FO de fe subtenderent ad Terram P, aequarentur inter se.
Sed anguli illi (per ca quae in praecedente Propostione expolui
mus) Tunt mocus Nodorum, quo tempore Luna in Circulo ar-
cum PMI, in FIlipsi arcum pm percurrit: _e propterea mocus
Nrodorum in Circulo e FIliph aequarentur inter lc. Hlaec ita (C
haberent, si modo fe eNer ad ce ut fY ad cY, id cA, I fe aequa-
lIS CNCE
et
=. Verum ob similia criangula f8P, cep, cA f8
ad ce ut se ad cp; ideoque f8 aequalis est E eXf,
CP
se
; dE PrOPterCa
anoulus, quem fe revera subtendie, est ad angulum priorem, quem
FC subtendit, hoc est, mocus Nodorum in Fllips ad motum
cexsP ad priorem f5 scu
Nodorum in Circulo, ut haec fe seu.
CCXFY
et
 id CAt, ut fPZCY ad fYXCp, (Cu fP ad fY et cY ad cp)
hOC CH, SI pB ipA Z N paralleIA OCCUTFAE P P in B, UE FB ad FZ
ec FT ad F P; hoc eA, uE FB ad FP seu D p ad D F, adcoque
Ac area DPmd ad aream D P Md. EE PTOPTETCA, CUM AECa DO-
78E
AOriOE