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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 407, page id 1041163592:0441
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11
PRTNCTPTA MATTIEMAETOA.
407
p D X AZ proportionalis, de conjunctis rationibus, PLX F II
CA uE COntenEuM ZER X P D X AZ, _E PR X PHX AZ Ut TInrIvS.
RRX F D X AZ qu. id eA, uE arca P D d A ec A Z qu. COn-
Junctim. 2. P. D
Corot. 2. In data quaris Nodorum positione, motus horarius
medioeris est semissis morus horarii in Syzreiis Luna, ideoque est
2d 16. 35. 16r. 36. ue quadracum sinus distantix Nodorum a
5y2ysiis ad quadratum Radii, sive ut 1Z qu. 2d ATgu. Nam
Si Luna unitormi cum mocu perambulet semicirculum  Ag. Cum-
ma omnium arearum P D aM, quo tempore Luna persit a  ad
M, Crit area M d F quae ad circuli tangentem Q L termina.
cur; ec quo tempore Luna actinsit punctum n, summa illa crie
arca Fota L An quam linca PD describit, dein Luna pergente
2b n ad g, linea F D cadet extra circulum, ec arcam nge ad
circuli cangentem ge terminatam describet; quaes quoniam Nodi
prius regrediebantur, jam vero progrediuntur, lubduci debet de
area priore, e cum aequalis HE ATCX  F N, relinquot semicircu-
lum Na An. Pgitur summa omnium arcarum F D d MI, quo
cempore Luna semicirculum describit, est arca lemicirculi; se
summa omnium quo cempore Luna circulum describit cst area cir-
culi EociuS. AF arca F D aM, ubi Luna versatur in SyZygiis, eA
rectanoulum (ub arcu F M ex radio MT; ex summa omnium huie
aequalium arearum, quo tempore Luna circulum describie, cA
rectanculum sub circumterentia tota ex radio circuli; et hOC
rectanoulum, cum sit aequale duobus circulis, duplo majus est
quam rectangulum prius. Proinde Nodi, ea cum relocitate uni-
Formiter continuata quam habent in 5y2ygiis Lunaribus, spacium
duplo majus describerene quam revera describune; ec propterea
motus medioeris quocum, s uniformicer continuaretur, spaeium
a se inaequibili cum moru revera confectum describere pollent, elt
Temissis motus quem habent in Syzroiis Lunae. Unde cum mo-
tUS BOrariUS maximuS, ( Nodi in GUAdEAErIS VerTANEUE, RE
33. 10. 33. 22 motus medioeris horarius in hoc calu crie
16. 35. 16. 26. Fc cum mocus horarius Nodorum semper sIE
ut AZ qu. e area F D dM conjunctim, _ Propterca motus ho-
rarius Nodorum in SyZeiiS LUnX uE AZ qu. _ arca F D d MI
conjunctim, id est (ob dacam aream F D dM in SyZygiis de
Tcriptam) ut AZ qu. erit eriam morus medioeris ut AZ qu. acque
adeo hic MOTUS, uDi NOdi EXETA OU dEAEUTAS VeTLANEUF, CriF ad
b. 3,. 26. 36. uE AZ qu. 2d AF gu. d. F. D.
P R. 1).
1IIHIIII
1I
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