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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 411, page id 1041163592:0445
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IIIIIII
PRINOTPTA MATHIEMATICA.
percurrit P M, (exeteris paribus) ut ML, ec MP. eAt in dupli- LrnEN
cata ratione temporis. Ouare mocus Nodorum in SyzYsiis, eo reurios
tempore contectus quo Luna datas Orbis particulas percurrie, di-
minuitur in duplicaca ratione numeri 11073 ad numerum 11O23:
eAtque decrementum ad motum reliquum uc 100 ad 10973, 20
MOTUM VeTO EOTUM UE 100 2d 11073 quam proxime. DCCrE.
mentum autem in locis inter Octantes dc Syzrgias, ee incremen-
cum in locis inter Octantes ex Ouadraturas, elt quam proxime ad
hoc decrementum, ut motus torus in locis illis ad morum tocum
in 5yzysiis ec differentia inter quadrarum linus distantix Lunx 2
Duadratura ec semissem quadrati Radii ad semilrem quadrari Ra.
dii conjunctim. Inde si Nodi in Ouadracuris verlentur, de ca-
piantur loca duo aequaliter ab Octante hinc inde distantia, de alia
duo 2 5y27si2 ec Ouadratura iildem interrallis distantia, deque
decrementis motuum in locis duobus inter 5y2ygiam ec Octantem,
subducantur incrementa motuum in locis reliquis duobus, quae
sunt inter Octantem ex Ouadraturam; decrementum reliquum
requale erit decremento in Syzysia: uti rationem incunci Facile
constabit. Proindeque decrementum medioeres quod de Nodo-
rum motu medioeri lubduci debet, est pars quarta decremenci in
Sy2gia. Mocus totus horarius Nodorum in Syzygiis (ubi Luna
radio ad Terram ducto aream tempori proportionalem describere
(UpPOnCBACUE) CraL 32. 42. 7. Ec decrementum morus Nodo-
rum, quo tempore Luna jam velocior describit idem spacium,
cliximus essc ad hunc mocum uc 100 2d 11073; adeoque decre-
mentum illud est r71. 43. ZV, Cujus pars quarta 4. 257 483
motui horario medioeri superius invento 16. 21. 3. 30. Tub-
ducta, relinquit 10. 26. 37. 42. motum medioerem horarium
correctum.
Si Nodi versantur exera Ouadraturas, se spectentur loca bina 2
Sy2rgiis hinc inde aequaliter dictantia; summa mocuum Nodo-
rum, ubi Luna versacur in his locis, erit ad summam motuum,
ubi Luna in iisdem locis ex Nodi in Guadraturis vertanEur, UE
AZ qu. 2d ATqu. Ec decrementa motuum, a cautis jam expo-
Stis oriunda, erune ad invicem ut ipsi motus, adeoque motus reli-
qui crune ad invicem ut AZ qu. ad A qu. de motus mediocres
ut motus reliqui. Ps itaque motus medioeris horarius correctus,
in dato quocunque Nodorum situ, 2d 26. 26. 37. 42. ut AZ quo
ad ATqu.; id cAt, ue quadratum sinus distantiae Nodorum a 5y-
ersiis ad quadracum Radii.
786
P a
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