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PROPOSITIO XXXIV. PROBLEMA XV.
Deſignent A& aSyzygias; Q& qQuadraturas; N& nNo
dos; Plocum Lunæ in Orbe ſuo; pveſtigium loci illius in plano
Eclipticæ, & mTlmotum momentaneum Nodorum ut ſupra.
Et ſi ad lineam Tmdemittatur perpendiculum PG,jungatur pG,
& producatur ea donec occurrat Tlin g,& jungatur etiam Pg:
erit angulus PGpInclinatio orbis Lunaris ad planum Eclipticæ,
217[Figure 217]
ubi Luna verſatur in P; & angulus PgpInclinatio ejuſdem poſt
momentum temporis completum; adeoque angulus GPgVariatio
momentanea Inclinationis. Eſt autem hic angulus GPgad an
gulum GTg,ut TGad PG& Ppad PGconjunctim. Et prop
terea ſi pro momento temporis ſubſtituatur hora; cum angulus
GTg(per Propoſit. xxx.) ſit ad angulum 33″. 10′. 33iv. ut
dos; Plocum Lunæ in Orbe ſuo; pveſtigium loci illius in plano
Eclipticæ, & mTlmotum momentaneum Nodorum ut ſupra.
Et ſi ad lineam Tmdemittatur perpendiculum PG,jungatur pG,
& producatur ea donec occurrat Tlin g,& jungatur etiam Pg:
erit angulus PGpInclinatio orbis Lunaris ad planum Eclipticæ,
![](https://digilib.mpiwg-berlin.mpg.de/digitallibrary/servlet/Scaler?fn=/permanent/archimedes/newto_philo_039_la_1713/039-01-figures/039.01.444.1.jpg&dw=200&dh=200)
ubi Luna verſatur in P; & angulus PgpInclinatio ejuſdem poſt
momentum temporis completum; adeoque angulus GPgVariatio
momentanea Inclinationis. Eſt autem hic angulus GPgad an
gulum GTg,ut TGad PG& Ppad PGconjunctim. Et prop
terea ſi pro momento temporis ſubſtituatur hora; cum angulus
GTg(per Propoſit. xxx.) ſit ad angulum 33″. 10′. 33iv. ut