Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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DE MUNDI
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SYSTEMATE</
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PROPOSITIO XXXIV. PROBLEMA XV.
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Invenire Variationem horariam Inclinationis Orbis Lunaris ad
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planum Eclipticæ.
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<
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>Deſignent
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A
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&
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a
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Syzygias;
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Q
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&
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q
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Quadraturas;
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N
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&
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n
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No
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dos;
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P
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locum Lunæ in Orbe ſuo;
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p
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veſtigium loci illius in plano
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Eclipticæ, &
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mTl
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motum momentaneum Nodorum ut ſupra. </
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Et ſi ad lineam
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Tm
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demittatur perpendiculum
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PG,
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jungatur
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pG,
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& producatur ea donec occurrat
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Tl
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in
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g,
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& jungatur etiam
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Pg
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:
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erit angulus
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PGp
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Inclinatio orbis Lunaris ad planum Eclipticæ,
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ubi Luna verſatur in
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P
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; & angulus
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Pgp
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Inclinatio ejuſdem poſt
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momentum temporis completum; adeoque angulus
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GPg
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Variatio
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momentanea Inclinationis. </
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>Eſt autem hic angulus
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GPg
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ad an
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gulum
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GTg,
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ut
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TG
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ad
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PG
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&
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Pp
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ad
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PG
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conjunctim. </
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<
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>Et prop
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terea ſi pro momento temporis ſubſtituatur hora; cum angulus
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GTg
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(per Propoſit. </
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<
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>xxx.) ſit ad angulum 33″. </
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<
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>10′. </
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<
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>33
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iv
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. </
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<
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>ut </
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