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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 202, page id 1041163592:0236
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II
PHILOSOPHLSE NATORALIS
Scholium.
Si corpus aliquod perpendiculariter versus planum datum era-
hatUT, ex ex data lege attractionis guaeratur motus corporis: Sol-
recur Problema quaerendo (per PFOP. ZXXIX) motum corporis recta
descendentis ad hoc planum, et (per L egum Corol. 2.) Componen-
do mocum iltum cum uniformi motu, secundum lincas eidem plano
parallelas Facto. EE COntrA, Si quaeratur L ex accractionis in planum
secundum lincas perpendiculares Factae, ca conditione uF COrDuS aF-
eractum in data quacunque curra linea moreatur, Solvetur Proble-
ma operando ad exemplum Problemaris terrii.
Operationes aurem contrahi solene resolvendo ordinatim appli-
catas in Scries convergentes. VF si ad basem A in angulo quoris
dato ordinatim applicetur lonsitudo B, quae sic ut basis dignitas
quaelibee An; ec quaeratur vis qua corpus, secundum positionem
ordinatim axplicatae, vel in balem actractum vel a baS Fugatum,
moveri postit in curra linea quam ordinatim axplicata termi-
no suo suveriore semper actinsit: Suppono balem augeri Parte
quam minima O, ec ordinatim applicatam a F On resolvo in
m -n
Seriem infinitam An + = OA + mm-mn
et
2nn
m - 2n
OOA  eC. aC.
que hujus cermino in quo O duarum est dimentionum, id est, cer-
Mm-mM
mino
m - 21
2nn OOa n rim provortionalem eNe suDDOnO. P. A
isitur vis guXesiTa uE
M
2
mm-mn
nn
m - 2n
 vel quod perince cAt, ve
mm-m B m. OE s ordinacim axplicata Parabolam acringat,
nn
existente m = 2, _ n = F: Het vis uE data 2B, adeoque dabi-
Tur. Daca isieur ri corpus morebieur in Parabola, quemad-
modum Galilans demonstrarit. Duod si ordinatim applicaca
HIyperbolam attingat, existente m =O -T, eE n = L; ECL vis uE
2A=3 Seu 2B3: adeoque ris quxe sic ue cubus ordinatim applicata,
corpus movebitur in FIrperbola. Scd mistis hujusmodi Propoliti-
onibus, pergo ad alias quasdam de Motu, quas nondum attisi.
DE MOTD
PORPORVM