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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 107, page id 1041163592:0141
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PRTNCIDTA MAEEIEMAETCA.
lo
etiam secet communem illam diametrum AB (si opus est productam)
In T; Sicque SY ad hanc rectam, ec B  ad
hanc diametrum perpendicularis, atque Figi-
exe R F B latus rectum ponatur L. Constat
Der COr. 9. PrOP. ZVI, quod corporis in
linca R P B circa centrum Smoventis velo-
cicas in loco quovis P sit ad relocitatem cor-
Poris interrallo SF circa idem centrum Cir-
culum describentis in subduplicata ratione rec.
canguli Z L XS F ad SY quadratum. P. R au
tem ex Conicis AC B ad C P guE 2 A0 adL
adeoque ZC Pg X AO
ACB aequale L. ErSOVC.
locitates illae sunt ad inricem in subduplicata
ratione C F gX AOXSZ
ACB
adSY quad. POF-
FO CK Conicis cA CO ad BO ut BO ad FO,
ec composice vel dirisim uc CB ad BT.
Unde vel diridendo vel componendo Ac
BO-vel F CO ad BO ut CT ad BT, id cA
F
AC ad AOut C P ad B Q; indeque CF qX AO X SF
BQ9X ACXSF
ACB
mm
aequale est
AOX BC. . Minuacur jam in infinitum Pigurae R F B lacitu-
do CP, sic ut punctum P coeat cum puncto C, punctumque Scum
puncto B, e linea SF cum linea BC, lineaque ST cum linca B_:
ee corporis jam recta descendentis in linea CB velocitas Aet 2d
relocitarem corporis cenero B interrallo BC. C irculum describentis,
in subduplicata ratione ipsuS = QQZACXSY
AOXBC ad SYg, hoc est (nCS
lectis aequalitatis rationibus SF ad BC et BGg 2d 5T9) in sub-
duplicata ratione AC 2d AO sive = AB. Q. F. D.
Corol. L. Punctis B dc S cocuntibus, Ec FC 2d FS uE AC
ad AO.
Corol. 2. Corpus ad datam a cenero distantiam in Circulo quo
vis revolvens, motu suo tursum rerso ascendet ad duplam suam a
centro dictantiam.
Jo IX P. V
 N 1
PROLC