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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 205, page id 1041163592:0239
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1IIII
PRTNCIDTA MATTEMATIC A.
2)
lingulis separatim uniformis, at in dirersis diverla; _ per jam de- LrBEn
monstrata, sinus incidentix in planum primum Aa erit ad sinum PRrMVS.
emersentia ex plano secundo Bb, in data ratione; Et hic LInUs;
qui est sinus incidentiae in planum secundum Bb, erie ad sinum
emersentia ex plano tertio Cc, in data rationc; ex hic sinUS 2d
sinum emersentiae ex plano quarto D ds in data ratione; ee Sic in
infinitum: ec ex aequo, sinus incidentiae in planum primum ad (-
num emersentix ex plano ultimo in data ratione. Minuantur jam
planorum interralla ex augeatur numerus in intinitum, eo ut aetra-
ctionis vel impulsus actio, secundum lesem quamcunque astignatam,
continua reddarur; ex ratio sinus incidentix in planum primum ad
sinum emergentix ex plano ulcimo, semper data existens, cciam-
num dabitur. L. F. D
PRODOSITIOXOV. TILLOLLMAL LLLL
Tisdem positis; dico quod velocitas corporis ante incidentiam est
ad ejus velocitatem post emergentiam, ut sinus emerrentiae ad
sinum incidentiae.
Capiantur AF Td aequales, et erisantur perpendicula AG, d K
occurrentia lineis incidentia e emergentia GFI, PR, in ( de R.
In GTT capiatur T FT aequalis TK, ex ad planum Aa demittatur
normaliter PV. Et (per Legum Corol. 2) distinguatur mOrus cor
Poris in duos, unum planis Aa Bb, CC, ecc. perpendicularem, al
cerum iisdem parallelum. Vis accractionis rel impulsus, agendo sc-
cundum lincas perpendiculares, nil mutat mocum secundum paralle-
las, ec propterea corpus hoc motu conticiet aequalibus temporibus
aequalia illa secundum parallelas interralla, quae sunc incer lincam
AC dc punctum PI, interque punctum P ec lincam dR; hoc cA,
aequalibus cemporibus describet lineas CETI, TR. Proinde velo-
citas ante incidentiam est ad velocitarem post emeroentiam, ue
YFT 2d TK vel Y E id est uE A II vel Id ad V FI, hoc est
respectu ractii ZF rel YK) uc sinus emersentix ad sinum inci
dentix. d. F. D.
P L
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