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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 296, page id 1041163592:0330
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2. 56
PTTILOSOPMLS NATURALIS
Dn HorO Prioris autem generis relistentixe sune ad inricem uE vireS FOEX mo-
Ldnronon erices a quibus oriuncur, id est, ut vires corxe acceleratrices et quan
titaces maceriae in parcibus correlpondentibus; hoc cst (per IIy.
pothelin) uc quadrara relociratum directe ex dictanciae particula-
rum correlpondencium inverse ee quancitates materix in parcibus
correspondentibus directe: ideoque (cum distantix particularum Sy-
Aematis unius sint ad dittantias correspondentes parcicularum alte.
rius, ut diameter parciculae vel parcis in Systemate priore ad dia-
metrum parciculae vel partis correspondentis in altero, et quancita-
EeS materix sint ut densitates parrium ex cubi diametrorum) resi-
stencix lunc ad invicem uc quadrata relocitatum dc quadrara dia-
metrorum ex densitates parcium Systematum. Q. F. D. Poltc-
rioris generis relistentix lunt ut reflexionum correspondentium nu-
meii de vires conjunetim. Numeri autem rellexionum sunt ad in-
vicem ut velocitates partium correspondentium directe, et spatia
inter carum refexiones inverse. RE vires refexionum sunt ue re-
locitates de magnitudines ex denlicates partium correspondencium
conjunctim; id elt, ue velocitares ec diametrorum cubi ec densica-
Ees Partium. Et conjunctis his omnibus rationibus, resistentix
partium correspondentium sunt ad inricem ut quadrata reloci-
cum ex quadraca diametrorum ex densicates parcium conjunctim.
2. F. .
Corol. 1. TSitur si Systemara illa sine Fluida duo Flaltica ad
modum Aeris, ec parres corum quielcane inter sc: corpora autem
duo similia ec partibus Auidorum quoad magnicudinem ex densica-
cem proportionalia, ex inter partes illas similiter polita, secundum
lineas similiter politas uccunque projiciantur; vires autem acce-
leratrices, quibus parciculae Fluidorum se mucuo agitant, sinE UE
corporum projectorum diametri inverle, et quadrata velocitatum
directe: corpora illa temporibus proporcionalibus similes excita-
bune mocus in Fluidis, et spatia similia ac diametris luis proDor-
cionalia describent.
Corol. 2. Proinde in eodem Fluido projectile relox resistentiam pa-
ticur ouxe est in duplicata ratione relocicacis quam proxime. Nam
E rires, quibus particulae dictances se MuEuO aSIFaME, augerentur in
duplicata ratione relociraris, relctentia Foret in eadem ratione du-
plicata accurare; ideoque in Medio, cujus partes ab invricem distan-
e0s sele riribus nullis agitant, relistentia est in duplicata ratione re-
locitaris accurate. Sunto isitur Media eria A, B, C ex partibus
similibus et aequalibus ec secundum distantias aequales resularirer
dispo.