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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 235, page id 1041163592:0269
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PRINOIDLA MATELEMAEICA
235
CFI, (Ut moris CA) ec valor ordinatim applicatae resolvatur in sC- LIVEn
riem conversentem: Problema per primos Seriei terminOS eXPC- SECVRDOS.
dite solvetur, ut in exemplis sequentibus.
Lxempl. I. Sit Linea F F FT Q SemicirculuS super diametro P
descripeus, ec requiratur Medii densiras que Faciac ut Projellile
in hac linea moveatur.
Bisecetur diameter PO in A, dic AO n AC a CH e, e
CD o: ec erit D I9 Icu A& 4 = AD g = nn = a a = 240 - 00, CCu
ee = 240 =00, ec radice per mechodum nostram extracta, HCE
DF = C - 20 00 400 a0 a0
20 20 20 205 dc. Hlic Scribatur nn
Dro ee F aa e eradet DT = e -a0 nnoo anno
2 C
2C
CLC.0
Hlujusmodi series distinouo in terminos successivos in hunc mo-
dum. Terminum primum appello in quo quancitas infinite par
ra o non excac; secundum in quo quantitas illa est unius dimen-
honis, tertium in quo CxtaE
duarum, quartum in quo
erium est, ex sic in infini-
cum. EC primus terminus
qui hic estes denotabit sem-
Per longitudinem Ordinata
CFI insistentis ad initium
indetinita quantitatis o; (c-
cundus terminus qui hic cA
a
denotabie difterentiam
inter CFI ex D N, id est, lincolam M N quae abscindieur com-
Plendo parallelogrammum ETC D M, acque adeo policionem tan-
Sentis N semper determinat: ue in hoc casu capiendo M N ad
TTM NE CK - 2d 0, seu a ad e. Terminus certius qui hic est
3 100
20 designabit lineolam VN quae jacet inter tangentem _ cur-
vam adeoque determinat angulum contactus PET N seu curratu-
ram quam curra linea habet in FI. Si lincola illa PN Aniexe cA
magnicudinis, designabitur per terminum cercium una cum sc-
guentibus in infinitum. AC _ lincola illa minuatur in infinicum,
TermI