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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 122, page id 1066518432:0150
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122 DE V FRTBUS EF MIOTTDUS CORPORUM. LIB. I.
C O R OL L A R L U M TTI.
234. Flinc primum ex corporibus continue proportionalibus ul.
timo majorem celeritatem dabit per corpora quorcunque interposi.
ta continue proportionalia, quam si eidem quiescenti immediate
occurrisset.
F18.54.
S CH O L YO N.
235. Ex praecedentibus jam Facile elicietur regula determinandi
relocitatem, quam ultimum corpus quiescens ex serie quotcunque
continue proportionalium accipiet transmisso motu à primo in le-
cundum, tertium, quartum _C. Primum CorpuS dicatur A, ejus-
que celoritas ab initio AD, ultimum V: diridatur celeritas initia.
lis AD in puncto C, in reciproca ratione secundi corporis ad pri
mum, rel, quod idem est, in ratione cujuslibet corporis in seric pro.
Portionalium ad corpus, quod illud in eadem Peric proxime prece.
dit, ita uE AC ad CD sit in hac eadem ratione, deinde ratio totius
AD ad duplam CD continuetur in toc terminis uno minore quot
Tunc seriei corporum proportionalium, quorum ultimus sIE C, di-
co hanc O exponere celeritatem iltimo corpori V collatam ab om-
nibus praecedencibus. Adeoque si numerus terminorum fuerit n L I,
celeritas initialis AD primi corporis erit ad O celeritatem ultimo
V acquisitam, SICUE AD ad (2CD), hinc habebitu O = (2C. D):
AB = (2OD), Cumta scilicet AD instar unitatis, quod hoc l0.
co fieri licet.
236. Fvempl. Sint centum corpora in continua ratione dupla,
motusque primum incipiat a maximo, quaeritur  seu celeritas mi-
nimo V conterenda. IlOc CatU CTUNE AC = =3 CC CD = Z, atque
adco (2. CD)n = (5)00, est enim n = 99. Tgitur habemus  = (3)00, dt
L05- uS 9=99. Log- um Z; atqui L0g-U5 (4: 3) =0. 1249388 qui
Lorarichmus ductus in 99 dat 99. L05. (4: 3) = 12. 36894 12 = L08.
L ergo 9 == 2338520732310 quam proxime, nam hic numerus
109-mo illi, cujus characteristica est 12. proxime conrenit; atque
adeo celeritas, quam corpus centesimum accipere debet, est ad cele.
ritatem primi A ut 2338520732310 ad r proxime.
Sin rero motus a minimo incipiat, erit hujus celeritas ab initio
ad relocitatem, quam centesimo ec maximo dabit interpositis 98. re-
liquis concinue proportionalibus, sicur numerus 27103723483T46067