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# Title: LBr. 57, 1 · Bernoulli, Joh.
# Folio 251v, page id DE-611-HS-958803:0504
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uti indivisibile seu nullum in magnitudine, ab infinite parvo; ita interminatum ab infini–
te magno; et culculos quidem nostras ratiocinationesque ingrodi is
hic fieri debere
munum et infiaite
sermionom
at non indivisihile nea interminatum. Neque pronde aestimari posse spatium
absolute Interminatu
velut
re
interminata
3C3BA etc 3C, rectis finitis 3C3B, 3BA, et asymptor
ete, et curva (3C etc compree comprehenso vel quasi, cumpera non a
comprehendatur nec figuram constitunt, quandoauidem Ascimptota ad curvam
non perrenit  neque adeq ultimam sf abscidsam A0B, accurate
loquendo esse nullam, sen quasi o in cideret in A; nec ultimam
ordinatam oboC esse interminatam, quasi oBoc incideret in Asym
sedterminatam A. oB esse infinite parvam, et  oBoC esse infinite
ptotam.
sed
magnam inter quas media proportionalis sit ordinaria quantitas
latus scilicet quadrabi constantis quod aequatur rectangulo  cuicunque
ABCG atque adeo et rectangulo ne A.0B. oC. 0G quod est longi-
DarL
Atque ita
objectio neque enim duo spatia interminata supra dictataut sibi
horizontalubus
aequantur, aut a quadrilineis (: unum ab verticalibus, alterum al
us:) conflantur sed spatia  infinita s
a verlicatibussa verticatibus
t qu ambo debent esse quadrilinea et terminata
nempe zona dorizontalis totalis, ex prioribus numero infinitis
conflata, empe =B3C3B0BoC3C, et zona verticalis totalis
tidem ex prioribus numero infinitis composita 3C3G0G0C3C
quae dua
qua
aae infinitae quidem longitudine, sed tamen terminatae
onae
inter se aequantur
Hnc quod etiam in Hyperbola Conica per
MM
in ca corstat
VC. patet, detracto enim communi recti quemadmodum et universum, quod
cunq horizontalis respondenti verticali aequetur; nam si a duabus quadrilineis
vel Ze Lonis detrahas commune trilineum 3C∞ 3CE, oC. 3C, restatit
ed
un in uno rectangulum A3B3C. 3 A3B3C3G, in altero A0G0C0B
omamiu re quae duo rectangula aequantur inter se ut constat.
Atque haec quidem circa aestimationem virium naturamque corporis, pariter
ac circa calculum infinefesimalem,  excerpta exhis pariter ac praeceden-
tibus literis, Domino voldero, si videbitur, communicari possent. Inter nos
cesse nonet autem hoc addo quod et jam olim seho in dicto tractatu medito a ascripsi, dubitari geludit ex
Xi. 1
passe an lineae infinita, longitudi
utianet uti imaginariau radices in Algebra; semper
t cingantur
sufficere pro calcubu,
enim quod peres  infinita ista et infinite parva concluditur deductione ad ab2
sursum mea incomparabilium methodo, cujus aliquando leminata dedi in Actis,
an reveradetur quanti
Et si enim concedam nullu
vinci potest. Itaque mirari etiam non dobes, quod dubit
medi tas infinite parva, aut infinite magna utrinque terminata.
rem, etam asse portionem materiae quae non actu sit secta non tamen ideo deveritur ad inseca-
bilia, aut ad minimas portiones, imo nec ad infinite parvas, sed tantum ad minores per
jetuo  tamon ordinarias; similiter ut ad majores perpetuo in augendo alledium
sed ad rels
in exantrata A etio
siect
malcula in 
malculis
dari facile
concedo, et
tamen ae-
dari ani
malsula
intinite
ruas
redum
altima
sitalia insinito
infinite
paponpissic
crederea
A2