Cardano, Girolamo
,
De subtilitate
,
1663
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ſimiliterque iuncta. </
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<
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id
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s.011882
">Atque rurſus medios
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ordines quotquot neceſſarium fuit conſti
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tuit eodem opere. </
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<
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Pons C. Cæ
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ſaris.</
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Schema medietatis pontis ab vno latere.
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</
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<
s
id
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s.011886
">A, Sublicæ ſuperiores aduerſus flumen.
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</
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<
s
id
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s.011887
">BB, Sublicæ inferiores annexæ ponti.
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</
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<
s
id
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">C, Tigna bina ſuperiora.
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</
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<
s
id
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s.011889
">D, Trabs latitudinis duorum pedum.
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</
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<
s
id
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s.011890
">E, E, E, E, Fibulæ connectentes D, tra
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bem cum tignis ſuperioribus, & inferio
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ribus.
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</
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<
s
id
="
s.011891
">F, Tigna bina inferiora.
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emph.end
type
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italics
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<
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minis curſum poſitas, multis, aliis tranſ
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uerſis ſuperpoſitis inuicem etiam conne
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xis iungito: quibus longuriis ac craticulis
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ſuperſtratis pons efficitur. </
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>
<
s
id
="
s.011892
">Ad cuius ſecu
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ritatem tigna plurima in ſuperiori fluminis
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parte prona aduerſus fluuij impetum à
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toto opere ſeparata: in inferiore ſublicæ, &
<
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ipſæ aduerſus fluminis impetum, ſed ti
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lb
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gnis longè proniores, totique operi iun
<
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ctæ firmiter defigantur. </
s
>
<
s
id
="
s.011893
">Ita ſuperiora tigna,
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lb
/>
fluminis impetum & proiectas trabes exci
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pient, & ipſa moles, vt magis premetur ab
<
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vndis, mutuo complexu firmior reddetur.
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lb
/>
</
s
>
<
s
id
="
s.011894
">Sed hic pons ſtabilis eſt, omníque oneri
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ſufficiens. </
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>
<
s
id
="
s.011895
">At celerem fabricam explicabunt
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ſolæ funes & ergatæ, aut pelles inflatæ, aut
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lb
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tigna iuncta.
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/>
<
arrow.to.target
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="
marg1640
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</
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<
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id
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<
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id
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Theatra bi
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na cum ſcena
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complentia
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amphithe
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rum.</
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>
</
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<
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type
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<
s
id
="
s.011897
">Subtilior ſed minùs vtilis ratio amphi
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theatri, cuius meminit. </
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>
<
s
id
="
s.011898
">Plinius. </
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<
s
id
="
s.011899
">Ea ſic ſe
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habet. </
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>
<
s
id
="
s.011900
">Cùm filius M. </
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>
<
s
id
="
s.011901
">Scauri funebres lu
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dos patri editurus, pompam Curtij æqua
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/>
re non poſſet, quòd ille ſummo ſumptu
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eos edidiſſet, diuitiis longè præſtans, in
<
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duſtria ſuperare tentauit. </
s
>
<
s
id
="
s.011902
">Itaque duo thea
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tra ſemicirculi forma cum ſcena fabricauit,
<
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quæ edito ſcenæ ſpectaculo circumacta
<
lb
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cardilibus amphitheatrum explicarent: in
<
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cuius orcheſtradum ludos edit, dúmque an
<
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tè in ſcenis ſpectacula, populus gentium
<
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/>
dormitor ludibrio audaciæ duobus cardi
<
lb
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dinibus, & penſilij machina non ſolùm
<
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penderet, ſed etiam circumageretur: quæ
<
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ritur meritò, quum ſcena Latina à ſum
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mo theatri vertice diſtet nonaginta parti
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bus tota diametros eſt 120. vt Vitruuius
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docet, qua arte fieri poſſit, vt immota
<
lb
/>
ſcena ambo theatra in vnum coëant am
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phitheatrum. </
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>
<
s
id
="
s.011903
">Ponantur igitur ſemicircu
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li duo A B C, & A D C, puncta me
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dia B & D. </
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>
<
s
id
="
s.011904
">Sintque arcus A E & C F,
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lb
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maiores nonaginta tertia minores nonagin
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ta ſexta. </
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>
<
s
id
="
s.011905
">Quare rectè A E & C F, maiores
<
lb
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erunt 87. & minores octoginta nouem. </
s
>
<
s
id
="
s.011906
">Igitur
<
lb
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poſitis cardinibus in E & F, erunt G E &
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H F, maiores 59. 2/3 minores 59. 11/12 Sunt
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enim minores dimidio diametri, quia cardi
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nes diſtant à punctis B & D, quæ ſunt me
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dia ſemicirculorum, & ea diſtantia, vt ſup
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ponitur, maior eſt tribus partibus, & minor
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ſex. </
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>
<
s
id
="
s.011907
">Igitur A E & C F, prominebunt vltra
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directum AC, id eſt vltra ſemidiametrum
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plus quàm partibus vigintiſeptem 1/12 &
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minus, quàm vigintinouem. </
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>
<
s
id
="
s.011908
">1/3 Sed ſcena
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prominet triginta partibus vltra ſemidia
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metrum, quia diſtat nonaginta partibus à
<
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punctis B & D, igitur A & C, circumacta
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non tangent ſcenam. </
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>
<
s
id
="
s.011909
">Sed neque inuicem
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impediens ſe, quia AE & AF, ſunt mino
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/>
res centum ſexaginta nouem 2/3 in 1/60
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partis, ſed A B & A D, ſunt maiores cen
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tum ſexaginta nouem 2/3 in. </
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>
<
s
id
="
s.011910
">1/26 Nam A B
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AD quadrata, iuncta ſunt æqualia quadra
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tis AF & AE, quia ſunt æqualia quadrato
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totius dimetientis. </
s
>
<
s
id
="
s.011911
">Quum igitur AB & AD,
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lb
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ſint inuicem æquales, & A E & A F inæ
<
lb
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quales, erunt AB & A D, iunctæ maiores
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AE & AF, iunctis 1/18 partis vnius. </
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<
s
id
="
s.011912
">Igitur
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eſt inuenire ſitum, in quo theatra circum
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uoluta non ſe impedient. </
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<
s
id
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s.011913
">Oportet autem ſenſim, alternatímque
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circumagere, quum (vt dixi) diſcrimen quo
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ſeparari inuicem poſſunt, vix 1/18 vnius
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partis ſuperet. </
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</
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<
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type
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main
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<
s
id
="
s.011914
">Sunt & duo alij modi, ſed minus elegan
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lb
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tes, quibus fabricari hac ratione theatra
<
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poſſunt: verùm in altero theatra oui for
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mam referunt, vt non ſint rotunda: in reli
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qua quamuis in medio diuiſum ſit amphi
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theatrum, non tamen rectè, nec ſecundum
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dimetientem. </
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<
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<
s
id
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">Quarum ſubtilitatis exemplum eſt in tro
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chleis: conſtat hac ratione: Pondus A an
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nectitur trochleæ inferiori, in qua duo or
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biculi B & C, qui circumuertuntur. </
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<
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<
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Ponderum
<
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<
expan
abbr
="
fã
">familiè</
expan
>
leuan
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dorum ratio</
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>
</
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<
s
id
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s.011917
">In ſuperiore trochlea, duo alij D & E, fu
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/>
nis circumagitur circa D, & deſcendit per F
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lb
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ad C, & aſcendit per G, & circumuertitur
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lb
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ad E, deſcendens per H, circumuertitur ipſi
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lb
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B, & aſcendens trochleæ nectitur in K. </
s
>
<
s
id
="
s.011918
">Igi
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lb
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tur ex L pondus trahitur, & quia ſuſtinetur
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lb
/>
ab FGHK, non erit niſi quarta pars ponde
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lb
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ris A, quæ à ſingulis funibus ſuſtinetur, qua
<
lb
/>
re à quarta parte roboris ſurſum trahi po
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/>
terit. </
s
>
<
s
id
="
s.011919
">Et ſi in ſingulis trochleis tres eſſent
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/>
orbiculi, à ſexta roboris parte: atque ita puer
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lb
/>
poterit immenſum pondus ſurſum trahere,
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/>
niſi quantum funium grauitas, orbiculorum
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lb
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aſperitas, & motus difficultas obſtant. </
s
>
<
s
id
="
s.011920
">Sed
<
lb
/>
quia temporum proportio eſt, vt potentia
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lb
/>
rum per binos orbiculos, quadruplo, per ter-</
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