Benedetti, Giovanni Battista de
,
Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]
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179
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DISPVTATIONES.
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<
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xml:space
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">Quod in vniuerſum nec etiam poteſt eſſe verum in pleno, quia cap .14. iam pro-
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baui, non eandem proportionem eſſe inter ſuperſicies corporum, & ipſa corpora.</
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<
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">Quomodo dignoſcatur proportio uelocitatis duorum ſimilium
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corporum omogeniorum inaqualium.</
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<
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xml:space
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">CAP. XVIII.</
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<
s
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xml:space
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">ETiam ſi reperire in qua proportione motus naturaliter moueantur duo corpo-
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ra, figura & materia ſimilia, inęqualia tamen ad inuicem, non facile ſit, oſten-
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dam tamen qua ratione id conſequi poſſimus.</
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<
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<
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xml:id
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xml:space
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">Proponantur nobis, exempli gratia, duo corpora
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et
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ſphęrica, inęqualia inui-
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cem, omogenea tamen materia, quorum
<
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>.a.</
var
>
maius ſit; </
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>
<
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xml:space
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">ſi voluerimus inuenire in qua
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nam velocitatis proportione naturaliter mouerentur. </
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<
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xml:space
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">Volo vt inquiratur corpus
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>.i.</
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>
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ſphęricum, alia tamen & diuerſa materia conſtans, ſed pondere ęquale corpori
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>.o.</
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>
&
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ſuperſicie tam proportionata ſuperficiei corp oris
<
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>.a.</
var
>
quàm eſt ea, quæ eſt ſui ponde-
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ris ad pondus ipſius
<
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>.a</
var
>
. </
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>
<
s
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xml:space
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preserve
">Hoc facto, indagetur, quænam erit proportio inter ſu-
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perficies corporum
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et
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quę ſemper dupla eſt, vel ſubdupla ei quæ eſt diametro-
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rum; </
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>
<
s
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xml:space
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">ut iam cap .15. dixi, & hęc proportio ſuperficierum ſphęricarum
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<
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et
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ſub
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trahatur ab æqualitate, quod igitur remanebit, erit proportio
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type
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inter duo
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corpora
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et
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ideſt inter
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et
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vt exempli gratia, ſi proportio ſuperficiei
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ſuperfi
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ciei ipſius
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ſeſquitertiα
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eſſet, ſub
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trahendo eam ab ęqualitate, rema-
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neret
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ſubſeſquitertia, vnde
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velocitas corporis maioris ( quod in
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pręſenti loco ſupponitur eſſe
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>.o.</
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>
) ei,
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quę eſt corporis minoris, quale eſt
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corpus
<
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>.i.</
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>
ſubſeſquitertia eſſet; </
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>
<
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xml:space
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dicamus quòd
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eſſet velocius ipſo
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o. in proportione ſeſquitertia ex ſe
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cundo ſuppoſito ſecundi capitis huius libri. </
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>
<
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tam velox eſt quam ipſum
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ex
<
num
value
="
11
">.
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11.</
num
>
cap. ergo proportio velocitatis ipſius
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>
ſeſquitertia erit ei. quæ eſt ipſius
<
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.</
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<
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">Quam ſit inanis ab Ariſtotele ſuſcepta demonſtratio quod
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uacuum non detur.</
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<
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facilè cognoſci poteſt irritam eſſc eam ratio
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nem, quam Ariſtoteles .8. cap. lib. 4. phyſicorum ad deſtruendum vacuum,
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finxit. </
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<
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xml:space
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">Vtigitur idem facilius oſtendamus, compræhendamus imaginatione infini-
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ta media corporea, quorum vnum altero rarius ſit, in qua placuerit nobis ex propor
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tionibus, incipiendo ab uno, imaginemur etiam corpus
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>.Q.</
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>
denſius primo medio, cu-
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ius corporis, totalis grauitas ſit
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>.a.b.</
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>
& poſitum in ipſo medio, amittat partem
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>.e.b.</
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>
ip-
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ſius grauitatis, & in ſecundo medio amittat
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>
& ſic per gradus vnde nobis patebie
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