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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[6. PHYSICA, ET MATHEMATICA RESPONSA. FO. BAPTISTAE BεNεDICTI PATRITII Veneti, Philoſophi Mathematici.]
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IO. BABPT. BENED.
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                <head xml:id="echoid-head386" xml:space="preserve">DE ICTV BOMBARDAE SECVNDVM
                  <lb/>
                diuerſas eleuationes. Et de quibuſdam erroribus Nico-
                  <lb/>
                lai Tartaleæ, circa idem.</head>
                <head xml:id="echoid-head387" style="it" xml:space="preserve">Fllustri D. Ioſepho Cambiano ex Ruffia Dominis, aquiti
                  <lb/>
                ſtrenuo, & tormentis bellicis Serenißimi Ducis
                  <lb/>
                Sabaudia Prafecto.</head>
                <p>
                  <s xml:id="echoid-s3242" xml:space="preserve">EXcogitaui quędam dum ocio frui licuit per abſentiam Ducis Sereniſſimi,
                    <lb/>
                  quæ ad te ſcribere placuit, vt ſi probaueris in lucem quandoque profer-
                    <lb/>
                  re non dubitem, ſi deſpexeris, ocius ſupprimam, ſunt autem huiuſmodi.</s>
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                <p>
                  <s xml:id="echoid-s3243" xml:space="preserve">Vnde fiat vt tormentum bellicum vehementi
                    <unsure/>
                  feriat ictu ſuperius delato
                    <lb/>
                  quam orizontali, vt Tartalea ſcribit, quæſito ſecundo libr. primi quæſitorum, à ne-
                    <lb/>
                  mine adhuc (quod ſciam) traditum eſt.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3244" xml:space="preserve">Rationes verò Tartaleæ nullius ſunt momenti, quia ſi validæ eſſent, ſequeretur
                    <lb/>
                  vt inclinata bombarda, adeo vt angulus ſub orizonte factus æqualis eſſet ei, qui ſu
                    <lb/>
                  pra orizontem eſt, ictum bombardę in vtroque huiuſmodi ſitu eundem eſſe
                    <reg norm="futurum" type="context">futurũ</reg>
                  .
                    <lb/>
                  </s>
                  <s xml:id="echoid-s3245" xml:space="preserve">& ſi aliqua differentia oriretur ratione granitatis pilæ ab ipſa bombarda emiſſæ, hoc
                    <lb/>
                  fieret, vt ſcilicet velocior eſſet in motu inclinato quam in eleuato cum pondus, mo-
                    <lb/>
                  tui adeo non opponatur. </s>
                  <s xml:id="echoid-s3246" xml:space="preserve">Id quod non ita se habet, vera enim cauſa vnde fiat, vt bom
                    <lb/>
                  barda eleuata vehementius feriat, quàm ea quæ eſt minus alta, eadem eſt ferè, in ge-
                    <lb/>
                  nere, cum ea, qua aliquod corpus materia magis denſa, ſed ſimile & ęquale alteri cor
                    <lb/>
                  pori materiæ minus denſæ velocius mouetur ab vna eademq́ue, aut æquali vi
                    <lb/>
                  compulſum. </s>
                  <s xml:id="echoid-s3247" xml:space="preserve">Eſt eadem etiam in ſpecie ei, qua maiorem effectum producit
                    <lb/>
                  puluis, qui in locis ſubterraneis ponitur quum vaſis optimè colligatis ferro in-
                    <lb/>
                  cluditur. </s>
                  <s xml:id="echoid-s3248" xml:space="preserve">Eſt etiam ſimilis ei, qua longius impellitur pila, qua ludimus, ab ali-
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                  quo inſtrumento ligneo, quando percutitur contra, quam cum ſecundum ſuum mo-
                    <lb/>
                  tum proijcitur. </s>
                  <s xml:id="echoid-s3249" xml:space="preserve">Id quod inde fit, quia virtus mouens maiori vi, & intenſiori huiuſ-
                    <lb/>
                  modi corpus percutit, quia corpus quod moueri debet, quanto magis reſiſtit virtu-
                    <lb/>
                  ti mouenti (certum tamen terminum præſcribendo) in exiguo eo temporis ſpatio,
                    <lb/>
                  tanto maiorem virtutem colligit, quæ ipſum deinde tanto cum impetu mo-
                    <lb/>
                  uet, & tanto magis impellens concomitatur, vt maiorem effectum efficiat, quam ſi
                    <lb/>
                  ad mouendum ſeſe facilè reddidiſſet. </s>
                  <s xml:id="echoid-s3250" xml:space="preserve">Atque hoc ſupradictis ictibus eleuatis acci-
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                  dit, quia grauitas pilæ, ea eſt quæ reſiſtens virtuti mouenti, dat ei commoditatem
                    <lb/>
                  colligendi dictam virtutem, multo magis quam eſſet ea, quæ ad depreſſiorem eleua
                    <lb/>
                  uationem eam
                    <reg norm="immpelleret" type="context">ĩmpelleret</reg>
                  . </s>
                  <s xml:id="echoid-s3251" xml:space="preserve">Et quia huiuſmodi multiplicatio virtutis, nullam propor
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                  tionem cum pondere pilæ gerit, volo inferre quod dum colligitur tanta virtus, col-
                    <lb/>
                  ligitur multo plus eo, quod ad impellendam dictam pilam ſufficeret, ratione magnæ
                    <lb/>
                  velocitatis augumenti, quia quanto plus temporis ei conceditur ad commutandam
                    <lb/>
                  puluerem in ignem, tanto maior quantitasignis progignitur, vnde fit, vt tanto ma-
                    <lb/>
                  iori loco indigeat, quamobrem tanto magis impellit, ſed vt dixi, tanta cum veloci-
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                  tate
                    <reg norm="adaugetur" type="simple">adauget̃</reg>
                  , vt huiuſmodi virtus longè ſuperet
                    <reg norm="reſiſtentiam" type="context context">reſiſtẽtiã</reg>
                    <reg norm="ponderis" type="context">põderis</reg>
                  pilæ, & ſic eſt cau
                    <lb/>
                  fa, ut effectus, quod
                    <reg norm="experientia" type="context">experiẽtia</reg>
                  innot eſcit
                    <reg norm="producatur" type="simple">producat̃</reg>
                  . </s>
                  <s xml:id="echoid-s3252" xml:space="preserve">Sed ea ratio, qua ſeſe
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                  author
                    <lb/>
                  in tertio quæſito ad aliquod impoſſibile, circa iter ipſius pilæ Legatum Hiſpanum </s>
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