Tartaglia, Niccolo, Quesiti et inventioni diverse, 1554

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                <s id="s.001785">
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                la delli lor moti contr arij (cioe delli lor aſcenſi) ſe conchiude eſſer la medeſima, ma traſ
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                mutatiuamente.
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                S.A. E
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                ſſemplificatemi tal propoſitione.
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                NIC. </s>
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                <s id="s.001786">Si
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                a anchora li dui corpi.a.b.&.c.de uno medeſimo genere, & di grandezza diuer
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                ſa, & ſia lo.a.b.maggiore, & ſia la potentia del.a.b.la.d.e.& del.c.la.f. </s>
                <s id="s.001787">& per­
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                che il corpo di potentia, ouer grauita maggiore (per la ſeconda petitione) deſcende piu
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                uelocemente, ſia adunque la uelocita nel deſcender del corpo.a.b.la.g.h. & quella del
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                corpo.c.la.
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                k.
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                hor dico, che la proportione della potentia. </s>
                <s id="s.001788">d. e. alla potentia. </s>
                <s id="s.001789">f. & quella
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                della uelocita.g.h.alla uelocita.
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                k.
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                eſſer una medeſima, & quella delli lor moti contrarij
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                eſſer quella medeſima, ma traſmutatiuamente, cioe che la proportione della uelocita
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                del corpo.a.b.alla uelocita del corpo.c.nel moto contrario (cioe nell'aſcendere) eſſer,
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                ſi come quella della potentia.f.alla potentia.d.e.ouer, come del corpo.c.al corpo.a.b.
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                la qual coſa ſe dimoſtra per il medeſimo modo, che fu dimoſtrata la precedente, cioe
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                ſe la proportione della potentia.d.e.alla po
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                tentia.f.non è (per l'auerſario) ſi come quel
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                la della uelocita.g.h.alla uelocita.
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                k.
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                neceſſa
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                riamente la ſara maggiore, ouer menore,
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                hor poniamo che la ſia menore, della poten­
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                tia.d.e.ne aßignaremo la parte.d.eguale al­
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                la.f.& coſi della uelocita.g.h.ne aßignare­
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                mo la parte.g.eguale alla.
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                k.
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                & arguiremo,
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                come nella
                  <expan abbr="precedẽte">precedente</expan>
                ,
                  <expan abbr="dicẽdo">dicendo</expan>
                che la pportio
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                ne di tutta la potentia.d.e.alla ſua parte.d.
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                </s>
                <s id="s.001790">ſara (per la ſeconda parte della. </s>
                <s id="s.001791">7. del quin-
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                io di Euclide) ſi come quella della medeſima potentia.d.e.alla potentia.f. (per eſſer la
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                d.&.f.eguale) & ſimilmente la proportione de tutta la uelocita.g.h.alla ſua parte.g.
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                </s>
                <s id="s.001792">eſſer, ſi come quella della medeſima.g.h.alla.
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                k. </s>
                <s id="s.001793">A
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                dunque la proportione di tutta la po­
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                tentia.d.e.alla ſua parte.d.ſara menore di quella di tutta la uelocita.g.h.alla ſua par­
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                te.g. </s>
                <s id="s.001794">Onde (per la. </s>
                <s id="s.001795">30. del quinto di Euclide) la proportione di tutta la medeſima po­
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                tentia.d.e.al ſuo reſiduo.e.hauera maggior proportione, che tutta la uelocita.g.h.al
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                ſuo reſiduo.h.la qual coſa ſaria contra la opinione dell'auerſario qual
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                , che la
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                proportione della maggior potentia alla menore eſſer menore di quella della maggior
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                uelocita alla menore. </s>
                <s id="s.001796">Et con li medeſimi argomentiſe procederia quando che quel ſup­
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                poneſſe che la proportione della maggior potentia alla menore fuſſe maggiore di quel
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                la della maggior uelocita alla menore, diſtrutto adunque l'oppoſito rimane il propoſi­
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                to, hor per la ſeconda parte della noſtra concluſione, dico, che la proportione della ue­
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                locita delli deſcenſi, & delli contrari moti, cioe delli aſcenſi de detti corpi è una medeſi­
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                ma, ma traſmutatiuamente, cioe che la proportione della uelocita del corpo.a.b. eſſen
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                do da qualche altra uertu impoſta nell'altro braccio della libra in alto elleuato (ponia­
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                mo per fin alla linea della direttione) alla uelocita del corpo.c.dalla medeſima uertu,
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                pur in alto elleuato per fin all medeſima linea della direttione ſara, ſi come quella del­
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                la uelocita.
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                k.
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                alla uelocita.g.h.ouer della potentia.f.alla petentia.d.e.ouer del cor-
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                </s>
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