Tartaglia, Niccolo, Quesiti et inventioni diverse, 1554

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              <p type="main">
                <s id="s.001946">
                  <pb pagenum="93" xlink:href="042/01/186.jpg"/>
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                do circindle le due quarte parte de circuli, ſopra el centro.c.le quale ſiano.a.g. </s>
                <s id="s.001947">&. </s>
                <s id="s.001948">b.
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                f.& eſſendo dutte dal ponto.a.&.b.due linee contingente, le quale ſiano.a.e.&.b.d.
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                </s>
                <s id="s.001949">Eglie manifeſto langolo.e.a.g.della detta contingentia, eſſer menore de langolo. </s>
                <s id="s.001950">d. </s>
                <s id="s.001951">b.
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                f.e pero manco obliquo é il deſcenſo fatto per.a.g. </s>
                <s id="s.001952">del deſcenſo fatto per. </s>
                <s id="s.001953">b. f, e pero
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                (per la terza petitione) piu graue ſara il corpo.a.del corpo.b, in tal ſito, ch'è il pro­
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                poſito.
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                S. A. </s>
                <s id="s.001954">E
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                ue ho inteſo, ſeguitati.
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                N. </s>
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              <p type="head">
                <s id="s.001955">QVESITO. XXXV. PROPOSITIONE VIII.</s>
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              <p type="main">
                <s id="s.001956">Se
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                li brazzi della libra ſaranno proportionali alli peſi in quella impoſti, talmen­
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                te, che nel brazzo piu corto ſia appeſo il corpo piu graue, quelli tai corpi, ouer
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                peſi ſeranno equalmente graui, ſecondo tal poſitione, ouer ſito.
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                S.A. D
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                atime uno eſ
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                ſempio.
                  <emph.end type="italics"/>
                N. S
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                ia come prima la regola, ouer libra,a.c.b. </s>
                <s id="s.001957">& ui ſiano appeſi. </s>
                <s id="s.001958">a.&.b. et
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                ſia la proportione del.b.al.a.ſi come del brazzo.a.c.al brazzo.b.c. </s>
                <s id="s.001959">Dico, che tal li­
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                bra non declinara in alcuna parte di quella, & ſe poßibil fuße (per lauerſario) che de­
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                cl inar poteſſe, poniamo che quella declini dalla parte del b.& che quella diſcenda, &
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                tranſiſca in obliquo, ſi come ſta la linea.d.c.e.in luoco della.a.c.b.& attaccatoui.d.co
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                me.a.&.e.come.b.& la linea.d.f.deſcenda orthogonalmente, & ſimelmente aſcenda
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                la.e.h. </s>
                <s id="s.001960">Hor eglie manifeſto (per la. </s>
                <s id="s.001961">16. &. </s>
                <s id="s.001962">29. del primo di Euclide) che li dui triango
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                li.d.f.c.&.e.h.c.eßer de angoli equali. </s>
                <s id="s.001963">Onde per la. </s>
                <s id="s.001964">4. del ſeſto di Euclide) quelli ſa­
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                ranno ſimili, & conſequentemente de lati proportionali, adunque la proportione del
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                d.c.al.c.e.è ſi come del.d.f.al.e.h.& perche ſi come del.d.c.al.c.e.coſi è dal peſo.b. </s>
                <s id="s.001965">al
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                peſo.a. (dal preſuppoſito) adunque la proportione dal.d.f.al.e.b.ſara ſi come dal pe­
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                ſo.b.al. </s>
                <s id="s.001966">peſo.a.ſia adunque dal.c.d.tolto la parte.c.l.equale alla.c.b.ouer alla. </s>
                <s id="s.001967">c. e. &
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                ſia poſto. </s>
                <s id="s.001968">l. </s>
                <s id="s.001969">equale al. b. in grauita, & deſcenda el perpendicolo. </s>
                <s id="s.001970">l. m. </s>
                <s id="s.001971">Adunque per­
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                che eglie manifeſto la. </s>
                <s id="s.001972">l. m. & la. </s>
                <s id="s.001973">e. h. eſſer equale, la proportione della. </s>
                <s id="s.001974">d.
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                </s>
                <s id="s.001975">f. alla. </s>
                <s id="s.001976">l. m. ſaraſi come delle ſimplice grauita del corpo. b. alla ſimplice graui­
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                ta del corpo. a. ouer della ſimplice grauita del corpo.l. alla ſimplice grauita del cor­
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                po d. (perche li dui corpi.a.&.d.ſono ſuppoſtiuno medeſimo) & ſimelmente el cor­
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                po.b.&.l.per eſſer ſuppoſta la grauita del. l. equale alla grauita del. b.) e per tanto
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                dico, che la proportione di tutta la.d.c.alla.l. </s>
                <s id="s.001977">c. ſara ſi come la grauita del corpo.l.
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                alla grauita del corpo.d. </s>
                <s id="s.001978">Onde ſe li detti dui corpi graui, cioe.d.&.l.fuſſeno ſimplice
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                mente equali in grauita, stanti poi in limedeſimi ſiti, ouer luochi, doue, che al preſen
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                te uengono ſuppoſti, el corpo.d.ſaria piu graue del corpo.l.ſecondo elſito (per la. </s>
                <s id="s.001979">4.
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                propoſitione) in tal proportione, qual é di tutto il brazzo.d.c.al brazzo.l.c.& per
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                che il corpo.l.è ſimplicemente (dal preſuppoſito) piu graue del corpo.d.ſecondo la me
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                deſima proportione (cioe, ſi come la proportione del brazzo.d.c.al brazzo.l.c.adun
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                que li detti dui corpi.d.&.l.nel ſito della equalita ueneranno ad eſſere egualmente
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                graui, perche per tanto quanto il corpo.d.è piu graue del corpo.l. per uigor del ſito,
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                ouer luoco, per quel medeſimo el corpo.l. è ſimplicemente piu graue del corpo.d.e pe
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                vo nel detto ſito della equalita uengono à restare egualmentè graui. </s>
                <s id="s.001980">Adunque quella
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                potentia, ouer grauita, che ſara ſufficiente ad elleuare il corpo.a.dal ſito della equali­
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                ta, al ponto, doue che al preſente è (cioe per fin al ponto.d.) quella medeſima ſaraſoſa
                  <emph.end type="italics"/>
                </s>
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