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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          <div xml:id="echoid-div340" type="chapter" level="2" n="3">
            <div xml:id="echoid-div381" type="section" level="3" n="21">
              <p>
                <s xml:id="echoid-s1950" xml:space="preserve">
                  <pb o="164" rhead="IO. BAPT. BENED." n="176" file="0176" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0176"/>
                et
                  <var>.m.g.k.</var>
                ſint recti. </s>
                <s xml:id="echoid-s1951" xml:space="preserve">Imaginemur
                  <reg norm="quoque" type="simple">quoq;</reg>
                virtutem ipſius
                  <var>.g.</var>
                applicatam eſſe extremo
                  <var>.
                    <lb/>
                  n.</var>
                cum inclinatione tamen contraria, ideſt ad inferiorem partem, quæ quidem virtus
                  <lb/>
                communi quodam conceptu eandem poſſidebit vim ſuſtentandi immobilem diame
                  <lb/>
                trum
                  <var>.g.i.k.</var>
                quam habebat,
                  <reg norm="quando" type="wordlist">qñ</reg>
                erat in
                  <var>.g.</var>
                cum inclinatione ad ſuperiorem partem,
                  <lb/>
                & ſic etiam diameter
                  <var>.n.l.m.</var>
                non magis ab una, quàm ab alia parte declinabit, quia
                  <lb/>
                cum quædam virtus in
                  <var>.n.</var>
                reperiatur æqualis medietati uirtutis ipſius
                  <var>.i.</var>
                quæ uirtus ip
                  <lb/>
                ſius
                  <var>.i.</var>
                uim habet deprimendi ipſum
                  <var>.g.</var>
                ideſt
                  <var>.m.</var>
                pro dimidia ſui ipſius parte, ſequitur
                  <var>.
                    <lb/>
                  n.m.</var>
                debere immobilem permanere. </s>
                <s xml:id="echoid-s1952" xml:space="preserve">Nunc ſi alia diameter rotulæ mobilis erit de-
                  <lb/>
                ſumpta, quæ ſit
                  <var>.p.q.o.</var>
                cuius centrum ſit
                  <var>.q.</var>
                in ſitu parallelo ipſi
                  <var>.n.l.m.</var>
                & ſic collocata,
                  <lb/>
                vt coniungendo
                  <var>.o.</var>
                cum
                  <var>.n.</var>
                anguli
                  <var>.m.n.o.</var>
                et
                  <var>.n.o.p.</var>
                ſint recti: </s>
                <s xml:id="echoid-s1953" xml:space="preserve">ſi imaginati fuerimus
                  <reg norm="tranſ" type="context">trãſ</reg>
                  <lb/>
                latum eſſe
                  <reg norm="pondusipſius" type="simple">pondusipſiꝰ</reg>
                  <var>.n.</var>
                in
                  <var>.o.</var>
                  <reg norm="cum" type="context">cũ</reg>
                  <reg norm="eadem" type="context">eadẽ</reg>
                inclinatione ad depræſſiorem partem, illud ip
                  <lb/>
                ſum, ac ſi eſſet in
                  <var>.n.</var>
                communi conceptu, ſine alicuius diametri mutatione præſtabit.
                  <lb/>
                </s>
                <s xml:id="echoid-s1954" xml:space="preserve">Et ſi centrum
                  <var>.q.</var>
                fixum eſſet, & extremo
                  <var>.p.</var>
                appoſitum fuiſſet pondus ipſius
                  <var>.o.</var>
                cum in
                  <lb/>
                clinatione ad ſuperiorem partem, idem etiam planè pręſtaret, etiam ſi nullum ullius
                  <lb/>
                diametri ſitum, communi ſcientia, mutaret, cum extremum
                  <var>.m.</var>
                deorſum ſit ductum
                  <lb/>
                à. g. uirtute dimidiæ partis ipſius
                  <var>.i.</var>
                & ab alia huic ſimili
                  <var>.m.</var>
                quoque deorſum ſit tra-
                  <lb/>
                ctum ab .o: quod quidem
                  <var>.o.</var>
                deorſum eſt alteratum, ob inclinationem ad ſuperius
                  <lb/>
                à uirtute poſita in
                  <var>.p.</var>
                ſupponendo centrum
                  <var>.q.</var>
                fixum. </s>
                <s xml:id="echoid-s1955" xml:space="preserve">Sed ſi loco centri fixi, imagina
                  <lb/>
                bimur in
                  <var>.q.</var>
                pondus aliquod æquale ipſi
                  <var>.i.</var>
                quod duplum erit in uirtute ad eam, quæ
                  <lb/>
                eſt ipſius
                  <var>.p.</var>
                & ipſius quoque .g: ſequetur
                  <reg norm="etiam" type="context">etiã</reg>
                eadem immobilitas horum trium dia-
                  <lb/>
                metrorum. </s>
                <s xml:id="echoid-s1956" xml:space="preserve">Quia cum ſit huiuſmodi pondus ſeu virtus in
                  <var>.q.</var>
                cum inclinatione con-
                  <lb/>
                traria virtuti in
                  <var>.p.</var>
                quæ æquipollet dimidiæ parti ipſius
                  <var>.q.</var>
                & ſic ei quæ eſt ipſius
                  <var>.o.</var>
                ſi-
                  <lb/>
                militer quia
                  <var>.o.</var>
                tractum eſt ſupra ab
                  <var>.n.</var>
                virtute ipſius
                  <var>.g.</var>
                quod
                  <var>.m.</var>
                deorſum trudit; </s>
                <s xml:id="echoid-s1957" xml:space="preserve">idcir
                  <lb/>
                co quanta erit vis quam habebit virtus in
                  <var>.q.</var>
                ferendi deorſum diametrum
                  <var>.p.o.</var>
                tanta
                  <lb/>
                quoque virtutes ipſorum
                  <var>.p.</var>
                et
                  <var>.o.</var>
                æquales, & æqualiter diſtantes à
                  <var>.q.</var>
                ipſum ad ſupe-
                  <lb/>
                riorem partem inclinabunt. </s>
                <s xml:id="echoid-s1958" xml:space="preserve">Quamobrem nec aſcender, nec deſcendet, nec locum
                  <lb/>
                mutabit. </s>
                <s xml:id="echoid-s1959" xml:space="preserve">Supponamus nunc quartum diametrum rotulæ
                  <var>.s.t.r.</var>
                quæ ſit ſecunda rotu
                  <lb/>
                larum fixarum, parallela ipſi
                  <var>.p.o.</var>
                & in eo ſitu, quo coniungendo extrema
                  <var>.r.p.</var>
                anguli
                  <lb/>
                  <var>o.p.r.</var>
                et
                  <var>.p.r.s.</var>
                ſint recti, & imaginemur virtutem ipſius
                  <var>.p.</var>
                reperiri in
                  <var>.s.</var>
                cum inclinatio
                  <lb/>
                ne tamen contraria, ideſt deorſum verſus, ex his
                  <reg norm="idem" type="context">idẽ</reg>
                quoque planè ſequetur, ideſt
                  <reg norm="quod" type="simple">ꝙ</reg>
                  <lb/>
                nulla
                  <reg norm="harum" type="context">harũ</reg>
                quatuor diametrorum mouebitur. </s>
                <s xml:id="echoid-s1960" xml:space="preserve">quia eundem
                  <reg norm="effectum" type="context">effectũ</reg>
                  <reg norm="cum" type="context">cũ</reg>
                inclinatione
                  <lb/>
                deorſum verſus efficeret dicta virtus in
                  <var>.s.</var>
                quem in
                  <var>.p.</var>
                cum inclinatione ſurſum verſus.
                  <lb/>
                </s>
                <s xml:id="echoid-s1961" xml:space="preserve">et iam dictum eſt virtutem ipſius
                  <var>.g.</var>
                dimidium virtutis ipſius
                  <var>.i.</var>
                trahere
                  <var>.m.</var>
                quæ
                  <reg norm="mediam" type="context">mediã</reg>
                  <lb/>
                  <handwritten xlink:label="hd-0176-01" xlink:href="hd-0176-01a" number="18"/>
                te
                  <var>.n.</var>
                attrahit
                  <var>.o.</var>
                eodem robore, et
                  <var>.s.</var>
                eadem vi trahit
                  <var>.p.</var>
                medio ipſius
                  <var>.r</var>
                . </s>
                <s xml:id="echoid-s1962" xml:space="preserve">Hucuſque
                  <reg norm="ſcien- tificè" type="context">ſciẽ-
                    <lb/>
                  tificè</reg>
                nouimus pondus, aut virtutem ipſius
                  <var>.s.</var>
                quæ eſt dimidium
                  <reg norm="ipſius" type="simple">ipſiꝰ</reg>
                  <var>.i.</var>
                ſuſtinere uim
                  <lb/>
                ipſorum
                  <var>.i.</var>
                et
                  <var>.q.</var>
                nam quater tantum, quanta ipſamet virtus ipſius
                  <var>.s.</var>
                eſſe conſpicitur.
                  <lb/>
                </s>
                <s xml:id="echoid-s1963" xml:space="preserve">Et ſi adiunctę nobis eſſent duæ aliæ diametri cum ijſdem planè conditionibus
                  <reg norm="ijſdem" type="context">ijſdẽ</reg>
                  <lb/>
                rationibus vtentes, cognoſceremus quod eadem medietas ipſius
                  <var>.i.</var>
                ſexies tantum
                  <reg norm="pon" type="context">põ</reg>
                  <lb/>
                deris, quanta ipſa exiſteret, ſeſtineret. </s>
                <s xml:id="echoid-s1964" xml:space="preserve">Vnde
                  <reg norm="manifeſtum" type="context">manifeſtũ</reg>
                euadit,
                  <reg norm="quod" type="simple">ꝙ</reg>
                eidem medietati
                  <lb/>
                ipſius
                  <var>.i.</var>
                in
                  <var>.s.</var>
                nonnihil virtutis addendo, dictæ diametri, illicò
                  <reg norm="mouerentur" type="context">mouerẽtur</reg>
                ſitu. </s>
                <s xml:id="echoid-s1965" xml:space="preserve">Et quia
                  <lb/>
                rotulæ in quolibet puncto, aliquam diametrum habent, neceſſariò ſequitur
                  <reg norm="quod" type="simple">ꝙ</reg>
                infe-
                  <lb/>
                riores ad ſuperiores accedere debeant. </s>
                <s xml:id="echoid-s1966" xml:space="preserve">Attamen ſi forte extremum immobile ip-
                  <lb/>
                ſius funis non pendet à puncto
                  <var>.e.</var>
                trochleæ ſuperioris, ſed alligatum fuerit ad
                  <reg norm="medium" type="context">mediũ</reg>
                  <lb/>
                inferioris trochleæ ut ad punctum
                  <var>.i.</var>
                ope unius trochleę ſuperioris immobilis vt in fi
                  <lb/>
                gura
                  <var>.A.</var>
                videre licet, clarè patebit
                  <reg norm="quod" type="simple">ꝙ</reg>
                à tribus virtutibus æqualibus pondus in
                  <var>.i.</var>
                  <reg norm="poſitum" type="context">poſitũ</reg>
                  <lb/>
                ſuſtinebitur: </s>
                <s xml:id="echoid-s1967" xml:space="preserve">hoc eſt à
                  <var>.g.</var>
                ab
                  <var>.i.</var>
                & ab
                  <var>.k.</var>
                  <reg norm="quarum" type="context">quarũ</reg>
                vnaquęque tertia pars erit ipſius
                  <var>.i.</var>
                in con
                  <lb/>
                c
                  <unsure/>
                ontrariam
                  <reg norm="partem" type="context">partẽ</reg>
                , hoc eſt tertia pars reſiſtentiæ. </s>
                <s xml:id="echoid-s1968" xml:space="preserve">propterea
                  <reg norm="quod" type="simple">ꝙ</reg>
                ex æquo inter ſe
                  <reg norm="diſtant" type="context">diſtãt</reg>
                . </s>
              </p>
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