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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DE MECHAN.
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          <div xml:id="echoid-div340" type="chapter" level="2" n="3">
            <div xml:id="echoid-div346" type="section" level="3" n="4">
              <p>
                <s xml:id="echoid-s1738" xml:space="preserve">
                  <pb o="145" rhead="DE MECHAN." n="157" file="0157" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0157"/>
                grauius, quia tantò minus pendebit à centro
                  <var>.o.</var>
                & ratiocinando, vt ſuperius dixi-
                  <lb/>
                mus, inueniemus eundem effectum verum eſſe. </s>
                <s xml:id="echoid-s1739" xml:space="preserve">In ſtateris, rectè & propriè appella
                  <lb/>
                ri poteſt
                  <var>.x.i.s.</var>
                aut
                  <var>.n.o.u.</var>
                orizontalis, ſed in omni vectium ſpecie, hoc
                  <reg norm="tantum" type="context">tãtum</reg>
                per quan
                  <lb/>
                dam ſimilitudinem dicetur. </s>
                <s xml:id="echoid-s1740" xml:space="preserve">Idem contemplari licet ſupponendo centrum in medio
                  <lb/>
                inter
                  <var>.o.</var>
                et
                  <var>.i.</var>
                quod vnuſquiſque ex ſe abſque alterius auxilio facile præſtare poterit.</s>
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                <handwritten xlink:label="hd-0156-01" xlink:href="hd-0156-01a"/>
                <handwritten xlink:label="hd-0156-02" xlink:href="hd-0156-02a"/>
                <figure xlink:label="fig-0156-01" xlink:href="fig-0156-01a">
                  <image file="0156-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0156-01"/>
                </figure>
                <handwritten xlink:label="hd-0156-03" xlink:href="hd-0156-03a"/>
                <figure xlink:label="fig-0156-02" xlink:href="fig-0156-02a">
                  <image file="0156-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0156-02"/>
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            </div>
            <div xml:id="echoid-div348" type="section" level="3" n="5">
              <head xml:id="echoid-head203" style="it" xml:space="preserve">De quibuſdam rebus animaduerſione dignis.</head>
              <head xml:id="echoid-head204" xml:space="preserve">CAP.V.</head>
              <p>
                <s xml:id="echoid-s1741" xml:space="preserve">NOn omittenda mihi
                  <reg norm="videntur" type="context">vidẽtur</reg>
                quædam, quæ ad
                  <reg norm="tractationem" type="context">tractationẽ</reg>
                vectium admodum
                  <lb/>
                ſunt neceſſaria. </s>
                <s xml:id="echoid-s1742" xml:space="preserve">Quod autem quærimus, in eo conſiſtit, quòd aliqui vectes
                  <lb/>
                adhibeantur ad opus, quorum centrum, quod Græci
                  <reg norm="hypomochlion" type="context">hypomochliõ</reg>
                appellant vnum
                  <lb/>
                eſt ex extremis ipſius vectis, & pondus, quod ſurſum eleuari debet, inter ipſa-
                  <lb/>
                met extrema iacet, propinquum tamen hypomochlio, vt exempli gratia, ſi vectis
                  <lb/>
                eſſet infraſcripta figura
                  <var>.o.s.u.x.</var>
                cuius hypomochlion eſſet in puncto
                  <var>.o.</var>
                & pondus in
                  <lb/>
                puncto
                  <var>.n.</var>
                clarum erit,
                  <reg norm="quod" type="simple">ꝙ</reg>
                cum eleuari debeat
                  <var>.n.</var>
                oportebit quoque opera manus ele-
                  <lb/>
                uari
                  <var>.u</var>
                . </s>
                <s xml:id="echoid-s1743" xml:space="preserve">Nunc conſiderandum eſt quomodo pondus
                  <var>.n.</var>
                annitatur ad
                  <var>.u</var>
                . </s>
                <s xml:id="echoid-s1744" xml:space="preserve">Hanc ob cau
                  <lb/>
                ſam imaginabimur rectas lineas
                  <var>.n.o</var>
                :
                  <var>n.i</var>
                :
                  <var>n.e</var>
                :
                  <var>n.t.</var>
                et
                  <var>.n.u.</var>
                quarum
                  <var>.n.i.</var>
                verſus mundi cen
                  <lb/>
                trum ſit poſita, et
                  <var>.n.t.</var>
                faciat angulum
                  <var>.i.n.t.</var>
                æqualem angulo
                  <var>.i.n.o</var>
                . </s>
                <s xml:id="echoid-s1745" xml:space="preserve">Nunc ponendo ali
                  <lb/>
                quam virtutem in
                  <var>.i.</var>
                æquali inclinatione ad ſuperius conſtante, vt
                  <var>.n.</var>
                ad inferius (re-
                  <lb/>
                mota tamen grauitate materiæ vectis) huiuſmodi virtus, totum pondus ipſius
                  <var>.n.</var>
                com
                  <lb/>
                muni quadam ſcientiæ notione ſuſtinebit. </s>
                <s xml:id="echoid-s1746" xml:space="preserve">& ſi
                  <reg norm="pondus" type="context">põdus</reg>
                ipſius
                  <var>.n.</var>
                eſſet in
                  <var>.x.</var>
                è directo ſu-
                  <lb/>
                per
                  <var>.o.</var>
                totum pondus ſuper hypomochlio ſe haberet, & tanta virtus ipſius hypomo-
                  <lb/>
                chlij ſufficeret ad reſiſtendum pro ſuſtinendo, quanta eſt grauitas ipſius ponderis,
                  <lb/>
                ſed ipſum iterum ponamus in
                  <var>.n.</var>
                ibi clarum erit, quòd ſi alia virtus à parte inſeriori
                  <lb/>
                ad ſuperiorem vectis non opponitur, excepto tamen hypomochlio, oportebit virtu
                  <lb/>
                te cuiuſdam partis ponderis
                  <var>.n.</var>
                (abſque conſideratione tamen, vt iam dixi, ponderis
                  <lb/>
                materiæ vectis) vt vectis à parte
                  <var>.s.u.</var>
                deprimatur, & dixi vnius cuiuſdam partis pon-
                  <lb/>
                deris
                  <var>.n.</var>
                quia alia
                  <reg norm="eiuſdem" type="context">eiuſdẽ</reg>
                ponderis pars annititur ipſi hypomochlio
                  <var>.o.</var>
                  <reg norm="mediante" type="context">mediãte</reg>
                linea
                  <lb/>
                  <var>o.n.</var>
                quæ angulos rectos cum
                  <var>.o.x.</var>
                non facit. </s>
                <s xml:id="echoid-s1747" xml:space="preserve">Si autem à puncto
                  <var>.t.</var>
                opponet ſeſe huiuſ-
                  <lb/>
                modi reſiſtentia, vt vectis non deprimatur, clarum erit communi ſcientia,
                  <reg norm="quod" type="simple">ꝙ</reg>
                virtus
                  <lb/>
                ponderis
                  <var>.n.</var>
                diuiſa erit per medium æqualiter, cuius vna medietas ſuper
                  <var>.o.</var>
                quieſcet,
                  <lb/>
                & alia ſuper
                  <var>.t.</var>
                mediantibus duabus lineis
                  <var>.n.o.</var>
                et
                  <var>.n.t</var>
                . </s>
                <s xml:id="echoid-s1748" xml:space="preserve">Imaginemur nunc reſiſtentiam
                  <lb/>
                t. ablatam eſſe,
                  <reg norm="poſitamque" type="simple">poſitamq;</reg>
                in
                  <var>.e.</var>
                clarum quoque erit,
                  <reg norm="quod" type="simple">ꝙ</reg>
                maior pars ponderis
                  <var>.n.</var>
                ipſi
                  <var>.e.</var>
                  <lb/>
                annitetur beneficio lineæ
                  <var>.n.e.</var>
                quàm ipſi
                  <var>.o.</var>
                cum linea
                  <var>.n.i.</var>
                inclinationis ipſi
                  <var>.e.</var>
                ſit pro
                  <lb/>
                pinquior quam
                  <var>.o.</var>
                quia omnis reſiſtentia aut in
                  <var>.i.</var>
                aut in
                  <var>.e.</var>
                aut in
                  <var>.t.</var>
                aut in
                  <var>.u.</var>
                eſt loco
                  <lb/>
                centri, quemadmodum eſt
                  <var>.o.</var>
                & alter alterius opera iuuatur. </s>
                <s xml:id="echoid-s1749" xml:space="preserve">Si verò eadem reſiſten
                  <lb/>
                tia poſita erit in
                  <var>.u.</var>
                clarum quoque erit,
                  <reg norm="quod" type="simple">ꝙ</reg>
                minor pars ponderis
                  <var>.n.</var>
                annitetur ipſi
                  <var>.u.</var>
                  <reg norm="quam" type="context">quã</reg>
                  <lb/>
                ipſi
                  <var>.o.</var>
                cum dicta
                  <var>.n.i.</var>
                à centro
                  <var>.u.</var>
                longius quam à centro
                  <var>.o.</var>
                diſter, & proportio partis
                  <lb/>
                ponderis
                  <var>.n.</var>
                in
                  <var>.o.</var>
                ad propor-
                  <lb/>
                tionem partis ponderis
                  <var>.n.</var>
                in
                  <lb/>
                  <anchor type="figure" xlink:label="fig-0157-01a" xlink:href="fig-0157-01"/>
                u. non erit
                  <reg norm="ſecundum" type="context">ſecũdum</reg>
                propor
                  <lb/>
                tionem angulorum
                  <var>.u.n.i.</var>
                et
                  <lb/>
                  <var>o.n.i.</var>
                ſed ſecundum propor
                  <lb/>
                tionem
                  <var>.u.i.</var>
                ad
                  <var>.i.o.</var>
                quod cla
                  <lb/>
                rè compræhendi poteſt ab </s>
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