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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THEOREM. ARIT.
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            <div xml:id="echoid-div226" type="math:theorem" level="3" n="118">
              <p>
                <s xml:id="echoid-s1070" xml:space="preserve">
                  <pb o="81" rhead="THEOREM. ARIT." n="93" file="0093" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0093"/>
                componitur ex
                  <var>.d.c.</var>
                dupla .ad
                  <var>.a.c.</var>
                pri-
                  <lb/>
                  <anchor type="figure" xlink:label="fig-0093-01a" xlink:href="fig-0093-01"/>
                mam partem, & ex
                  <var>.d.e.</var>
                numero dato.
                  <lb/>
                </s>
                <s xml:id="echoid-s1071" xml:space="preserve">tertia verò pars
                  <var>.e.b.</var>
                compoſita eſt ex
                  <var>.
                    <lb/>
                  e.f.</var>
                æquali
                  <var>.a.e.</var>
                hoc eſt æquali compoſi-
                  <lb/>
                to ex prima, & ſe cunda parte, & ex
                  <var>.f.
                    <lb/>
                  b.</var>
                numero dato vt proponebatur.</s>
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            <div xml:id="echoid-div228" type="math:theorem" level="3" n="119">
              <head xml:id="echoid-head137" xml:space="preserve">THEOREMA
                <num value="119">CXIX</num>
              .</head>
              <p>
                <s xml:id="echoid-s1072" xml:space="preserve">INter alia problemata ab antiquis inuenta, hoc etiam ponitur. </s>
                <s xml:id="echoid-s1073" xml:space="preserve">Aliquis inter-
                  <lb/>
                rogat quot ſint horæ, alius verò reſpondit tot eſſe, quot duæ tertiæ præteriti
                  <lb/>
                temporis ſimul iuncta cum tribus quintis futuri temporis totius dieri naturalis effi-
                  <lb/>
                ciunt. </s>
                <s xml:id="echoid-s1074" xml:space="preserve">Nunc quæritur quot ſint horę.</s>
              </p>
              <p>
                <s xml:id="echoid-s1075" xml:space="preserve">Antiqui, hoc etiam problema ſoluebant mediante regula falſi, ſed mihi alio mo
                  <lb/>
                do ſoluendum eſſe dictum problema videtur. </s>
                <s xml:id="echoid-s1076" xml:space="preserve">Accipio enim ex quinque, tres vni-
                  <lb/>
                tates, pro parte futuri temporis, quas quidem in tres vnitates præteriti temporis
                  <lb/>
                duco, vnde proueniunt mihi nouem vnitates, quod productum coniungo
                  <reg norm="cum" type="context">cũ</reg>
                quin-
                  <lb/>
                que futuri temporis, vnde veniunt .14. vnitates, ex regula poftea de tribus ita dico
                  <lb/>
                ſi ex .14. mihi prouenit .9. quid reſultabit ex .24. & prouenient mihi horæ .15. cum
                  <lb/>
                tribus ſeptimis vnius horæ, hoc eſt minuta ferè .26.</s>
              </p>
              <p>
                <s xml:id="echoid-s1077" xml:space="preserve">Pro cuius ratione, quinque vnitates, feu partes temporis futuri ſignificentur à
                  <lb/>
                linea
                  <var>.e.u.</var>
                quarum trium ſigniſicentur a linea
                  <var>.e.i.</var>
                ſumpta deinde ſit linea
                  <var>.e.o.</var>
                æqualis
                  <lb/>
                lineæ
                  <var>.e.i.</var>
                et
                  <var>.e.a.</var>
                tripla ſit ad
                  <var>.o.e.</var>
                vel ad
                  <var>.e.i.</var>
                quod idem eſt, vnde
                  <var>.a.e.</var>
                compoſita erit
                  <lb/>
                ex
                  <var>.a.o.</var>
                (hoc eſt ex duabus tertijs ip ſius
                  <var>.a.e.</var>
                ) & ex
                  <var>o.e.</var>
                (hoc eſt ex. tribus quintis ip-
                  <lb/>
                ſius
                  <var>.e.u.</var>
                ) vnde
                  <var>.a.u.</var>
                ad
                  <var>.a.e.</var>
                eandem rationem obtinebit, quæ .14. ad .9. </s>
                <s xml:id="echoid-s1078" xml:space="preserve">propterea igi
                  <lb/>
                tur poſſumus recte ratiotinari
                  <lb/>
                  <anchor type="figure" xlink:label="fig-0093-02a" xlink:href="fig-0093-02"/>
                fi .14. nobis dat .9. quid dabit .24.
                  <lb/>
                qui quidem .24. nobis dabit .15.
                  <lb/>
                cum min .26. quod rectè factum
                  <lb/>
                erit ex
                  <ref id="ref-0012">.20. ſeptimi Euclidis</ref>
                .</s>
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                <figure xlink:label="fig-0093-02" xlink:href="fig-0093-02a">
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            <div xml:id="echoid-div230" type="math:theorem" level="3" n="120">
              <head xml:id="echoid-head138" xml:space="preserve">THEOREMA
                <num value="120">CXX</num>
              .</head>
              <p>
                <s xml:id="echoid-s1079" xml:space="preserve">SVpponunt etiam antiqui tres ſocios nummos habere, quorum ſumma primi &
                  <lb/>
                ſecundi cognita ſit, item ſumma primi & tertij cognita & ſumma ſecundi &
                  <lb/>
                tertij item cognita, at que ex huiuſmodi tribus aggregatis veniunt in cognitionem
                  <lb/>
                particularem vniuſcuiuſque illorum.</s>
              </p>
              <p>
                <s xml:id="echoid-s1080" xml:space="preserve">Gemafriſius ſoluit hoc problema ex regula ſalſi. </s>
                <s xml:id="echoid-s1081" xml:space="preserve">At ego tali ordine progredior.
                  <lb/>
                </s>
                <s xml:id="echoid-s1082" xml:space="preserve">Sit verbi gratia, ſumma primi cum ſecundo .50. & ſecundi cum tertio .70. & primi
                  <lb/>
                cum tertio .60. harum trium ſummarum accipiantur duæ quæuis, vt puta .50. & .70
                  <lb/>
                quæ coniunctæ ſimul dabunt .120. à qua ſumma detrahatur reliqua, ideſt .60. &
                  <lb/>
                reſtabit nobis .60. cuius medietas erit .30. hoc eſt numerus nummorum ſecundi
                  <lb/>
                ſocij quo numero detracto à .70. hoc eſt à ſumma ſecundi cum tertio remanebit .40.
                  <lb/>
                hoc eſt numerus tertij ſocij, & hic numerus deſumptus à .60. reſiduus erit nume-
                  <lb/>
                rus primi ſocij.</s>
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