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-div214" type="math:theorem" level="3" n="113">
              <p>
                <s xml:id="echoid-s996" xml:space="preserve">
                  <pb o="75" rhead="THEOREM. ARIT." n="87" file="0087" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0087"/>
                gulum
                  <var>.e.x.</var>
                erit minutorum .149. & ſecundorum .43. et
                  <var>.o.x.</var>
                minutorum .60. & ſecun.
                  <lb/>
                20. vt in dicta epiſtola, vnde rectangulum
                  <var>.o.f.</var>
                erit min .89. & ſecun .23. & quia re-
                  <lb/>
                ctangulum
                  <var>.o.i.</var>
                æquale eſt rectangulo
                  <var>.a.o.</var>
                ergo
                  <var>.o.i.</var>
                ſimiliter continebit min .8704.
                  <lb/>
                Nunc quia
                  <var>.a.c.</var>
                vel
                  <var>.o.u.</var>
                denotat iter vnius diei Saturni et
                  <var>.u.e.</var>
                vnius diei Iouis vt di-
                  <lb/>
                ximus ergo
                  <var>.u.o.</var>
                erit minutorum .2. ſecun
                  <var>.o.</var>
                & tertiarum .40. videlicet tertiarum
                  <num value="7240">.
                    <lb/>
                  7240.</num>
                ſuppoſito periodo totaliipſius Saturni dierum .10740. et
                  <var>.u.e.</var>
                erit
                  <reg norm="minutorum" type="context">minutorũ</reg>
                .
                  <lb/>
                4. ſecun .59. & ter .27. vel circa hoc eſt tertiarum .17967. vnde
                  <var>.o.e.</var>
                erit tertiarum
                  <num value="10727">.
                    <lb/>
                  10727.</num>
                </s>
                <s xml:id="echoid-s997" xml:space="preserve">Nuncſi dixerimus cum
                  <var>.o.e.</var>
                tertiarum .10727. dat
                  <var>.o.u.</var>
                vel
                  <var>.a.c.</var>
                (nam tam
                  <lb/>
                vna quam altera eſt tertiarum .7240.) quid dabit
                  <var>.a.u.</var>
                vel
                  <var>.o.c.</var>
                (quia tam vna quam
                  <lb/>
                altera eſt partium .4328.) clarum erit quòd dabit
                  <var>.o.n.</var>
                vel
                  <var>.u.t.</var>
                uel
                  <var>.e.i.</var>
                quia tam vna
                  <lb/>
                quam altera erit partium .2921. quæ partes coniunctæ cum fuerint cum partibus ip-
                  <lb/>
                ſius
                  <var>.a.u.</var>
                dabunt totam
                  <var>.a.t.</var>
                  <reg norm="partium" type="context">partiũ</reg>
                .7249. quæ erunt tot dies, hoc eſt periodus quæſita.</s>
              </p>
              <p>
                <s xml:id="echoid-s998" xml:space="preserve">Alia methodo ſimiliter poſſumus idem cognoſcere, ſcilicet dicendo ſi rectangu
                  <lb/>
                lum
                  <var>.f.o.</var>
                quod eſt minutorum .89. & ſecun .23. hoc eſt ſecundorum .5363. dat rectan
                  <lb/>
                gulum
                  <var>.o.x.</var>
                minutorum .60. & ſecun .20. hoc eſt ſecun .3620. quid dabit
                  <var>.a.u.</var>
                partium
                  <lb/>
                4328. vnde veniet
                  <var>.u.t.</var>
                partium .2921. ſimiliter, eo quod eadem proportio eſt rectan
                  <lb/>
                guli
                  <var>.f.o.</var>
                ad
                  <var>.o.x.</var>
                quæ
                  <var>.e.o.</var>
                ad
                  <var>.o.u.</var>
                ex prima ſexti, vel .18. 19. ſeptimi ſeu .15. quinti.</s>
              </p>
              <p>
                <s xml:id="echoid-s999" xml:space="preserve">Poſſet etiam aliquis dicere ſi
                  <var>.f.o.</var>
                dat
                  <var>.o.x.</var>
                quid dabit
                  <var>.o.a.</var>
                vnde veniet
                  <var>.o.t.</var>
                quo
                  <lb/>
                diuiſo per
                  <var>.o.u.</var>
                daret
                  <var>.u.
                    <lb/>
                  t.</var>
                quia ita ſe habet
                  <var>.a.o.</var>
                  <lb/>
                  <anchor type="figure" xlink:label="fig-0087-01a" xlink:href="fig-0087-01"/>
                ad
                  <var>.o.t.</var>
                vt
                  <var>.a.u.</var>
                ad
                  <var>.u.t.</var>
                ex
                  <lb/>
                ſupra hic iam citatis.</s>
              </p>
              <div xml:id="echoid-div215" type="float" level="4" n="2">
                <figure xlink:label="fig-0087-01" xlink:href="fig-0087-01a">
                  <image file="0087-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0087-01"/>
                </figure>
              </div>
              <p>
                <s xml:id="echoid-s1000" xml:space="preserve">Sed ego, in dicta epi-
                  <lb/>
                ſtola, aliam methodum
                  <lb/>
                obſeruaui, quæ eſt multi
                  <lb/>
                plicando minuta .8704.
                  <lb/>
                per .30.
                  <reg norm="productumque" type="simple">productumq́;</reg>
                di
                  <lb/>
                uiſi per min .5363. quaſi
                  <lb/>
                dicens. </s>
                <s xml:id="echoid-s1001" xml:space="preserve">Si
                  <var>.o.f.</var>
                dat
                  <var>.o.i.</var>
                  <lb/>
                quid dabit
                  <var>.e.f</var>
                . </s>
                <s xml:id="echoid-s1002" xml:space="preserve">Vnde exiam ſupradictis propoſitionibus veniet
                  <var>.e.i.</var>
                & quia permu-
                  <lb/>
                tando ita ſe habet
                  <var>.o.f.</var>
                ad
                  <var>.e.f.</var>
                vt
                  <var>.o.i.</var>
                ad
                  <var>.e.i.</var>
                ideo dixi, ſi min .89. cum ſecun .23. dat .30
                  <lb/>
                quid dabit min .8704.</s>
              </p>
            </div>
            <div xml:id="echoid-div217" type="math:theorem" level="3" n="114">
              <head xml:id="echoid-head132" xml:space="preserve">THEOREMA
                <num value="114">CXIIII</num>
              .</head>
              <p>
                <s xml:id="echoid-s1003" xml:space="preserve">PRoponunt veteres & quærunt aliud, nempe ſi duo iter agentes, eodem in-
                  <lb/>
                ſtanti diuerſis è locis proficiſcantur, ita vt vnus locum vnde alter profectus
                  <lb/>
                eſt petat,
                  <reg norm="alterque" type="simple">alterq́;</reg>
                altero velocior ſit, quo loco
                  <reg norm="quanue" type="context">quãue</reg>
                die ſibi inuicem occurrent.</s>
              </p>
              <p>
                <s xml:id="echoid-s1004" xml:space="preserve">Exempli gratia, Patauio profectus quidam Taurinum petit, eodem inſtanti al-
                  <lb/>
                ter Taurino Patauium,
                  <reg norm="eſtque" type="simple">eſtq́;</reg>
                iter .400. milliarium, ille tamen vndecim diebus, hic
                  <lb/>
                9. motu regulari & vniformi appellit. </s>
                <s xml:id="echoid-s1005" xml:space="preserve">Quærimus quot milliaria quiſque confece-
                  <lb/>
                rit,
                  <reg norm="quotque" type="simple">quotq́;</reg>
                diebus iter egerit, priuſquam ſibi occurrant.</s>
              </p>
              <p>
                <s xml:id="echoid-s1006" xml:space="preserve">Iubent nos veteres dies vtriuſque inuicem inter ſe multiplicare,
                  <reg norm="eritque" type="simple">eritq́;</reg>
                produ-
                  <lb/>
                ctum .99. item etiam in ſummam colligere,
                  <reg norm="eritque" type="simple">eritq́;</reg>
                ſumma .20. per quam
                  <reg norm="productum" type="context">productũ</reg>
                .
                  <lb/>
                99.@diuiſerimus dabuntur dies .4. cum .19. vigeſimis vnius diei. </s>
                <s xml:id="echoid-s1007" xml:space="preserve">At pro milliaribus
                  <lb/>
                vtriuſque, pro eo qui .11. diebus iter conficit, multiplicatis .400. per .4. et .19. vigeſi
                  <lb/>
                mis, tum diuiſo per .11. dabitur numerus .180. à Patauio Taurinum & è contra, qui </s>
              </p>
            </div>
          </div>
        </div>
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