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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                <s xml:id="echoid-s1407" xml:space="preserve">
                  <pb o="111" rhead="THEOREM. ARIT." n="123" file="0123" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0123"/>
                ſecunda verò eſſet .5. pro additione ad tertiam partem ſimplicium, tertia autem eſ-
                  <lb/>
                ſet .11. pro additione ad quartam partem ſimplicium, quarta demum eſſet .23. pro
                  <lb/>
                additione quintæ partis ſimplicium, quarum partium .2. 5. 11. 23. ſumma eſt .41. vt
                  <lb/>
                diximus. </s>
                <s xml:id="echoid-s1408" xml:space="preserve">Hæc igitur ſumma .41. ſubducenda eſt à numero .100. propoſito, vnde re-
                  <lb/>
                linquetur .59. pro ſumma partium ſimplicium numeri propoſiti, quarum prima erit
                  <lb/>
                2. cum vndecim vigeſimisquartis ex diuiſione huiuſmodi .59. per .24. ſummam par-
                  <lb/>
                tium ſimplicium ex viregulæ de tribus, dicendo ſi .24. prouenit nobis ab .1. prima
                  <lb/>
                partium ſimplicium, à quo proueniet nobis .59? </s>
                <s xml:id="echoid-s1409" xml:space="preserve">vnde proueniet à .2. cum vndecim
                  <lb/>
                vigeſimisquartis pro prima parte quæſita, ſecunda verò iuxta propoſitum, erit .6.
                  <lb/>
                cum .22. vigeſimisquartis, tertia autem .12. cum nouem vigeſimisquartis, quarta po­
                  <lb/>
                ſteà .25. cum .18. vigeſimisquartis, quinta demum erit .52. cum .12. vigeſimisquartis,
                  <lb/>
                quarum omnium ſumma erit .100.</s>
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              <p>
                <s xml:id="echoid-s1410" xml:space="preserve">STifelius in primo exemplo regulæ falſi, ita inquit.</s>
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              <p>
                <s xml:id="echoid-s1411" xml:space="preserve">Quæratur numerus, à cuius dimidio ſubtractæ partes tertia, & quarta relin-
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                quatur .300.</s>
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                <s xml:id="echoid-s1412" xml:space="preserve">Ipſe enim ſupponit .300. pro reſiduo cognito alterius numeri incogniti, deinde
                  <lb/>
                accipit .24. pro prima poſitione numeri cogniti, à cuius medietate abſcindit tertiam
                  <lb/>
                & quartam partem ipſius medietatis, vnde remanet .5. qui quidem numerus .5. ex
                  <num value="22">.
                    <lb/>
                  22.</num>
                quinti vel .15. ſeptimiſe ha-
                  <lb/>
                bebit ad .24. vt .300. ad
                  <reg norm="numerum" type="context">numerũ</reg>
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                  <anchor type="figure" xlink:label="fig-0123-01a" xlink:href="fig-0123-01"/>
                quæſitum, </s>
                <s xml:id="echoid-s1413" xml:space="preserve">quare cum quis multi
                  <lb/>
                plicauerit .300. per .24. & produ-
                  <lb/>
                ctum diuiſerit per .5. proueniet
                  <num value="1440">.
                    <lb/>
                  1440.</num>
                numerus quæſitus, ex vi
                  <lb/>
                regulæ de tribus.</s>
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              <p>
                <s xml:id="echoid-s1414" xml:space="preserve">Conſideremus igitur
                  <reg norm="meam" type="context">meã</reg>
                di-
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                ſpoſitionem numerorum huiuſ-
                  <lb/>
                modi exempli, in figura hic ſup-
                  <lb/>
                poſita
                  <var>.F.</var>
                in qua videre licebit
                  <lb/>
                quo pacto ipſe etiam Stifelius ac
                  <lb/>
                cipiat diuiſorem .5. vt
                  <reg norm="differentiam" type="context">differentiã</reg>
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                errorum & non ut differentiam
                  <lb/>
                duorum conſequentium .5. et .10
                  <lb/>
                ſicuti eſt re uera, ut diuiſor dico,
                  <lb/>
                ex rationibus à me hic ſupra ad-
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                ductis, quamuis vna & eadem ſit
                  <lb/>
                quantitas neceſſariò ut patet.</s>
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                <s xml:id="echoid-s1415" xml:space="preserve">ACcipiamus adhuc aliud exemplum à Tartalea propoſitione .9.
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                , &
                  <reg norm="oppoſitum" type="context">oppoſitũ</reg>
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                priori; </s>
                <s xml:id="echoid-s1416" xml:space="preserve">nam ſicut in illo numerus ſimplex habebatur per ſubtractionem ſum-
                  <lb/>
                mæ numerorum adijciendorum, in hoc fitèconuerſo, hoc eſt per additionem nu-
                  <lb/>
                merorum ſubtrahendorum.</s>
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              <p>
                <s xml:id="echoid-s1417" xml:space="preserve">Problema igitur ita ſe habet. </s>
                <s xml:id="echoid-s1418" xml:space="preserve">Fuit quidam mercator qui habebat aliquot au-
                  <lb/>
                reos, cuius quantitas poſteà quærenda erit, hic enim fecit duo itinera, ut aliquod
                  <lb/>
                dictis aureis mediantibus lucrum faceret, in primo autem itinere duplicauit nume-
                  <lb/>
                rum ſuorum aureorum, ex quibus poſteà conſumpſit .4. pro aliquibus expenſis, in </s>
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