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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<p>
<s xml:id="echoid-s1407" xml:space="preserve">
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
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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-
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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.
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cum .22. vigeſimisquartis, tertia autem .12. cum nouem vigeſimisquartis, quarta po­
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ſteà .25. cum .18. vigeſimisquartis, quinta demum erit .52. cum .12. vigeſimisquartis,
<lb/>
quarum omnium ſumma erit .100.</s>
</p>
<p>
<s xml:id="echoid-s1410" xml:space="preserve">STifelius in primo exemplo regulæ falſi, ita inquit.</s>
</p>
<p>
<s xml:id="echoid-s1411" xml:space="preserve">Quæratur numerus, à cuius dimidio ſubtractæ partes tertia, & quarta relin-
<lb/>
quatur .300.</s>
</p>
<p>
<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/>
<reg norm="numerum" type="context">numerũ</reg>
<lb/>
</figure>
quæſitum, </s>
<s xml:id="echoid-s1413" xml:space="preserve">quare cum quis multi
<lb/>
plicauerit .300. per .24. & produ-
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ctum diuiſerit per .5. proueniet
<num value="1440">.
<lb/>
1440.</num>
numerus quæſitus, ex vi
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regulæ de tribus.</s>
</p>
<p>
<s xml:id="echoid-s1414" xml:space="preserve">Conſideremus igitur
<reg norm="meam" type="context">meã</reg>
di-
<lb/>
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
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cipiat diuiſorem .5. vt
<reg norm="differentiam" type="context">differentiã</reg>
<lb/>
errorum & non ut differentiam
<lb/>
duorum conſequentium .5. et .10
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ſicuti eſt re uera, ut diuiſor dico,
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ex rationibus à me hic ſupra ad-
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ductis, quamuis vna & eadem ſit
<lb/>
quantitas neceſſariò ut patet.</s>
</p>
<p>
<s xml:id="echoid-s1415" xml:space="preserve">ACcipiamus adhuc aliud exemplum à Tartalea propoſitione .9.
<reg norm="datum" type="context">datũ</reg>
, &
<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/>
<lb/>
merorum ſubtrahendorum.</s>
</p>
<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-
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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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