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-s1389" xml:space="preserve">Diſponantur igitur huiuſmo-
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</figure>
di numeri tali ordine, vt fim-
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plex ſumma, quæ ab vna reli-
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quarum ſuperatur, & aliam ſupe-
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rat, medium locum teneat; </s>
<s xml:id="echoid-s1390" xml:space="preserve">@t
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in propoſito exemplo ſumma
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mediocris eft .48. quę à ſumma
<num value="60">.
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60.</num>
ſuperatur, & ſuperat ſum-
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mam .39. locata igitur fit hęc .48.
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inter illas, ſuæ verò primæ partes
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fimiliter conftitutæ ſint ſupra di-
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ctas ſummas, cum ſuis
<reg norm="differentijs" type="context">differẽtijs</reg>
,
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& tria producta iam dicta, vt in fi
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guris
<var>.C.</var>
et
<var>.D.</var>
arithmeticis
<lb/>
clarè patet: </s>
<s xml:id="echoid-s1391" xml:space="preserve">figura enim
<var>.C.</var>
eft
<lb/>
pro exemplo ipſius plus ſimpli-
<lb/>
citer: </s>
<s xml:id="echoid-s1392" xml:space="preserve">figura verò
<var>.D.</var>
pro exem-
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plo ipſius plus, & minus. </s>
<s xml:id="echoid-s1393" xml:space="preserve">Et fic
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</figure>
in figura
<var>.C.</var>
habebimus tres
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numeros confequentes .60. 48.
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39. & tres antecedentes .10. 8.
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6. cum dimidio, vnam, & ean-
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dem proportionem terminantes,
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ex .24. quinti, vt diximus; </s>
<s xml:id="echoid-s1394" xml:space="preserve">qua-
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re eorum differentiæ fimiliter
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proportionales erunt, quod etiam
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vidimus. </s>
<s xml:id="echoid-s1395" xml:space="preserve">Supponamus nunc nos
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ignorare æqualitatem maximi
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producti cum reliquis duobus,
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accipiendo ſolum pro hypoteſi,
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quòd dicta producta oriantur
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ex lateribus iam dictis.</s>
</p>
<p>
<s xml:id="echoid-s1396" xml:space="preserve">Demonſtrandum nobis nunc relinquetur, maximum productum æquale effere-
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liquis duobus; </s>
<s xml:id="echoid-s1397" xml:space="preserve">hoc eſt productum .168. æquale effe productis .90. et .78. quorum
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duorum productorum alterum .90. ſcilicet, generatur à differentia .9. quæ eft ſe-
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cundę, & tertię ſummæ, in primum numerum antecedentem, qui eſt .10. alterum vc-
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ro productum .78. ſcilicet, generatur à differentia .12. quę eſt primę, & ſecundę, ſum
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mę in tertium numerum antecedentem, qui eſt .6. cum dimidio, maximum vero
<lb/>
productum .168. ſcilicet generatur à differentia maxima .21. quę eft primę, & tertię
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ſummę (& ſemper ęqualis prioribus duabus differentijs .12. et .9.) in ſecundum nu-
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merum antecedentem, qui eſt .8.</s>
</p>
<p>
<s xml:id="echoid-s1398" xml:space="preserve">Conſtituantur igitur duo producta fimul iuncta ęqualia duobus .90. et .78.
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lateralibus ſupra vnam aliquam rectam lineam
<var>.q.p.</var>
<reg norm="fitque" type="simple">fitq́;</reg>
productum
<var>.f.g.</var>
ęquale
<num value="90">.
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90.</num>
productum verò
<var>.g.n.</var>
ęquale .78. fit etiam baſis
<var>.g.p.</var>
vt .9. et
<var>.g.q.</var>
vt .12. vnde
<var>.g.i.</var>
<lb/>
vel
<var>.q.n.</var>
erit vt .6. cum dimidio .et
<var>.g.d.</var>
vel
<var>.p.f.</var>
vt .10. & ideo
<var>.i.d.</var>
differentia erit .3. </s>
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