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-s1456" xml:space="preserve">
ſed exceſſus quartæ ſupra tertiam eſt .10. vnde ſupra ſecundam erit .18. & ſupra pri-
<lb/>
mam erit .24. quæ omnia ſimul addita erunt .44. & in qualibet harum trium remane-
<lb/>
bit una pars æqualis primæ quantitati, </s>
<s xml:id="echoid-s1457" xml:space="preserve">quare ſi ex .96. detractus fuerit numerus .44.
<lb/>
reliquus 52. erit quadruplus primæ, </s>
<s xml:id="echoid-s1458" xml:space="preserve">quare prima pars valebit .13. ſecunda .19. ter-
<lb/>
tia .27. & quarta .37. quarum omnium ſumma eſt .96.</s>
</p>
<p>
<s xml:id="echoid-s1459" xml:space="preserve">EX poſitionibus autem Tartaleæ in noſtra figura
<var>.K.</var>
digeſtis, videre poſſumus
<lb/>
quo pacto
<reg norm="colligantur" type="context">colligãtur</reg>
huiuſ
<lb/>
modi
<reg norm="conſequentes" type="context">conſequẽtes</reg>
numeri ſimpli-
<lb/>
ces .36. et .52. more figuræ
<var>.E.</var>
quia
<lb/>
</figure>
colliguntur primò partes compoſi
<lb/>
tæ .9. 15. 23. 33. ex quarum ſumma
<lb/>
80. ſubtrahitur .36. ſumma ſim-
<lb/>
plex ex ſimplicibus partibus .9. 9.
<lb/>
9. 9. &
<reg norm="reſiduum" type="context">reſiduũ</reg>
quod eſt .44. ſubdu
<lb/>
citur ex .96. ſumma compoſita &
<lb/>
propoſita, vnde remanet .52. pro
<lb/>
ſumma ſimplici, ex numero dato,
<lb/>
<lb/>
quæ .36 ad .9. & proptereà ſuper-
<lb/>
flua eſt ſecunda poſitio,
<reg norm="quando" type="context">quãdo</reg>
ſci
<lb/>
mus inuenire tales duos numeros
<lb/>
conſequentes, vt in hoc exemplo
<lb/>
ſunt .36. et .52. quia ex regula de
<lb/>
tribus poſteà elicitur veritas quæ-
<lb/>
ſita. </s>
<s xml:id="echoid-s1460" xml:space="preserve">
<reg norm="Idem" type="context">Idẽ</reg>
dico de 33. problemate.</s>
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<p>
<s xml:id="echoid-s1461" xml:space="preserve">PRO quo .33. problemate acci
<lb/>
piantur poſitiones primi
<reg norm="exem" type="context">exẽ</reg>
<lb/>
pli Tonſtalli hoc eſt .33. et .31. vt in figuris hic ſubiectis
<var>.P.Q.</var>
facile quis poteſt vi-
<lb/>
dere, vbi in figura P. videbit nume-
<lb/>
ros compoſitos, in figura verò
<var>.Q.</var>
cer
<lb/>
</figure>
net numeros ſimplices, à quibus pro
<lb/>
ueniunt rationes per ſe huiaſmodi
<lb/>
operationis, in figura autem
<var>.R.</var>
vide
<lb/>
bitur meus ordo, & iſtæ tres figuræ ſi
<lb/>
miles
<reg norm="erunt" type="context">erũt</reg>
tribus illis primis
<var>.A.B.C.</var>
<lb/>
ita quòd cum quis illas intellexerit, il
<lb/>
lico etiam iſtas cognoſcet, vbi
<reg norm="etiam" type="context">etiã</reg>
<lb/>
videbit quam confusè
<reg norm="ratiocinentur" type="context">ratiocinẽtur</reg>
ij
<lb/>
qui ignorant hunc meum ordinem
<lb/>
ſimplicium
<reg norm="numerorum" type="context">numerorũ</reg>
, à quibus fluit
<lb/>
tota ratio (vt ſupra dixi) huiuſcemo
<lb/>
di operationis.</s>
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