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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ſed exceſſus quartæ ſupra tertiam eſt .10. vnde ſupra ſecundam erit .18. & ſupra pri-
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mam erit .24. quæ omnia ſimul addita erunt .44. & in qualibet harum trium remane-
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bit una pars æqualis primæ quantitati, </
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<
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">quare ſi ex .96. detractus fuerit numerus .44.
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reliquus 52. erit quadruplus primæ, </
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tia .27. & quarta .37. quarum omnium ſumma eſt .96.</
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<
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">EX poſitionibus autem Tartaleæ in noſtra figura
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digeſtis, videre poſſumus
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quo pacto
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huiuſ
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modi
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numeri ſimpli-
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ces .36. et .52. more figuræ
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quia
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colliguntur primò partes compoſi
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tæ .9. 15. 23. 33. ex quarum ſumma
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80. ſubtrahitur .36. ſumma ſim-
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plex ex ſimplicibus partibus .9. 9.
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9. 9. &
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quod eſt .44. ſubdu
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citur ex .96. ſumma compoſita &
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propoſita, vnde remanet .52. pro
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ſumma ſimplici, ex numero dato,
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cuius proportio ad .13. eadem eſt
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quæ .36 ad .9. & proptereà ſuper-
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flua eſt ſecunda poſitio,
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ſci
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mus inuenire tales duos numeros
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conſequentes, vt in hoc exemplo
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ſunt .36. et .52. quia ex regula de
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tribus poſteà elicitur veritas quæ-
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ſita. </
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dico de 33. problemate.</
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piantur poſitiones primi
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pli Tonſtalli hoc eſt .33. et .31. vt in figuris hic ſubiectis
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facile quis poteſt vi-
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dere, vbi in figura P. videbit nume-
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ros compoſitos, in figura verò
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cer
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net numeros ſimplices, à quibus pro
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ueniunt rationes per ſe huiaſmodi
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operationis, in figura autem
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vide
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bitur meus ordo, & iſtæ tres figuræ ſi
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miles
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tribus illis primis
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ita quòd cum quis illas intellexerit, il
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lico etiam iſtas cognoſcet, vbi
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videbit quam confusè
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ij
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qui ignorant hunc meum ordinem
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ſimplicium
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, à quibus fluit
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tota ratio (vt ſupra dixi) huiuſcemo
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di operationis.</
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