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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IO. BAPT. BENED.
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118
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0118
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<
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xml:space
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">SEDijdem errores proueniunt exſummis partium ſimplicium.</
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xml:space
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">Vtexempli gratia, in figura
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ſumma propoſita partium ſimplicium eſt .39.
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vt diximus, eo quòd ab ipſo .50. detraxerimus .11. ſumma ſcilicet numerorum adij
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ciendorum ad efficiendas partes compofitas, ſumma poſteà fimplicium partium
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primæ poſitionis, erit .60. eo quòd prima pars erat .10. ſecunda autem ſimplex 20.
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tertia verò fimplex .30. iuxta ordinem propoſiti. </
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">Summa deinde ſimplicium
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fecundæ poſitionis effet .48. quia prima eius pars erat .8. ſecunda verò ſimplex .16.
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tertia autem ſimplex .24. vnde prima ſumma excederet datam .39. per .21. differen-
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tiæ, ſecunda verò per .9. vt ſupra vidimus de ſummis compoſitis à dato .50. compo-
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fito, & hoc quidem mirandum non eft, quod ſcilicet tres ſummæ fimplicium par-
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tium ſintinuicem inæqua-
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les, ijſdem differentijs me-
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diantibus, quibus
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dictæ tres ſummæ compofi
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tæ, cum ab vnaquaque
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ablatus fit nume-
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rus .11. æqualiter, vnde ex
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neceſſitate, permutando,
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differentiæ
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dæ erant æquales inuicem
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ex
<
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ius noſtri lib.</
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ſummæ enim
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compofitæ erant .71. 59. et
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50. fimplices verò .60. 48.
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et .39. differentes à primis
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per .11. vt dictum eft, qua
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re veritas ita manabit à compofitis, quemadmodum à fimplicibus, ſed à fimplici-
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bus per ſe, & a compofitis per accidens vtiam iam videbimus.</
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<
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">ANtiquorumigitur primus m odus vtitur regula detribus, hocordine, multi-
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plicando ſcilicet ſecundum errorem, qui eft .9. cum differentia primarum par
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tium pofitarum, quæ eft .2. & productum diuidendo per differentiam errorum, quæ
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eft .12. proueniens poftea quod eft .1. cum dimidio additur hoc loco primæ parti ſe-
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cundæ poſitionis.
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quòd benè ſe habet. </
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">Vbi animaduertendum eſt, quod ille
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numerus .12. non eft accipiendus per ſe vt differentia errorum hoc eft .21. et .9. nifi
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peràccidens, fed benè perfe, vt
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inter .60. er .48. ſimplices ſummas, quem
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admodum .9. in hoc propoſito eft differentia per ſe inter .48. et .39 per accidens ve-
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ro inter .59. et .50.</
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<
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">Cognoſcendum igitur eft mediante .24. quinti Eucli. quod eadem proportio
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eft primæ ſummæ (ſimplicium dico) ad ſuam primam partem, quæ ſecundæ ſum-
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mæ ad ſuam, & tertiæ ſummæ ad fuam fimiliter (vbi rectè etiam feciffent hoc in lo-
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co antiqui ſi multiplicauiffent tertiam ſummam fim plicem cum prima parte prioris
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fummæ fimplicis, & productum diuififfent per primam ſummam, vnde prima pars
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quæſita tertiæ ſummæ orta fuiffet, abſque ullo negotio ipfius plus velminus) </
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<
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habebimus tres terminos antecedentes ab vna parte, & tres terminos conſequen-
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tesab alia parte continentes vnam
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proportionem, vnde ex .19. quinti,
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vel .12. ſeptimi eorum differentiæ proportionales erunt, hoc eft,
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eadem propor </
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