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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<
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xml:space
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ſitquinque librarum, quorum vnum ſit aureum, aliud argenteum, reliquum verò
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mixtum ex ijs duobus metallis, vnde corpus aureum ſimplex minus erit, & argen
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teum maius corpore mixto, quod nulli dubium eſt, ſit nunc pondus corporis aquei
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ęqualis corpori aureo,
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.3. aquei verò ęqualis miſto, ſit
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3.
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quarta par
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te, aquei demum æqualisargenteo, librarum .4. cum dimidia, vnde exijs, quæ in præ
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cedenti theoremate, & in .126. theoremate diximus, ſi imaginatione concipiemus
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alia duo corpora ſimplicia, auri, & argenti, ſed æqualium magnitudinum mixto,
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habebimus proportionem ponderis aurei ad pondus corporis mixti vt
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librarum
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cum quarta vnius ad .3. libras, & proportio ponderis mixti ad pondus argentei erit,
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vt proportio librarum .4. cum dimidia ad tres libras cum quarta parte vnius libræ,
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& proportio ponderis aurei ad pondus argentei vt librarum .4. cum dimidia ad li-
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bras .3: hoc eſt aurei ad mixtum, vt .13. ad .12. & mixti ad argenteum, vt .18. ad .13.
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& aurei ad argenteum, vt .3. ad .2. ideſt, vt .18. ad .12.</
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<
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">Nunc inueniantur duo numeri ita inter ſe proportionati, vt .3. ad .2. habentes ta-
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men inter ipſos numerum ita proportionatum ad maximum, vt .12. ſe habet ad
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13
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13.</
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& ita proportionatum ad minimum, vt ſe habet .18. ad .13. quod hoc modo in-
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ueniemus, multiplicabimus .18. per .12. & proueniet nobis .216. pro numero me-
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dio, poſteà multiplicabimus .18. per .13. & proueniet .234. pro maximo,
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multi
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plicando .12. per .13. proueniet .156. pro minimo, ita quod .234. correſpondebit
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ponderi corporis aurei: </
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">216. verò ponderi mixti, et .156. ponderi argentei æqua-
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lium magnitudinum.</
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<
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">Cum autem proportiones horum trium corporum inuenerimus, ſi ordinem theo
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rematis .122. ſequemur, habebimus quod quærebamus, & inueniemus in præſenti
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exemplo proportionem ponderis auri ad pondus argenti in corpore mixto eſſe, vt
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180
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180.</
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ad .36. ſed quia ſuppoſitum fuit corpus mixtum eſſe quinque librarum, propte-
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reà dicemus. </
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<
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xml:space
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">Si .216. hoc eſt toti corpori mixto correſpondent quinque libræ tunc
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parti .180. hoc eſt auro in ipſo corpore mixto, correſpondent libræ .4. cum duabus
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vncijs, ex regula detribus, reſiduum verò quinque librarum, ideſt vnciæ decem,
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correſpondent parti .36. hoc eſt argento in dicto corpore mixto.</
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<
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xml:space
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">Sed ſi tria corpora dicta fuiſſent inuicem ita proportionata, vt .40. 47. 60. </
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proportio auri ad argentum in corpore mixto eſſet vt .13. ad .7. quapropter
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pon
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dus mixti fuiſſet .120. librarum, </
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<
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xml:space
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">tunc aurum ipſius eſſet librarum .78. argentum ve-
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rò librarum .42. ex eadem regula.</
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<
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xml:space
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">Pro quarum rerum ſpeculatione nil aliud oportet nunc dicere cum ſatis dictum à no
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bis ſuperius fuerit, vno excepto, hoc eſt rationem reddere, qua motus fui ad inue
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niendos illos .3. numeros ita inter ſe diſpoſitos, vt dictum eſt, quæ quidem ratio fuit,
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vt haberemus .3. numeros ita inter ipſos ordinatè diſpoſitos, vt ſunt pondera trium
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illorum corporum æqualium magnitudinum. </
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<
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">Proptereà quòd quamuis inter pri-
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mos .3. numeros ponderum corporum aqueorum eædem fuerint proportiones pon
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derum corporum metallicorum, nihilominus medius numerus extra proprium lo-
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cum, & inordinatè inueniebatur, reſpectu extremorum, vnde medius numerus in
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ſuo vero ſitu inter .18. et .12. fuiſſent .16.
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.8. tertijs decimis, ſed vt
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incom
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moditatem euitemus, præcepi, vt multiplicarentur extrema per .13. vnde produ-
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cti fuerunt numeri .234. et .156. in
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proportione, quæ eſt .18. ad .12. ex .18. ſepti
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mi, iuſſi etiam multiplicari .18. per .12. vt nobis prodiret .216. ad quem numerum,
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numerus .234. ita ſe haberet, ut .13. ad .12. ex .19. ſeptimi, quod autem ita ſit propor </
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