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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38
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0038
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numerum inquam, cui differentia duorum quæſitorum æquanda eſt, in ſeipſum
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multiplicare, atque huic quadrato, ſecundum numerum propoſitum iungere, cui,
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productum numerorum quæſitorum æquale eſſe debet, & ex hac ſumma eruere qua
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dratam radicem, quæ coniuncta dimidio primi numeri propoſiti, dabit maiorem
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duorum numerorum & ex eadem radice detracto dimidio primi numeri, minorem
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numerum duorum quæſitorum.</
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<
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">Exempli gratia, ſi proponeretur .12. cui differentia vnius numeri ab altero æqua-
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ri deberet, tum proponeretur .64. cui productum multiplicationis duorum quæſi-
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torum ſimul
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eſſet. </
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.36. cui coniuncto ſecundo, nempe .64. totum eſſet .100.
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ex quo detracta quadrata radice .10. etipſi coniuncto ſenario, dimidio primi nume
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ri, & ex eadem detracto eodem dimidio .6. pro maiore numero proueniret .16. &
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pro minore .4.</
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differentia cognita duorum incognitorum
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numerorum
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et
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quorum productum datum ſiue cognitum ſit
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: conſide-
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remus nunc
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dimidium
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datæ differentiæ, & ex compoſito
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imaginetur
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quadratum
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in quo protracta ſit
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æquidiſtans lateri
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& tam ab ipſa
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re
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mota, quam
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ab
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vnde
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quadratum erit
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dimidiæ ſcilicet differentiæ datæ
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et
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rectan-
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gulum æquale erit rectangulo
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vt cuilibet licet
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per ſe conſiderare, vnde ſequitur gnomonem
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æqualem eſſe producto
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ideo cognitus, qui
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gnomon, ſi coniunctus fuerit quadrato
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cognito
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ex radice
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cognita (vt dimidia toralis differentię
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e.o.</
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datæ) habebimus quadratum totale
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cogni-
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tum, & ita eius radicem
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cognitam & reliqua om
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nia conſequenter quæ quidem ſpeculatio eadem eſt
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quæ .6. ſecundi ſeu .8. noni Euclidis.</
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ti theoremate allatis, hocipſum concludere.</
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.</
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">CVR ij, qui aliquo propoſito numero, inuenturi ſunt duos numeros inter ſe
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differentes, quorum quadratorum ſumma altero numero propoſito æqualis
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ſit, rectè primum numerum propoſitum in ſeipſum multiplicant, quod quadratum
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exſecundo numero
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, & dimidium reſidui ſumunt, quod productum erit
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multiplicationis duorum numerorum interſe, in reliquis præcedentis theorematis
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ordinem ſequuntur.</
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<
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">Exempli gratia, ſi proponeretur .12. tanquam numerus, cui differentia duorum
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numerorum quæſitorum æquanda eſt, proponerentur præterea .272. quibus ſum-
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ma quadratorum duorum numerorum quæſitorum æquari deberet, oporteret ſanè
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primum numerum, nempe .12. in ſeipſum multiplicare, cuius
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hoc loco
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eſſet .144. atque hoc detrahere ex ſecundo numero, ſupereſſet .128. ſumpto
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deinde dimidio huiuſce numeri, népe .64. producto in quam duorum numerorum
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<
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. </
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<
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">Cum hoc .64. proſtea et duodenario primo propoſito numero, præceden
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tis theorematis ordinem ſequeremur.</
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