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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THEOR. ARITH.
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21
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0021
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<
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xml:space
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aut partitionem oriri ex regula de tri-
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bus, quandoquidem ſinguli diuidentes æquipollent vni integro, & loco illius ſu-
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muntur. </
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<
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xml:space
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obſeruare de tri-
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bus
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, ſi viginti æquipollent vni, quibus
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<
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? </
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<
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xml:space
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ſequenti figura facile deprehendetur, in qua linea
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ſignificat viginti, et
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var
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vni- tatem
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tatẽ</
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<
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, et
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vnitates lineares
<
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: </
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<
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xml:space
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et
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<
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vnitates lineares, et
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centum vnitates ſuperficiales, ex quo manife-
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ftè deprehenditur quòd quemadmodum multiplicare, nihil aliud eſt, quam inueni
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re
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ex duobus lateribus propoſitis, it a partiri nihil aliud eſt, quam da-
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to vno latere inuenire aliud latus producti propoſiti.</
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<
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<
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xml:space
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<
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dicimus tantundem numeri, immediate produci
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mus ſuperficiem,
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vnitate in huiuſmodi numero, qui numerus
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type
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pro-
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ducatur in vnitatem, mente concipiendus eſt tanqua m linearis, tanquam linea in-
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quam diuiſa in totidem particulas lineares, ſingulas continuas & æquales vnitati
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propoſitæ. </
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verò productus fuerit numerus in vnitate ſuperficialis, erit ac ſi tot eſ-
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ſent vnitates quadratæ, quod ſi ita non eſſet, nulla mentio facienda eſſet quo-
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rumuis
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. </
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regula de tribus reduci poteſtad praxim
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theorema.</
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<
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xml:space
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">Quare cupientes ſcire quæ ſint illæ partes, quæ ſunt tres quartę, ipſarum quin-
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que ſextarum, dicemus ſi quatuor dant tria, quid dabunt
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ſextæ? </
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<
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vigeſimas quartas, quæ quindecim ſunt tres quartæ ipſius .20. viginti
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ſex
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tæ vigintiquatuor, quandoquidem nos numerum quęrimus, cui ita proportionentur
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<
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ſextæ alterius numeri, ſicut quatuor ad tria, vnde ſic ſe habent .20. ad .15. ſi-
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cut .4. ad .3. ipſe autem .20.
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ſextę partes ſunt vigintiquatuor, vt per ſe
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eſt.</
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<
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xml:space
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">Ex eadem regula de tribus, huiuſmodi quęſito reſponderi poteſt, ſi conſtituamus
<
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prædictas
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ſextas eſſe numerum, cuius tres quartæ quęrantur, dicentes, ſi vnus
<
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integer dat tres quartas, quid dabunt
<
reg
norm
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quinque
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type
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ſextæ? </
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<
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xml:space
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">quare ſequentes regulam de
<
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tribus, dabuntur quindecim vigeſimæ quartæ. </
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<
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xml:space
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">vt quis
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ſcire poſſit, quæ pars aut partes numeri propoſiti ſit aliquis numerus.</
s
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</
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<
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<
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xml:space
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">Exempli gratia, ſcire cupienti, quæ pars aut partes ipſius vigintiquatuor ſint ſex-
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decim, conſtituentur .24. tanquam vnum totum, cuius pars aut partes ſint ſexdecim,
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dicemus igitur ſi .24. dant ſexdecim, quid dabit vnum? </
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xml:space
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masquartas, quæ cum ad primos numeros reductæ fuerint, erunt duæ tertiæ.
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</
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<
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xml:space
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">Eadem ratione qui ſcire uellet, quæ partes aut pars eſſent tres quartæ, octo no-
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narum, diceret, ſi octo nonæ danttres quartas, quid dabit vnum? </
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<
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trigeſimęſecundæ.</
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<
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<
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<
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>
<
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type
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numeri propoſiti. </
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<
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xml:space
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quærat, cuius numeri, duodecim ſint duæ tertiæ partes. </
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<
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xml:id
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xml:space
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