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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46
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0046
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<
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xml:space
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">11. dabuntur .110. quo producto multiplicato cum .12. dabuntur .1320. hoc pro
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ueniens per primum nempe .10. diuiſum dabit .132. numerum æqualem producto
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ſecundi in tertium numerorum propoſitorum, ſcilicet .132.</
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<
s
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xml:space
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">Hoc vt ſpeculemur, primus numerus ſignificetur line
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ſecundus
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tertius
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e.a.</
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productum verò
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in
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ſit
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ipſius ve
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rò
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per
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corporeum
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ſit
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tum
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xlink:href
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<
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in
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ſit
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. </
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<
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">Dico
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quod di-
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uiſo numero corporeo
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per
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primum
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type
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<
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norm
="
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type
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>
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niens æquale erit numero producti
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>.e.c</
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>
. </
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<
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xml:space
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">Qua-
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re in primis cogitandum eſt, quod cum produ-
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ctum
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ortum fuerit ex multiplicatione
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in
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: dictum
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toties ingredietur
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quo-
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ties vnitas reperitur in
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eadem ratione, to-
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ties
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in
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quot vnitates erunt in
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. </
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ſequitur quòd diuiſo
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per
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proueniens ſit
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<
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corporeum, æquale nihilominus producto
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ſuperficiali.</
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<
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<
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xml:space
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.</
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<
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xml:space
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">CVR diuidens propoſitum numerum in tres partes ſic ſe habentes vt produ-
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ctum primi in ſecundam, in tertia
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, præbeat numerum alteri nu-
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mero propoſito æqualem. </
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<
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xml:space
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">Rectè ſecundum numerum per quemcunque alium mino
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rem primo diuidit, qui diuidens vna erit ex tribus partibus quæſitis, proueniens
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autem erit productum vnius in alteram reliquarum duarum, quarum ſumma cogni
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ta erit, detracto numero diuidente ex primo dato, quam quidem ſi diſtinguere
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quis voluerit, vtetur theoremate .45.</
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<
s
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xml:space
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">Exempli gratia, proponitur numerus .20. in tres partes diuidendus, quæ ſic ſe
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habeant, ut productum primæ in ſecundam in tertia multiplicatum det .90. itaque
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ſumenda erit pro prima vna pars ipſius .20. quæcunque illa ſit, verbi gratia .2. qua
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ſecundus numerus, nempe .90. diuidatur, dabitur igitur .45. quod erit productum
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cæterarum partium inter ſe, quarum ſumma eſt .18. quam ſummam ſi diſtinguere
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volueris in cęteris duabus partibus ſeparatis, vteris .45. theoremate, vt quàm citiſ-
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ſimè quod cupis exequaris, erunt autem partes .3. et .15.</
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<
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xml:space
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">In cuius ſpeculationis gratiam nihil aliud occurrit, quàm quod præcedenti theo-
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remate, & ſuperiore .45. allatum eſt.</
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xml:space
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.</
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<
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<
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numerum in .3. eiuſmodi partes, vt quadratum vnius ſit æquale
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producto reliquarum duarum inter ſe, idem omnino eſt cum 51. theoremate.
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<
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xml:space
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">Nam qui ſumet quamlibet partem propoſiti numeri, quæ tertia parte maior tamen
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non ſit,
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in duas tales partes diuiſerit, vt prima ſumpta, media proportio
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nalis ſit ex probatione .51. theoremate allata, propoſitum conſequetur.</
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.</
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<
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xml:space
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">ID ipſum alia ratione ab ea diuerſa
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.51. theoremate adduximus,
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poteſt.</
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