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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THEOREM. ARIT.
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113
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0113
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<
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xml:space
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">25. ad radicem cubam .10000. quæ quidem proportiones æquales inuicem ſunt, cu
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tam vna, quàm alia, ſit tertia pars totius.</
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<
s
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xml:space
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">Pro cuius ratione cogitem is
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eſſe aliquod totum, quod multiplicare cupimus
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per duas tertias, quod
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nihil aliud eſt, quàm accipere duas tertias partes vnius
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totius ſuperficialis, imaginemur igitur hoc totum
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lineare diuiſum eſſe in tertias
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partes mediantibus
<
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>.e.</
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et
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>.d</
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>
. </
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<
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">& tunc multiplicando ipſum per 2. tertias lineares produ-
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ctum erit
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ſex vnitatum ſuperficialium, quod quidem productum poſteà diuiſum
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per .3. dabit
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>.d.c.</
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hoc eſt duas tertias ſuperficiales (quæ eſt tertia pars ipſius
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>.a.c.</
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) &
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ęquales numero
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>.c.b.</
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duabus vnitatibus linearibus, ideſt duabus tertijs ipſius
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>.a.b</
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>
. </
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<
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">No
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tandum etiam eſt, quòd cum ferè omnia reducantur ad regulam de tribus, proptereà
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etiam multiplicatio alicuius quantitatis per aliam quantitatem, nihil aliud eſt quàm
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quædam operatio ipſius regulæ de tribus, vt eyempli gratia volo multiplicare .25.
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per 20. hoc nihil aliud eſt niſi quærere alium numerum ita proportionatum ad .25.
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vt 20. ſe habetad vnum, vnde multiplicando .25. cum .20. & productum diuidendo
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per vnum exregula de tribus, prouentus eſt idem numerus ipſius producti, & propte
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rea cum volumus multiplicare aliquem numerum per fractos hoc nihil aliud eſt
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quàm quærere aliquem numerum ita proportionatum ad ipſum numerum datum,
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vt ſe habet numerator ad denominatorem, exempli gratia ſi .24. aliquis voluerit mul
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tiplicare per duo tertia hoc idem eſt vt ſi quæreret numerum ad quem .24. ita ſe
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habeat, vt .3. ad .2. & idem dico de proportionibus, hoc eſt quod aliud non eſt mulri-
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plicare aliquam proportionem per fractos, quàm aliam proportionem quærere ad
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data ſe habeat, vt denominator ſe
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ad
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; </
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<
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xml:space
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">& hoc exregula de tribus
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perficitur,
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in primo loco, quilocus eſt diuiſoris, numerato
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verò in
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loco,
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poſteà pro
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portionem per
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, &
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type
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<
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type
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0113-01
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do per denominatorem, prouentus demum erit
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proportio, ad quam data ſe habebit, vt denomi-
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nator ſe
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ad numeratorem ex ratione ipſius re
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gulę de tribus. </
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<
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">Ratio verò methodi
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datam
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per fractos, ex ſe ſatis patet,
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cum idem ſit modus diuidendi quemhbet nume
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rum integrum per fractos. </
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<
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& alterius eſt ratio.</
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<
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.</
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<
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">NIcolaus Tartalea in .3. lib. quintæ partis numerorum ſoluit .24. quæſitum ſi-
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bi propoſitum à Hieronymo Cardano, via particulari & non generali. </
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<
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">Quæ-
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ſitum autem tale eſt quamlibet propoſitam rectam lineam in duas partes ita diuide
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re via Euclidis, ut cubus totius lineæ ad cubos partium ſe habeat in proportione
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tripla.</
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<
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">Tartalea igitur inquit quòd vt ſatisfiat ſpeculatiuis ingenijs ſoluendum ſit huiuſ-
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modi quæſitum, ſecando lineam propoſitam
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>.a.b.</
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>
in tres æquales partes, quarum vna
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fit
<
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>.c.b.</
var
>
vnde problema ſolutum erit.</
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<
s
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">Verum dicit, ſed hæc non eſt methodus generalis, proptereà, quod cum tale
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problema alterius fuiſlet proportionis quam triplæ, talis methodus nihil valeret.</
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