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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140 - 149
150 - 159
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220 - 229
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IO. BAPT. BENED.
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<
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xml:space
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merus linea
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ſignificetur, quam di-
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uiſam cogitemus in puncto
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in partes
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quæſitas, ex quo præſupponitur duas li-
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neas
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et
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duo quadrata eſſe, quæ
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in altera figura ſignificetur per
<
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et
<
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>.e.</
var
>
<
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productum autem radicum cognitum
<
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<
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f.</
var
>
quandoquidem datum eſt, cuius qua-
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dratum æquale erit producto quadra-
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torum
<
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>.d.e.</
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adinuicem, nempe
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in
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ex .19. theoremate huius. </
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gratia ſit
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cognitum, quo facto, doctrinam .45. theorematis libri huius ſecuti,
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propoſitum conſequemur.</
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.</
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differentia ſit quadratorum ipſarum radicum.</
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gratia, quoslibet duos numeros pro radicibus ſumpſerimus, vt potè .3. et
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<
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5.</
num
>
quorum differentia eſt .2. certè ſi differentiam hanc per ſummam radicum ſcili-
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cet .8. multiplicauerimus, dabitur numerus .16. quod productum differentia eſt
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ſuorum quadratorum, nempeinter .9. et .25.</
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<
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xml:space
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ſignificentur, quarum vna ſit
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&
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altera
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>
ipſarum autem differentia
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>
ex quo
<
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>.t.
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c.</
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æqualis erit
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. </
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cum diametro
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parallela lateri
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à
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puncto
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var
>.c.</
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& altera à puncto
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>.t.</
var
>
& à puncto
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var
>
tertia
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ipſi
<
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>.n.i.</
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& à puncto
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quarta
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parallela ipſi
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o.</
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inueniemus
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productum eſſe differentiæ
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t.</
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in ſumma radicum
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& cum
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et
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ſint
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quadrata radicum prædictarum: </
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n.u.</
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cum vtrunque horum productorum æquale ſit
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x.u.</
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ex quo gnomon
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æqualis erit producto
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b.n.</
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quod ſcire cupiebamus.</
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<
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<
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xml:space
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rentia radicum quadratarum æqualis ſit alteri numero propoſito, cuius ta-
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men quadratum dimidij primi quadratum non excedat. </
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in ſeipſum multiplicant, productum verò ex primo numero detrahunt,
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di
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midium reſidui quadrant, & quadratum hoc ex quadrato dimidij primi ſubtrahunt,
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atque ita radice quadrata reſidui, dimidio primi coniuncta, pars maior datur, qua
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ex ipſo dimidio detracta, pars minor relinquitur.</
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<
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">Exempli gratia, propoſito numero .20. ita ut propoſitum eſt, diuidendo, nem-
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pe vt differentia radicum quadratarum dictarum partium æqualis ſit binario, bina-
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rium hocin ſeipſum multiplicabimus, cuius quadratum .4. è primo numero .20. de </
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