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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30 - 39
40 - 49
50 - 59
60 - 69
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80 - 89
90 - 99
100 - 109
110 - 119
120 - 129
130 - 139
140 - 149
150 - 159
160 - 169
170 - 179
180 - 189
190 - 199
200 - 209
210 - 219
220 - 229
230 - 239
240 - 249
250 - 259
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270 - 279
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rhead
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IO. BAPT. BENED.
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120
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file
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0120
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0120
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<
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<
s
xml:id
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xml:space
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preserve
">Diſponantur igitur huiuſmo-
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number
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163
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file
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0120-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0120-01
"/>
</
figure
>
di numeri tali ordine, vt fim-
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plex ſumma, quæ ab vna reli-
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quarum ſuperatur, & aliam ſupe-
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rat, medium locum teneat; </
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<
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xml:space
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">@t
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in propoſito exemplo ſumma
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mediocris eft .48. quę à ſumma
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value
="
60
">.
<
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60.</
num
>
ſuperatur, & ſuperat ſum-
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mam .39. locata igitur fit hęc .48.
<
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inter illas, ſuæ verò primæ partes
<
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fimiliter conftitutæ ſint ſupra di-
<
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ctas ſummas, cum ſuis
<
reg
norm
="
differentijs
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type
="
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">differẽtijs</
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,
<
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& tria producta iam dicta, vt in fi
<
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guris
<
var
>.C.</
var
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et
<
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>.D.</
var
>
arithmeticis
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clarè patet: </
s
>
<
s
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xml:space
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preserve
">figura enim
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>.C.</
var
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eft
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pro exemplo ipſius plus ſimpli-
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citer: </
s
>
<
s
xml:id
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xml:space
="
preserve
">figura verò
<
var
>.D.</
var
>
pro exem-
<
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plo ipſius plus, & minus. </
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>
<
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xml:id
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xml:space
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">Et fic
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xlink:href
="
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number
="
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file
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0120-02
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xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0120-02
"/>
</
figure
>
in figura
<
var
>.C.</
var
>
habebimus tres
<
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numeros confequentes .60. 48.
<
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39. & tres antecedentes .10. 8.
<
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6. cum dimidio, vnam, & ean-
<
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dem proportionem terminantes,
<
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/>
ex .24. quinti, vt diximus; </
s
>
<
s
xml:id
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xml:space
="
preserve
">qua-
<
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re eorum differentiæ fimiliter
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proportionales erunt, quod etiam
<
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vidimus. </
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>
<
s
xml:id
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xml:space
="
preserve
">Supponamus nunc nos
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ignorare æqualitatem maximi
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producti cum reliquis duobus,
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accipiendo ſolum pro hypoteſi,
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quòd dicta producta oriantur
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ex lateribus iam dictis.</
s
>
</
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<
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<
s
xml:id
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xml:space
="
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">Demonſtrandum nobis nunc relinquetur, maximum productum æquale effere-
<
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liquis duobus; </
s
>
<
s
xml:id
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xml:space
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preserve
">hoc eſt productum .168. æquale effe productis .90. et .78. quorum
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duorum productorum alterum .90. ſcilicet, generatur à differentia .9. quæ eft ſe-
<
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cundę, & tertię ſummæ, in primum numerum antecedentem, qui eſt .10. alterum vc-
<
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/>
ro productum .78. ſcilicet, generatur à differentia .12. quę eſt primę, & ſecundę, ſum
<
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/>
mę in tertium numerum antecedentem, qui eſt .6. cum dimidio, maximum vero
<
lb
/>
productum .168. ſcilicet generatur à differentia maxima .21. quę eft primę, & tertię
<
lb
/>
ſummę (& ſemper ęqualis prioribus duabus differentijs .12. et .9.) in ſecundum nu-
<
lb
/>
merum antecedentem, qui eſt .8.</
s
>
</
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<
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>
<
s
xml:id
="
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"
xml:space
="
preserve
">Conſtituantur igitur duo producta fimul iuncta ęqualia duobus .90. et .78.
<
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lateralibus ſupra vnam aliquam rectam lineam
<
var
>.q.p.</
var
>
<
reg
norm
="
fitque
"
type
="
simple
">fitq́;</
reg
>
productum
<
var
>.f.g.</
var
>
ęquale
<
num
value
="
90
">.
<
lb
/>
90.</
num
>
productum verò
<
var
>.g.n.</
var
>
ęquale .78. fit etiam baſis
<
var
>.g.p.</
var
>
vt .9. et
<
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>.g.q.</
var
>
vt .12. vnde
<
var
>.g.i.</
var
>
<
lb
/>
vel
<
var
>.q.n.</
var
>
erit vt .6. cum dimidio .et
<
var
>.g.d.</
var
>
vel
<
var
>.p.f.</
var
>
vt .10. & ideo
<
var
>.i.d.</
var
>
differentia erit .3. </
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