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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48
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0048
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tum .12. cum dimidio erit .155. quod æquale erit ſummæ quadratorum duarum par
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tium, nempe .100. cum .55.</
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<
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xml:space
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">Hoc vt
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type
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, numerus diuiſibilis propoſitus ſignificetur linea
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& ſum
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ma radicum, noſtro modo ſumptarum, linea
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quarum prima & maior ſit
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>.e.f.</
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>
ſe-
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cunda
<
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>.f.g.</
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tertia
<
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>.g.h.</
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>
cogitemus etiam lineam
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>.a.d.</
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>
ea ratione diuiſam eſſe qua
<
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>.e.h.</
var
>
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patebit cnim ex modo præcedentis theorematis vnamquanque partium
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>.a.d.</
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>
ita ſe
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habituram ad ſuum totum ſicut ſe habent ſingulæ
<
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>.e.h.</
var
>
ad ſuum. </
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>
<
s
xml:id
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"
xml:space
="
preserve
">Quod ideo dico, vt
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intelligamus rectè nos dicere. </
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<
s
xml:id
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xml:space
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">Si
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>.e.h.</
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dat
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>.a.d.</
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ergo
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>.e.f.</
var
>
dabit
<
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>.a.b.</
var
>
<
reg
norm
="
atque
"
type
="
simple
">atq;</
reg
>
ita de cæteris.
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</
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<
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xml:id
="
echoid-s495
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xml:space
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preserve
">Quare permutando ſic ſe habebit
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>.a.b.</
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ad
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>.b.c.</
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>
ſicut
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>.e.f.</
var
>
ad
<
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>.f.g.</
var
>
idem dico de reliquis.
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</
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<
s
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xml:space
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">Igitur ex .18. ſexti aut .11. octaui, eadem erit proportio quadrati
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ad
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quadratum
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type
="
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">quadratũ</
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>
<
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>.
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b.c.</
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>
quæ quadrati
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>.e.f.</
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>
ad quadratum
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>.f.g.</
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>
tota enim ſunt æqualia, cum eorum partes
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ſimiles inter ſe ſunt æquales. </
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<
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xml:space
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">Idem dico de proportione qu@drati
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>.a.b.</
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>
nempe ita
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ſe habere ad
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>.c.d.</
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>
ſicut quadratum
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>.e.f.</
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>
ad quadratum
<
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>.g.h.</
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>
ex quo ex .24. quinti pro-
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portio quadrati
<
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>.a.b.</
var
>
ad ſummam quadratorum duarum partium
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>.b.c.</
var
>
et
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>.c.d.</
var
>
ſic ſe ha
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/>
bebit ut quadrati
<
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>.e.f.</
var
>
ad ſummam quadra-
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torum
<
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>.f.g.</
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>
et
<
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>.g.h</
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>
. </
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>
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xml:space
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">At quadratum
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æquale
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fig-0048-01
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xlink:href
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number
="
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file
="
0048-01
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xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0048-01
"/>
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figure
>
eſt ſummæ quadratorum
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>.f.g.</
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et
<
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>.g.h.</
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>
igitur
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ſic etiam ſe habebit quadratum
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>.a.b.</
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>
nempe
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æquale quadratis
<
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>.b.c.</
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>
et
<
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>.c.g</
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>
. </
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<
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xml:space
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">Idipſum de cæ
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teris dignitatibus dices,
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.21. theoremate huius libri.</
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n
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<
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xml:space
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">THEOREMA
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value
="
57
">LVII</
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.</
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<
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style
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">SImile</
emph
>
quoque problema ab antiquis indeterminatum proponitur, quod eiuſ-
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modi eſt.</
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</
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<
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<
s
xml:id
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xml:space
="
preserve
">An numerus aliquis in tres eiuſmodi partes di@idi poſſit, vt quadratum vnius æ-
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quale ſit ſummæ quadratorum cæterarum duarum partium ſimul cum producto
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vnius in alteram.</
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</
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<
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<
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xml:space
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">Exempli gratia, ſi proponatur numerus .50. vt iam dictum eſt diuidendus, repe
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riendus erit alius quilibet numerus, qui tamen ſumma ſit trium radicum ſic ſe ha-
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bentium, vt quadratum vnius æquale ſit ſummæ quadratorum duarum partium ſi-
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mul cum producto vnius in alteram, eum autem qui primò occurrit ſumamus, utpo
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tè .30. qui ſumma eſt numerorum .6. 10. 14. partium ſic ſe habentium, vt quadratum
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ipſius .14. æquale ſit ſummæ quadratorum cæterarum partium ſimul cum produ-
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cto vnius in alteram, agamusq́ue regula de tribus, ac dicamus, ſi .30. valet
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value
="
50
">.
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50.</
num
>
quid valebit .14. nempe .23. cum tertia parte. </
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<
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xml:space
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">Idem efficiemus in cæte-
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ris partibus, quarum vna erit .16. cum duabus tertijs, altera verò .10. abſque @ractis,
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ex quo quadratum primæ erit .544. cum .4. nonis, ſecundæ .277. cum ſeptem nonis,
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tertiæ .100. & productum ſecundæ in tertiam .166. cum .6. nonis, quod productum,
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cum quadratis ſecundæ & tertiæ collectum erit .544. cum .4. nonis.</
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<
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<
s
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xml:space
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preserve
">Huius rei ſpeculatio eadem eſt, quę fuit præcedentis theorematis vſquequo no-
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ueris eandem proportionem eſſe quadrati
<
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>.a.b.</
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>
ad ſummam quadratorum
<
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>.b.c.</
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>
et
<
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>.c.
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d.</
var
>
quæ quadrati
<
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>.e.f.</
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>
ad ſummam quadratorum
<
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>.f.g.</
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>
et
<
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>.g.h</
var
>
. </
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<
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xml:id
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xml:space
="
preserve
">Sed cum hic non demus
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quadratum
<
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>.e.f.</
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>
æquale ſummæ quadratorum
<
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>.f.g.</
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>
et
<
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>.g.h.</
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>
fed maius ex producto
<
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>.g.h.</
var
>
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in
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>.f.g.</
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>
aut quod idem eſt, è contrario, ſubſequentes figuræ cogitandæ erunt, qua-
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rum
<
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>.i.</
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>
ſit quadratum
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>.a.b</
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>
: l. ſit quadratum
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>.e.f</
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>
: x. quadratum
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>.b.c</
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>
: y. quadratum
<
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>.f.g</
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>
: p.
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quadratum
<
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>.c.d</
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>
: q. quadratum
<
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>.g.h</
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>
: k. ſit productum
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>.b.c.</
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>
in
<
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>.c.d</
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>
: m. ſit productum
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>.f.</
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>
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