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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            <div xml:id="echoid-div333" type="section" level="3" n="14">
              <pb o="140" rhead="IO. BAPT. BENED." n="152" file="0152" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0152"/>
              <p>
                <s xml:id="echoid-s1686" xml:space="preserve">Ponamus nunc quadratum lateris
                  <var>.a.u.</var>
                eſſe .12. clarum erit quodlibet quadratum
                  <lb/>
                aliorum duorum laterum
                  <var>.a.q.</var>
                et
                  <var>.u.q.</var>
                futurum nouem, ex ijs quæ poſteriore loco dixi
                  <lb/>
                mus, & quia quadratum ipſius
                  <var>.q.a.</var>
                eſt tantò minus aliorum duorum quadratorum
                  <lb/>
                ſumma, quantum eſt duplum producti ipſius
                  <var>.q.a.</var>
                in
                  <var>.a.o.</var>
                ex .13. ſecundi, ſed alia duo
                  <lb/>
                quadrata ſimul collecta faciunt .21. à quo numero ſubtrahendo quadratum ipſius
                  <var>.a.
                    <lb/>
                  q.</var>
                ideſt nouem, remanebit numerus .12. pro duplo producti ipſius
                  <var>.q.a.</var>
                in
                  <var>.a.o.</var>
                cuius
                  <lb/>
                dupli me-
                  <lb/>
                  <anchor type="figure" xlink:label="fig-0152-01a" xlink:href="fig-0152-01"/>
                dia pars, id-
                  <lb/>
                eſt ſimplex
                  <lb/>
                productum
                  <lb/>
                ipſius
                  <var>.q.a.</var>
                  <lb/>
                  <reg norm="in" type="wordlist">ĩ</reg>
                  <var>a.o.</var>
                erit 6.
                  <lb/>
                Sed
                  <reg norm="quia" type="simple">ꝗa</reg>
                qua
                  <lb/>
                dratum ip-
                  <lb/>
                ſius
                  <var>.q.a.</var>
                eſt
                  <lb/>
                nouem,
                  <lb/>
                eius radix
                  <var>.
                    <lb/>
                  q.a.</var>
                crit .3.
                  <lb/>
                per
                  <reg norm="quam" type="context">quã</reg>
                di-
                  <lb/>
                uidendo .6.
                  <lb/>
                productum
                  <lb/>
                ipſius
                  <var>.q.a.</var>
                  <lb/>
                in
                  <var>.a.o.</var>
                pro
                  <lb/>
                latere
                  <var>.a.o.</var>
                  <lb/>
                conſurgent
                  <lb/>
                duo, cum er
                  <lb/>
                go
                  <var>.a.o.</var>
                ſint
                  <lb/>
                duo tertia
                  <lb/>
                ipſius
                  <var>.a.q.</var>
                  <lb/>
                certi
                  <reg norm="erimus" type="simple">erimꝰ</reg>
                  <lb/>
                  <var>a.o.</var>
                eſſe latus dicti exagoni.</s>
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                <figure xlink:label="fig-0152-01" xlink:href="fig-0152-01a">
                  <image file="0152-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0152-01"/>
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            <div xml:id="echoid-div337" type="section" level="3" n="15">
              <head xml:id="echoid-head193" xml:space="preserve">CAP. XV.</head>
              <p>
                <s xml:id="echoid-s1687" xml:space="preserve">
                  <reg norm="DEſiderantes" type="context">DEſiderãtes</reg>
                ſcire deinde
                  <var>.l.k.</var>
                in figura
                  <var>.M.</var>
                quar
                  <lb/>
                  <anchor type="figure" xlink:label="fig-0152-02a" xlink:href="fig-0152-02"/>
                ti cap. tertiæ partis perſpectiuę Danielis
                  <lb/>
                Barbari, ſeu Zamberti, eſſe veram
                  <reg norm="altitudinem" type="context">altitudinẽ</reg>
                cor-
                  <lb/>
                poris octoaedri,
                  <reg norm="primum" type="context">primũ</reg>
                ſcire debemus
                  <reg norm="quod" type="simple">ꝙ</reg>
                  <reg norm="exiſtente" type="context">exiſtẽte</reg>
                  <var>.b.
                    <lb/>
                  h.</var>
                vt
                  <reg norm="etiam" type="context">etiã</reg>
                  <var>.b.l.</var>
                tripla ad
                  <var>.b.k.</var>
                vt ex ijs, quę ſuperius
                  <reg norm="iam" type="context">iã</reg>
                  <lb/>
                diximus, facile percipi poteſt; </s>
                <s xml:id="echoid-s1688" xml:space="preserve">ex penultima primi
                  <var>.
                    <lb/>
                  b.l.</var>
                in potentia, ſeſquioctaua erit ad
                  <var>.k.l.</var>
                ipſa et
                  <var>.k.
                    <lb/>
                  l.</var>
                dupla
                  <reg norm="inpotentia" type="context">inpotẽtia</reg>
                ad
                  <var>.h.k.</var>
                & ob id ducta
                  <reg norm="cum" type="context">cũ</reg>
                eſſet
                  <var>.h.
                    <lb/>
                  l.</var>
                exiſteret in potentia tripla ad
                  <var>.h.k.</var>
                & ſeſquialtera
                  <lb/>
                ad
                  <var>.l.k.</var>
                & ſeſquitertia ad
                  <var>.l.b.</var>
                & ſic ad
                  <var>.h.b.</var>
                vnde
                  <var>.l.h.</var>
                  <lb/>
                æqualis eſſet vni ex lateribus
                  <reg norm="trianguli" type="context">triãguli</reg>
                ęquilateri di-
                  <lb/>
                cti corporis. </s>
                <s xml:id="echoid-s1689" xml:space="preserve">Ex rationibus igitur ſuperius hîc poſi-
                  <lb/>
                tis
                  <var>.l.k.</var>
                erit altitudo dicta, id eſt diſtantia inter duas
                  <lb/>
                facies inuicem oppoſitas, octoaedri.</s>
              </p>
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                <figure xlink:label="fig-0152-02" xlink:href="fig-0152-02a">
                  <image file="0152-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0152-02"/>
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              <p>
                <s xml:id="echoid-s1690" xml:space="preserve">
                  <reg norm="Neque" type="simple">Neq;</reg>
                volo te ignorare
                  <reg norm="alium" type="context">aliũ</reg>
                  <reg norm="non" type="context">nõ</reg>
                  <reg norm="paruum" type="context">paruũ</reg>
                fuiſſe
                  <reg norm="errorem" type="context">errorẽ</reg>
                  <lb/>
                illius Zamberti: </s>
                <s xml:id="echoid-s1691" xml:space="preserve">cum
                  <reg norm="eodem" type="context">eodẽ</reg>
                capite affirmet angulos
                  <lb/>
                octoacdri rectos eſſe
                  <reg norm="cum" type="context">cũ</reg>
                ſint acuti,
                  <reg norm="nam" type="context">nã</reg>
                  <reg norm="vnuſquiſque" type="simple">vnuſquiſq;</reg>
                minor eſt angulo cubi ſolido.</s>
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