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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            <div xml:id="echoid-div331" type="section" level="3" n="13">
              <p>
                <s xml:id="echoid-s1664" xml:space="preserve">
                  <pb o="138" rhead="IO. BAPT. BENED." n="150" file="0150" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0150"/>
                eſt angulum
                  <var>.p.q.u.</var>
                obtuſum eſſe; </s>
                <s xml:id="echoid-s1665" xml:space="preserve">Imaginemur ergo circa triang ulum
                  <var>.p.q.u.</var>
                circun-
                  <lb/>
                ſcriptum eſſe circulum, cuius portio
                  <var>.p.q.u.</var>
                minor erit medietate eiuſdem medij cir-
                  <lb/>
                culi, vt iam ex
                  <ref id="ref-0023">30. Eucli. lib. tertij</ref>
                nouiſti. </s>
                <s xml:id="echoid-s1666" xml:space="preserve">nunc imaginemur dictum circulum circum
                  <lb/>
                lineam
                  <var>.q.u.</var>
                loco axis verſus
                  <var>.x.</var>
                moueri, vnde girus eiuſdem, per quem tranſibat linea
                  <lb/>
                  <var>V.x.</var>
                remouebitur ab eadem linea non nihil cum motus erit à primo ſitu vſquequò
                  <lb/>
                ad ſecandam dictam lineam
                  <var>.V.x.</var>
                in alio quodam puncto inter
                  <var>.p.</var>
                et
                  <var>.x.</var>
                redibit; </s>
                <s xml:id="echoid-s1667" xml:space="preserve">quod
                  <lb/>
                quidem punctum ſi
                  <lb/>
                erit inter
                  <var>.o.</var>
                et
                  <var>.x.</var>
                angu
                  <lb/>
                  <figure xlink:label="fig-0150-01" xlink:href="fig-0150-01a" number="204">
                    <image file="0150-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0150-01"/>
                  </figure>
                lus
                  <var>.q.o.u.</var>
                maior erit
                  <lb/>
                angulo
                  <var>.q.p.u</var>
                . </s>
                <s xml:id="echoid-s1668" xml:space="preserve">Sed ſi
                  <lb/>
                idem
                  <reg norm="punctum" type="context">punctũ</reg>
                erit in-
                  <lb/>
                ter
                  <var>.p.</var>
                et
                  <var>.o.</var>
                dictus an-
                  <lb/>
                gulus
                  <var>.q.o.u.</var>
                minor
                  <lb/>
                erit
                  <var>.q.p.u.</var>
                de qua
                  <reg norm="qui- dem" type="simple context">ꝗ-
                    <lb/>
                  dẽ</reg>
                re tu ipſe median-
                  <lb/>
                te .20. lib. 3. et .16. lib.
                  <lb/>
                primi certior fieri po-
                  <lb/>
                tes. </s>
                <s xml:id="echoid-s1669" xml:space="preserve">Valde miror
                  <reg norm="quod" type="simple">ꝙ</reg>
                  <lb/>
                hæc Ioannis Cuſini di
                  <lb/>
                cta ad hæc vſque tempora tanto in prætio ſint habita, vt ab excellentibus ſcriptori-
                  <lb/>
                bus quaſi ſi proprij eorum ingenij partus eſſent, de verboad verbum vt theſauros, in
                  <lb/>
                fuis
                  <reg norm="ipſorummet" type="context">ipſorũmet</reg>
                libris reſcripta fuerint, quemadmodum iam omnes admonui in mea
                  <lb/>
                gnomonica Orontium, Munſterum,
                  <reg norm="aliosque" type="simple">aliosq́;</reg>
                permultos feciſſe.</s>
              </p>
            </div>
            <div xml:id="echoid-div333" type="section" level="3" n="14">
              <head xml:id="echoid-head192" xml:space="preserve">CAP. XIIII.</head>
              <p>
                <s xml:id="echoid-s1670" xml:space="preserve">
                  <emph style="sc">Ex</emph>
                ijs, qu æ de nonnullis effectibus ducendo in perſpectiua tertíum corpus regu
                  <lb/>
                lare,
                  <reg norm="quod" type="simple">ꝙ</reg>
                octo triangulis æquilateribus eſt term inatum, ſcire deſideras, hoc
                  <reg norm="vnum" type="context">vnũ</reg>
                  <lb/>
                eſt caput: </s>
                <s xml:id="echoid-s1671" xml:space="preserve">vnde fiat, aut quomodo probetur quaſlibet duas facies oppoſitas eiuſ-
                  <lb/>
                dem corporis octoaedri
                  <reg norm="inuicem" type="context">inuicẽ</reg>
                æquidiſtantes eſſe. </s>
                <s xml:id="echoid-s1672" xml:space="preserve">Quamobrem ſit hîc
                  <reg norm="ſubſcriptum" type="context">ſubſcriptũ</reg>
                  <lb/>
                  <reg norm="octoaedrum" type="context">octoaedrũ</reg>
                , cuius diameter vna ſit
                  <var>.b.q.</var>
                et
                  <var>.b.p.
                    <lb/>
                  l.</var>
                vna ex faciebus, cui opponatur facies
                  <var>.q.k.</var>
                  <lb/>
                  <figure xlink:label="fig-0150-02" xlink:href="fig-0150-02a" number="205">
                    <image file="0150-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0150-02"/>
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                d. quas
                  <reg norm="adinuicem" type="context">adinuicẽ</reg>
                æquidiſtantes eſſe contendo
                  <lb/>
                ſint aliæ duæ facies, quæ inter has ponuntur
                  <var>.
                    <lb/>
                  b.d.k.</var>
                et
                  <var>.q.p.l.</var>
                & à punctis extremis
                  <var>.b.q.</var>
                dia-
                  <lb/>
                metri. ductæ ſint quatuor lineæ
                  <var>.b.a</var>
                :
                  <var>b.u</var>
                :
                  <var>q.a</var>
                :
                  <var>q.
                    <lb/>
                  u.</var>
                ad puncta
                  <var>.a.</var>
                et
                  <var>.u.</var>
                diuidentia
                  <var>.k.d.</var>
                et
                  <var>.l.p.</var>
                per
                  <lb/>
                medium, vnde ex 4. primi Eucli. quatuor hæ
                  <lb/>
                lineæ adinuicem ęquales erunt
                  <reg norm="ſumendo" type="context">ſumẽdo</reg>
                eas vt
                  <lb/>
                baſes
                  <reg norm="triangulorum" type="context">triangulorũ</reg>
                  <var>.a.d.b</var>
                :
                  <var>u.l.b</var>
                :
                  <var>a.d.q.</var>
                et
                  <var>.u.l.q.</var>
                  <lb/>
                  <reg norm="adinuicem" type="context">adinuicẽ</reg>
                  <reg norm="quoque" type="simple">quoq;</reg>
                  <reg norm="æquidiſtabunt" type="simple context">æꝗdiſtabũt</reg>
                  <var>.a.b.</var>
                ab
                  <var>.u.q.</var>
                et
                  <var>.b.
                    <lb/>
                  u.</var>
                ab
                  <var>.q.a.</var>
                ex .27. primi; </s>
                <s xml:id="echoid-s1673" xml:space="preserve">
                  <reg norm="quia" type="simple">ꝗa</reg>
                ſi imaginabimur dia
                  <lb/>
                metrum
                  <var>.b.q.</var>
                tunc ex .4. aut ex .8. eiuſdem lib.
                  <lb/>
                habebimus angulos
                  <var>.a.b.q.</var>
                et
                  <var>.u.q.b.</var>
                æquales
                  <lb/>
                inuicem; </s>
                <s xml:id="echoid-s1674" xml:space="preserve">ſed ob eaſdem rationes
                  <var>.p.l.</var>
                paralle-
                  <lb/>
                la eſt ipſi
                  <var>.d.k.</var>
                vnde ex 15. lib. 11. facies
                  <var>.b.p.l.</var>
                  <lb/>
                parallela fit, aut æquidiſtans ipſi
                  <var>.q.d.k.</var>
                ideſt
                  <lb/>
                primum propoſitum.</s>
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