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-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div730" type="section" level="3" n="41">
              <div xml:id="echoid-div734" type="letter" level="4" n="4">
                <p>
                  <s xml:id="echoid-s4489" xml:space="preserve">
                    <pb o="380" rhead="IO. BAPT. BENED." n="392" file="0392" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0392"/>
                  negotio cordarum & arcuum poſſumus geometricè demonſtrare quod valde de-
                    <lb/>
                  ſideras.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4490" xml:space="preserve">Quapropter ſit circulus
                    <var>.b.a.e.q.</var>
                  in quo ſit
                    <reg norm="triangulum" type="context">triangulũ</reg>
                  æquilaterum
                    <var>.b.e.n.</var>
                  & quadra
                    <lb/>
                  tum
                    <var>.b.a.q.u.</var>
                  cuius periferiam probabo longiorem eſſe periferia trianguli. </s>
                  <s xml:id="echoid-s4491" xml:space="preserve">Sit enim
                    <lb/>
                  diameter circuli
                    <var>.b.q.</var>
                  qui etiam erit diameter quadrati, vt à te ſcire potes. </s>
                  <s xml:id="echoid-s4492" xml:space="preserve">Sit etiam
                    <lb/>
                    <reg norm="punctum" type="context">punctũ</reg>
                    <var>.b.</var>
                  commune tam anguli quadrati quam trianguli. </s>
                  <s xml:id="echoid-s4493" xml:space="preserve">vnde ſequitur quod dictus
                    <lb/>
                  diameter ſecabit latus
                    <var>.n.e.</var>
                  trianguli ad rectos & per æqualia in
                    <var>.t</var>
                  . </s>
                  <s xml:id="echoid-s4494" xml:space="preserve">Nam cum arcus
                    <var>.b.
                      <lb/>
                    e.</var>
                  æqualis ſit arcui
                    <var>.b.n.</var>
                  ex .27. tertij, remanet vt arcus
                    <var>.q.e.</var>
                  equalis ſit arcui
                    <var>.q.n.</var>
                  vnde
                    <lb/>
                  angulus
                    <var>.q.b.e.</var>
                  æqualis erit angulo
                    <var>.q.b.n.</var>
                  ex .26. eiuſdem. </s>
                  <s xml:id="echoid-s4495" xml:space="preserve">quare ex .4. primi anguli
                    <lb/>
                  ad
                    <var>.t.</var>
                  erunt recti, et
                    <var>.n.t.</var>
                  æqualis erit ipſi
                    <var>.t.e.</var>
                  vt diximus.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4496" xml:space="preserve">Deinde
                    <var>.b.e.</var>
                  et
                    <var>.q.a.</var>
                  ſeinuicem
                    <reg norm="ſecant" type="context">ſecãt</reg>
                  in puncto
                    <var>.o.</var>
                  vt ex ſe clarum patet, ducatur po
                    <lb/>
                  ſtea
                    <var>.q.e.</var>
                  vnde habebimus angulum
                    <var>.b.e.q.</var>
                  rectum ex .30. tertij, </s>
                  <s xml:id="echoid-s4497" xml:space="preserve">quare ex .18. primi
                    <var>.q.
                      <lb/>
                    o.</var>
                  longior erit ipſa
                    <var>.q.e.</var>
                  et
                    <var>.q.e.</var>
                  longior erit ipſa
                    <var>.e.t</var>
                  . </s>
                  <s xml:id="echoid-s4498" xml:space="preserve">quare
                    <var>.q.o.</var>
                  longior erit ipſa
                    <var>.t.e</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4499" xml:space="preserve">Vt probemus poſtea
                    <var>.b.a.o.</var>
                  longiorem eſſe ipſa
                    <var>.b.e.</var>
                  producatur
                    <var>.b.a.</var>
                  ita quod
                    <var>.a.
                      <lb/>
                    p.</var>
                  æqualis ſit ipſi
                    <var>.a.o.</var>
                    <reg norm="ducaturque" type="simple">ducaturq́;</reg>
                    <var>o.p.</var>
                  et
                    <var>.a.e.</var>
                  cum autem ex iam dicta .30. tertij angulus
                    <lb/>
                    <var>b.a.o.</var>
                    <reg norm="rectus" type="simple">rectꝰ</reg>
                  ſit, erit angulus
                    <var>.o.a.p.</var>
                  ſimiliter
                    <reg norm="rectus" type="simple">rectꝰ</reg>
                  ex .13. primi, vnde ex .5. et .32.
                    <reg norm="eiuſdem" type="context">eiuſdẽ</reg>
                    <lb/>
                  angulus
                    <var>.a.p.o.</var>
                  erit dimidium recti, & ſimiliter, exijſdem, angulus
                    <var>.b.q.a.</var>
                  eſt dimidium
                    <lb/>
                  recti </s>
                  <s xml:id="echoid-s4500" xml:space="preserve">quare angulus
                    <var>.a.p.o.</var>
                  æqualis erit angulo
                    <var>.a.q.b.</var>
                  ſed angulus
                    <var>.a.e.b.</var>
                  æqualis eſt an
                    <lb/>
                  gulo
                    <var>.a.q.b.</var>
                  ex .20. tertij, ergo angulus
                    <var>.b.p.o.</var>
                  æqualis erit angulo .b,
                    <var>e.a.</var>
                  angulus vero
                    <lb/>
                    <var>a.b.e.</var>
                  communis eſt ambobus triangulis
                    <var>.a.b.e.</var>
                  et
                    <var>.o.b.p</var>
                  . </s>
                  <s xml:id="echoid-s4501" xml:space="preserve">quare ex .32. primi anguli
                    <var>.
                      <lb/>
                    b.a.e.</var>
                  et
                    <var>.b.o.p.</var>
                  reliqui ex duobus rectis æqua
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0392-01a" xlink:href="fig-0392-01"/>
                  les inuicem erunt. </s>
                  <s xml:id="echoid-s4502" xml:space="preserve">Quare ex quarta ſexti,
                    <lb/>
                  et .18. quinti proportio
                    <var>.b.o.</var>
                  ad
                    <var>.b.p.</var>
                  erit, vt
                    <lb/>
                    <var>b.a.</var>
                  ad
                    <var>.b.e.</var>
                  ſed ex .18. primi
                    <var>.b.o.</var>
                  maior eſt
                    <lb/>
                  ipſa
                    <var>.b.a</var>
                  . </s>
                  <s xml:id="echoid-s4503" xml:space="preserve">quare ex .14. quinti
                    <var>.b.p.</var>
                  maior erit
                    <lb/>
                  ipſa
                    <var>.b.e.</var>
                  ſed
                    <var>.b.p.</var>
                  æquatur ipſis
                    <var>.b.a.</var>
                  cum
                    <var>.a.</var>
                  o
                    <lb/>
                  ex hypoteſi, ergo
                    <var>.b.a.</var>
                  cum
                    <var>.a.o.</var>
                  maior erit
                    <lb/>
                  ipſa
                    <var>.b.e.</var>
                  ſed
                    <var>.q.o.</var>
                  maior erat ipſa
                    <var>.t.e.</var>
                  vt ſupe
                    <lb/>
                  rius vidimus, </s>
                  <s xml:id="echoid-s4504" xml:space="preserve">quare
                    <var>.b.a.</var>
                  cum
                    <var>.a.o.</var>
                  et
                    <var>.o.q.</var>
                  ma
                    <lb/>
                  ior eſt ipſa
                    <var>.b.e.</var>
                  cum
                    <var>.e.t.</var>
                  hoc eſt dimidium
                    <lb/>
                  periferię ipſius quadrati,
                    <reg norm="maius" type="simple">maiꝰ</reg>
                  erit dimidio
                    <lb/>
                  periferię
                    <reg norm="ipſius" type="simple">ipſiꝰ</reg>
                    <reg norm="trianguli" type="context">triãguli</reg>
                  propoſiti, </s>
                  <s xml:id="echoid-s4505" xml:space="preserve">quare ex 14.
                    <lb/>
                  dicta tota periferia dicti trianguli, ſimiliter
                    <lb/>
                  probarem de omnibus alijs figuris regulari
                    <lb/>
                  bus eodem circulo inſcriptis.</s>
                </p>
                <div xml:id="echoid-div734" type="float" level="5" n="1">
                  <figure xlink:label="fig-0392-01" xlink:href="fig-0392-01a">
                    <image file="0392-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0392-01"/>
                  </figure>
                </div>
              </div>
            </div>
            <div xml:id="echoid-div737" type="section" level="3" n="42">
              <div xml:id="echoid-div737" type="letter" level="4" n="1">
                <head xml:id="echoid-head562" xml:space="preserve">CONSIDERATIONES NONNVLLÆ IN
                  <lb/>
                Archimedem.</head>
                <head xml:id="echoid-head563" style="it" xml:space="preserve">Doct ßimo atque Reuerendo Domino Vincentio
                  <lb/>
                Mercato.</head>
                <p>
                  <s xml:id="echoid-s4506" xml:space="preserve">
                    <emph style="sc">QVod</emph>
                  tibi aliàs dixi verum eſt, intellectum ſcilicet non omninò quieſcere cir
                    <lb/>
                  ca illas duas Archimedis propoſitiones, quæ in translatione Tartaleæ ſunt
                    <lb/>
                  ſub numeris .4. et .5. & in impreſſione Baſileæ ſub numeris .6. et .7. vbi
                    <lb/>
                  tractat </s>
                </p>
              </div>
            </div>
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