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-div614" type="section" level="3" n="24">
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                <p>
                  <s xml:id="echoid-s3872" xml:space="preserve">
                    <pb o="316" rhead="IO. BAPT. BENED." n="328" file="0328" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0328"/>
                  lum, cuius data ſit b aſis tantummodo ſimul cum angulo, qui ipſi baſi opponitur.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3873" xml:space="preserve">Imagineris igitur triangulum datum eſſe obtuſiangulum
                    <var>.a.b.g.</var>
                  cuius baſi
                    <var>.b.
                      <lb/>
                    g.</var>
                  ſit nobis data ſimul cum angulo
                    <var>.a.</var>
                  ei oppoſito, obtuſoq́ue; </s>
                  <s xml:id="echoid-s3874" xml:space="preserve">Conſidera etiam cir-
                    <lb/>
                  culum
                    <var>.a.b.g.q.</var>
                  ipſum trian gulum circunſcribentem, cuius diameter
                    <var>.q.e.p.</var>
                  tranſeat
                    <lb/>
                  per
                    <var>.m.</var>
                  punctum medium ipſius
                    <var>.b.g.</var>
                    <reg norm="tunc" type="context">tũc</reg>
                  protractis imaginatione
                    <var>.e.g.</var>
                  et
                    <var>.g.p.</var>
                  certi eri-
                    <lb/>
                  mus angulos. circa
                    <var>.m.</var>
                  rectos eſſe ex .3 tertij Eucli.
                    <reg norm="angulumque" type="simple">angulumq́</reg>
                    <var>.q.e.g.</var>
                  duplum eſſe an
                    <lb/>
                  gulo
                    <var>.q.p.g.</var>
                  ex .19. eiuſdem, vnde æqualem angulo
                    <var>.a.</var>
                  qui etiam duplus eſt angulo
                    <var>.q.
                      <lb/>
                    p.g.</var>
                  quapropter proportio arcus
                    <var>.q.g.</var>
                  ad arcum
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0328-01a" xlink:href="fig-0328-01"/>
                    <var>g.p.</var>
                  tibi cognita erit, & proportio etiam chor-
                    <lb/>
                  de
                    <var>.p.g.</var>
                  ad ſinum
                    <var>.m.g.</var>
                  arcus
                    <var>.g.p.</var>
                  & quia
                    <var>.m.g.</var>
                  vt
                    <lb/>
                  dimidium ipſius
                    <var>.b.g.</var>
                  tibi data eſt, cognoſces
                    <lb/>
                  etiam
                    <var>.p.g.</var>
                  vt
                    <var>.m.g.</var>
                  & ſic tertium latus
                    <var>.m.p.</var>
                  trian-
                    <lb/>
                  guli orthogonij
                    <var>.p.m.g.</var>
                  & q
                    <unsure/>
                  a ex .34. tertij quod
                    <lb/>
                  fit ex
                    <var>.p.m.</var>
                  in
                    <var>.m.q.</var>
                  eſt æquale ei quod fit ex
                    <var>.b.m.</var>
                    <lb/>
                  in
                    <var>.m.g.</var>
                  ideo cum diuiſum fuerit productum
                    <var>.b.</var>
                    <lb/>
                  m in
                    <var>.m.g.</var>
                  per
                    <var>.p.m.</var>
                  proueniet
                    <var>.m.q.</var>
                  quapropter
                    <lb/>
                  habebis totum
                    <var>.q.p</var>
                  .</s>
                </p>
                <div xml:id="echoid-div615" type="float" level="5" n="1">
                  <figure xlink:label="fig-0328-01" xlink:href="fig-0328-01a">
                    <image file="0328-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0328-01"/>
                  </figure>
                </div>
                <p>
                  <s xml:id="echoid-s3875" xml:space="preserve">Idem efficies, ſi
                    <reg norm="cum" type="context">cũ</reg>
                  angulus
                    <var>.a.</var>
                  acutus fuiſſet.</s>
                </p>
              </div>
              <div xml:id="echoid-div617" type="letter" level="4" n="3">
                <head xml:id="echoid-head479" style="it" xml:space="preserve">Modus inueniendi puncta elliptica via Pergei.</head>
                <head xml:id="echoid-head480" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3876" xml:space="preserve">MOdus inueniendi puncta elliptica, via .21. primi lib. Pergei ex datis axibus,
                    <lb/>
                  vt vbi alias ſignificati, talis eſt.
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0328-02a" xlink:href="fig-0328-02"/>
                  </s>
                  <s xml:id="echoid-s3877" xml:space="preserve">Sit exempli gratia maior axis propo-
                    <lb/>
                  ſitus
                    <var>.a.c.</var>
                  minor autem
                    <var>.b.d.</var>
                  cum ergo
                    <lb/>
                  volueris inuenire punctum circunfe-
                    <lb/>
                  rentiæ correſpondentem puncto
                    <var>.e.</var>
                    <lb/>
                  maioris axis, inueniemus primò la-
                    <lb/>
                  tus tetragonicum producti
                    <var>.a.g.</var>
                  in
                    <var>.g.
                      <lb/>
                    c.</var>
                  quod ſit
                    <var>.h.</var>
                    <reg norm="latusque" type="simple">latusq́</reg>
                    <reg norm="tetragonicum" type="context">tetragonicũ</reg>
                  pro-
                    <lb/>
                  ducti
                    <var>.a.e.</var>
                  in
                    <var>.e.c.</var>
                  quod ſit
                    <var>.i</var>
                  . </s>
                  <s xml:id="echoid-s3878" xml:space="preserve">deinde in-
                    <lb/>
                  ueniemus lineam
                    <var>.K.</var>
                  tertiam in con-
                    <lb/>
                  tinua proportionalitate cum
                    <var>.h.</var>
                  et
                    <var>.i.</var>
                    <lb/>
                  vnde
                    <var>.i.</var>
                  erit media proportionalis in-
                    <lb/>
                  ter
                    <var>.h.</var>
                  et
                    <var>.K.</var>
                  & vt
                    <var>.h.</var>
                  proportionalis erit
                    <lb/>
                  ad
                    <var>.K.</var>
                  inueniemus
                    <var>.e.f.</var>
                  cui
                    <var>.g.d.</var>
                  medie-
                    <lb/>
                  tas ſecundi axis ita ſe habeat, quæ po
                    <lb/>
                  ſtea iuncta axi maiori, ad angulosrectos in puncto
                    <var>.e.</var>
                  dabit ſitum puncti
                    <var>.f.</var>
                  quæſiti ex
                    <lb/>
                  dicta .21. primi lib. Pergei, ſed talis modus prolixus eſt.</s>
                </p>
                <div xml:id="echoid-div617" type="float" level="5" n="1">
                  <figure xlink:label="fig-0328-02" xlink:href="fig-0328-02a">
                    <image file="0328-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0328-02"/>
                  </figure>
                </div>
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