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-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div586" type="section" level="3" n="21">
              <div xml:id="echoid-div589" type="letter" level="4" n="3">
                <p>
                  <s xml:id="echoid-s3754" xml:space="preserve">
                    <pb o="304" rhead="IO. BAPT. BENED." n="316" file="0316" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0316"/>
                  rectè habebimus quod volumus. </s>
                  <s xml:id="echoid-s3755" xml:space="preserve">nam omnia latera ſunt inuicem ęqualia ex condi-
                    <lb/>
                  ti onibus circuli, angulus autem
                    <var>.a.</var>
                  rectus effectus fuit, </s>
                  <s xml:id="echoid-s3756" xml:space="preserve">tunc ſi imaginatione cogita-
                    <lb/>
                  ta fuerit diameter
                    <var>.b.c.</var>
                  ex .8. primi, concludemus angulum
                    <var>.d.</var>
                  eſſe rectum </s>
                  <s xml:id="echoid-s3757" xml:space="preserve">deinde ex .5
                    <lb/>
                  et .32. eiuſdem concludemus etiam reliquos angulos rectos eſſe.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3758" xml:space="preserve">Circa verò id quod mihi ſcripſiſti de igne perpetuo putans nugas eſſe, quod Ro-
                    <lb/>
                  mæ inuentæ fuerint lucernę ardentes in ſepulchris antiquorum. </s>
                  <s xml:id="echoid-s3759" xml:space="preserve">Ego quid em mi-
                    <lb/>
                  nimè puto eas nugas eſſe, propterea quod tales lucernas non vnus tantum aut duo
                    <lb/>
                  viderint, ſed multi homines fide digniſſimi. </s>
                  <s xml:id="echoid-s3760" xml:space="preserve">Prętera cum aisid nulla ratione poſſe
                    <lb/>
                  fieri. </s>
                  <s xml:id="echoid-s3761" xml:space="preserve">Reſpondeo quod maxima ratione poſſibile eſſe puto, quam quidem ra-
                    <lb/>
                  tionem ita eſſe oportet, quod primum lucerna ſit perfectè circuncluſa, vt
                    <lb/>
                  materia in ea conſtituta nullo modo exire poſſit, </s>
                  <s xml:id="echoid-s3762" xml:space="preserve">deinde quod materia inflamabilis
                    <lb/>
                  talis ſit, vt excrementum fuliginoſum ex flamma tranſmiſſum, tangendo ſuperfi-
                    <lb/>
                  ciem deuexam ipſius lucernæ, aptum ſit in
                    <reg norm="priſtinum" type="context">priſtinũ</reg>
                    <reg norm="humorem" type="context">humorẽ</reg>
                  conge
                    <unsure/>
                  lari, ſiue transfor-
                    <lb/>
                  mari, vnde materia prima per tres formas perpetuò tranſibit, hoc eſt per humorem,
                    <lb/>
                  ſiue oleum tale, vt diximus, per ignem, ſeu flammam, & per vaporem, ſeu exhala-
                    <lb/>
                  tionem fuliginoſam aptam condenſari, atque in priorem humorem illicò reuerti.</s>
                </p>
              </div>
            </div>
            <div xml:id="echoid-div591" type="section" level="3" n="22">
              <div xml:id="echoid-div591" type="letter" level="4" n="1">
                <head xml:id="echoid-head457" xml:space="preserve">DE DIVISIONE TRIANGVLI SECVNDVM
                  <lb/>
                propoſitam proportionem.</head>
                <head xml:id="echoid-head458" style="it" xml:space="preserve">Michaeli Angelo Muciaſco.</head>
                <p>
                  <s xml:id="echoid-s3763" xml:space="preserve">
                    <emph style="sc">QVod</emph>
                  mihi proponis, tale eſt, vt ſcilicet tibi modum ſcribam diuidendi
                    <lb/>
                  triangulum propoſitum ſecundum datam proportionem à linea tranſeun
                    <lb/>
                  te per punctum notatum extra triangulum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3764" xml:space="preserve">Tr
                    <unsure/>
                    <reg norm="iangulum" type="context">iangulũ</reg>
                    <reg norm="igitur" type="simple">igit̃</reg>
                  à te mihi propoſitum ſit
                    <var>.n.o.u.</var>
                  conſidero
                    <reg norm="primum" type="context">primũ</reg>
                  quod ſi
                    <lb/>
                  quis ipſum diuiſerit in duas partes mediante
                    <var>.e.s.</var>
                  parallela ad
                    <var>.n.u.</var>
                  ea proportione,
                    <lb/>
                  quam mihi proponis. </s>
                  <s xml:id="echoid-s3765" xml:space="preserve">deinde inuenerit in dicta
                    <var>.e.s.</var>
                  punctum
                    <var>.r.</var>
                  per quod tranſiens
                    <lb/>
                  alia linea à puncto
                    <var>.p.</var>
                  propoſito, ita quod efficiat duo triangula
                    <var>.m.r.e.</var>
                  et
                    <var>.r.s.x.</var>
                  inui-
                    <lb/>
                  cem æqualia, problema ſolutum erit.
                    <lb/>
                    <figure xlink:label="fig-0316-01" xlink:href="fig-0316-01a" number="336">
                      <image file="0316-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0316-01"/>
                    </figure>
                  eo quod triangulum
                    <var>.m.o.x.</var>
                  æquale
                    <lb/>
                  eſſet triangulo
                    <var>.e.o.s.</var>
                  & quadrilate-
                    <lb/>
                  rum reſiduum
                    <var>.m.n.u.x.</var>
                  etiam ęquale
                    <lb/>
                  eſſet quadrilatero
                    <var>.e.n.u.s</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s3766" xml:space="preserve">Sed dum punctum
                    <var>.r.</var>
                  uenarer, alia
                    <lb/>
                    <figure xlink:label="fig-0316-02" xlink:href="fig-0316-02a" number="337">
                      <image file="0316-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0316-02"/>
                    </figure>
                  via mihi in mentem venit, cognoui
                    <lb/>
                  igitur quod quum propoſitum expe-
                    <lb/>
                  ditum fuiſſer, hoc eſt,
                    <reg norm="quod" type="simple">ꝙ</reg>
                  ſi à puncto p.
                    <lb/>
                  protracta eſſet linea
                    <var>.p.m.</var>
                  quę trian-
                    <lb/>
                  gulum
                    <var>.n.o.u.</var>
                  in duas partes inuicem
                    <lb/>
                  ita proportionatas diuiſiſſet, vt ſe ha
                    <lb/>
                  bet
                    <var>.A.</var>
                  et
                    <var>.B.</var>
                  ita ſe haberet
                    <reg norm="productum" type="context">productũ</reg>
                    <lb/>
                    <figure xlink:label="fig-0316-03" xlink:href="fig-0316-03a" number="338">
                      <image file="0316-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0316-03"/>
                    </figure>
                    <var>n.o.</var>
                  in
                    <var>.o.u.</var>
                  ad productum
                    <var>.m.o.</var>
                  in
                    <var>.o.
                      <lb/>
                    x.</var>
                  vt trianguli
                    <var>.n.o.u.</var>
                  ad triangulum
                    <lb/>
                    <var>m.o.x.</var>
                  quod quidem non eſt diffi-
                    <lb/>
                  cile ſpeculari, ex methodo .24. ſexti, </s>
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