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-div642" type="section" level="3" n="28">
              <div xml:id="echoid-div655" type="letter" level="4" n="4">
                <p>
                  <s xml:id="echoid-s4130" xml:space="preserve">
                    <pb o="340" rhead="IO. BAPT. BENED." n="352" file="0352" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0352"/>
                  quapropter cogitemus
                    <var>.r.a.</var>
                  indeterminatam tranſire per centrum
                    <var>.s.</var>
                  ipſius circuli, ſi-
                    <lb/>
                  militer etiam
                    <var>.r.i.</var>
                  ad punctum medium lateris
                    <var>.e.o.</var>
                  deinde à tribus punctis,
                    <var>e.i.o.</var>
                  ima-
                    <lb/>
                  ginemur tres perpendiculares ad
                    <var>.r.a.</var>
                  hoc eſt
                    <var>.e.a</var>
                  :
                    <var>i.d.</var>
                  et
                    <var>.o.q.</var>
                  & vbi circulus ſecat
                    <var>.r.a.</var>
                    <lb/>
                  fit punctum
                    <var>.g.</var>
                  protractis deinde
                    <var>.g.n</var>
                  :
                    <var>g.x</var>
                  : et
                    <var>.g.u.</var>
                  habebimus triangulum
                    <var>.a.e.r.</var>
                  ſimi-
                    <lb/>
                  lem triangulo
                    <var>.g.u.r.</var>
                  vnde clarum erit productum
                    <var>.g.r.a.</var>
                  æquale eſſe producto
                    <var>.e.r.u.</var>
                    <lb/>
                    <reg norm="productumque" type="simple">productumq́</reg>
                    <var>.g.r.q.</var>
                  æquale eſſe producto
                    <var>.o.r.n.</var>
                  nam trianguli
                    <var>.g.r.n.</var>
                  et
                    <var>.o.r.q.</var>
                  ſunt in-
                    <lb/>
                  u
                    <unsure/>
                  icem ſimiles, ſed productum
                    <var>.g.r.a.</var>
                  ſimul cum producto
                    <var>.g.r.q.</var>
                  duplum eſt producto
                    <var>.
                      <lb/>
                    g.r.d.</var>
                  ex prima ſexti, eo quod
                    <var>.a.r.q.</var>
                  dupla eſt
                    <var>.d.r.</var>
                  & ideo productum
                    <var>.e.r.u.</var>
                  ſimul
                    <reg norm="cum" type="context">cũ</reg>
                    <lb/>
                  producto
                    <var>.o.r.n.</var>
                  duplum erit producto
                    <var>.i.r.x.</var>
                  quod quidem æquale eſt producto
                    <var>.g.r.
                      <lb/>
                    d.</var>
                  ex ſimilibus rationibus iam ſupradictis. </s>
                  <s xml:id="echoid-s4131" xml:space="preserve">Nunc ex ſimilibus rationibus producta
                    <var>.f.
                      <lb/>
                    r.b.</var>
                  et
                    <var>.K.r.c.</var>
                  dupla erunt producto
                    <var>.i.r.x</var>
                  . </s>
                  <s xml:id="echoid-s4132" xml:space="preserve">quare prima producta æqualia erunt ſecun-
                    <lb/>
                  dis. </s>
                  <s xml:id="echoid-s4133" xml:space="preserve">Quod eſt propoſitum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4134" xml:space="preserve">Ab huiuſmodi demonſtrat ione facilè videre poteris non eſſe generaliter verum,
                    <lb/>
                  id quod Nicolaus Tartalea inquit .43. quæſito vltimæ partis ſuorum tractatuum, hoc
                    <lb/>
                  eſt centrum circuli
                    <var>.r.n.g.</var>
                  ſemper eſſe in perpendiculari, quæ à puncto
                    <var>.r.</var>
                  ad lineam
                    <var>.e.
                      <lb/>
                    o.</var>
                  tranſit, protracta ipſa
                    <var>.e.o.</var>
                  quantum volueris, imò in quacunque alia linea ipſum eſ
                    <lb/>
                  ſe poteſt, nec non in aliqua parallela ipſi
                    <var>.e.o.</var>
                  quemadmodum ex te ipſo, medianti-
                    <lb/>
                  bus, hic ſupradictis rationibus videre poteris, vnde ex neceſſitate ſequitur illud pro
                    <lb/>
                  blema ſemper ferè falſum eſſe.</s>
                </p>
                <figure position="here" number="382">
                  <image file="0352-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0352-01"/>
                </figure>
                <figure position="here" number="383">
                  <image file="0352-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0352-02"/>
                </figure>
              </div>
              <div xml:id="echoid-div657" type="letter" level="4" n="5">
                <head xml:id="echoid-head503" style="it" xml:space="preserve">Alia ſpeculatio circa breuitatem radiorum incidentium
                  <lb/>
                & reflexorum.</head>
                <head xml:id="echoid-head504" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s4135" xml:space="preserve">ALius modus quem exercitationis gratia vltimò cogitaui, ad demonſtrandum
                    <lb/>
                  breuitatem radiorum incidentium, & reflexorum in ſpeculo plano, nunc ad
                    <lb/>
                  te ſcribo, quamuis prolixior ali quantulum ſit eo, quod ab antiquis traditus eſt.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4136" xml:space="preserve">Imaginemur itaque
                    <reg norm="lineam" type="context">lineã</reg>
                    <var>.p.h.</var>
                  pro
                    <reg norm="communi" type="context">cõmuni</reg>
                  ſectione ſuperficiei reflexionis
                    <reg norm="cum" type="context">cũ</reg>
                  ſpe-
                    <lb/>
                  culo
                    <var>.r.a.</var>
                  verò et
                    <var>.a.b.</var>
                  pro radijs dictis, qui ſemper
                    <reg norm="faciunt" type="context">faciũt</reg>
                  angulos
                    <var>.b.a.h.</var>
                  et
                    <var>.r.a.p.</var>
                    <reg norm="inuicem" type="context">inuicẽ</reg>
                  </s>
                </p>
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