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-div558" type="section" level="3" n="16">
              <div xml:id="echoid-div561" type="letter" level="4" n="3">
                <p>
                  <s xml:id="echoid-s3621" xml:space="preserve">
                    <pb o="292" rhead="IO. BAPT. BENED." n="304" file="0304" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0304"/>
                  cum
                    <var>.a.q.</var>
                  in puncto
                    <var>.u</var>
                  . </s>
                  <s xml:id="echoid-s3622" xml:space="preserve">Nunc verò ſi vmbra
                    <var>.t.q.</var>
                  tanto maior eſt
                    <var>.f.g.</var>
                  quanto .109. eſt
                    <lb/>
                  vno et
                    <var>.t.n.</var>
                  etiam
                    <reg norm="tanto" type="context">tãto</reg>
                  maior
                    <var>.c.e.</var>
                  ergò eadem proportio erit
                    <var>.q.t.</var>
                  ad
                    <var>.t.f.</var>
                  quę
                    <var>.n.t.</var>
                  ad
                    <var>.t.
                      <lb/>
                    c.</var>
                  ſed cum angulus
                    <var>.t.</var>
                  communis ſit ambobus triangulis
                    <var>.q.t.f.</var>
                  et
                    <var>.n.t.c.</var>
                  ſequitur ex .6.
                    <lb/>
                  ſexti dictos triangulos æ quiangulos eſſe. </s>
                  <s xml:id="echoid-s3623" xml:space="preserve">Vnde ſi anguli
                    <var>.t.n.c.</var>
                  et
                    <var>.t.q.f.</var>
                  æ quales inui
                    <lb/>
                  cem ſunt, ergo
                    <var>.q.f.</var>
                  æquidiſtans erit
                    <var>.n.c.</var>
                  quod eſt impoſſibile, quia nunc demonſtra-
                    <lb/>
                  uimus ipſas concurrere in puncto
                    <var>.u</var>
                  . </s>
                  <s xml:id="echoid-s3624" xml:space="preserve">Quare non eſt eadem proportio
                    <var>.q.t.</var>
                  ad
                    <var>.t.f.</var>
                  quæ
                    <lb/>
                    <var>n.t.</var>
                  ad
                    <var>.t.c.</var>
                  decipitur ergo Cardanus in .4. lib. de ſubtilitate.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3625" xml:space="preserve">Circa illud deinde quod à me quæris, hoc eſt, quæ ſit cauſa, quod nos videmus
                    <lb/>
                  radium ſolarem tardiſſimè moueri, cum alias tibi dixerim ipſum qualibet hora cir-
                    <lb/>
                  ca terram quindecim gradus perficere, reſpondeo, quod radius ille quem videmus,
                    <lb/>
                  exempli gratia, in aliquo cubiculo, nunquam eſt idem numero, ſed quia ipſi radij
                    <lb/>
                  nullo modo differunt inter ſe, niſi in numero, proptera putamus eundem ſemper eſſe,
                    <lb/>
                  cum ſemper alius, atque alius ſit, quorum vnuſquiſque (de illis loquor, qui ad hunc
                    <lb/>
                  terræ globum perueniunt) circa terram reuoluitur ſpatio .24. horarum, & cum quili
                    <lb/>
                  bet circulus diuidatur in .360. gradus, quorum vigeſimaquarta pars eſt .15. verum
                    <lb/>
                  eſt igitur, quod tibi iam dixeram.</s>
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              </div>
            </div>
            <div xml:id="echoid-div564" type="section" level="3" n="17">
              <div xml:id="echoid-div564" type="letter" level="4" n="1">
                <head xml:id="echoid-head430" xml:space="preserve">OPERATIONES DIVERSAE AB ALIIS
                  <lb/>
                Michaelis Stifelij.</head>
                <head xml:id="echoid-head431" style="it" xml:space="preserve">Conrado Terl.</head>
                <p>
                  <s xml:id="echoid-s3626" xml:space="preserve">
                    <emph style="sc">QVod</emph>
                  in .2. exemplo. II. cap. Stifelius ſcribit in .3. lib. pag .282. non nego
                    <lb/>
                  quin pulchrum ſit, ſed alijs pulchrioribus modis poſſumus illud idem de-
                    <lb/>
                  monſtrare; </s>
                  <s xml:id="echoid-s3627" xml:space="preserve">cogita igitur ſuperficiem rectangulam, cuius medietas ſit
                    <reg norm="triam" type="context">triã</reg>
                    <lb/>
                  gulus rectangulus
                    <var>.a.b.g.</var>
                  vnde ex ſuppoſito nobis cognita erit ſuperficies
                    <lb/>
                  ipſius trianguli, tanquam dimidium totius parallelogrammi rectanguli cogniti.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s3628" xml:space="preserve">Quare ex .25. ſecundi triangulorum
                    <reg norm="Monteregij" type="context">Mõteregij</reg>
                  , cognita nobis
                    <reg norm="erunt" type="context">erũt</reg>
                  latera
                    <var>.a.b.</var>
                  et
                    <var>.b.g</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s3629" xml:space="preserve">Alia etiam breuiori methodo idem poſſumus eſſicere, mediante angulo
                    <var>.b.</var>
                  recto,
                    <lb/>
                  eo quod cum nobis cognita ſit ſuperficies trianguli ſimul
                    <reg norm="cum" type="context">cũ</reg>
                  baſi
                    <var>.a.g.</var>
                  cognita etiam
                    <lb/>
                  nobis fit perpendicularis
                    <var>.b.d.</var>
                  à puncto
                    <var>.b.</var>
                  ad baſim, & conſequenter cognitum no-
                    <lb/>
                  bis erit productum ipſius
                    <var>.a.d.</var>
                  in
                    <var>.d.g.</var>
                  & quia nobis cognita eſt
                    <var>.a.g.</var>
                  & eius medietas, </s>
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