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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EPISTOL AE.
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          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div614" type="section" level="3" n="24">
              <div xml:id="echoid-div617" type="letter" level="4" n="3">
                <pb o="317" rhead="EPISTOL AE." n="329" file="0329" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0329"/>
                <p>
                  <s xml:id="echoid-s3879" xml:space="preserve">Accipeigitur huncalium.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3880" xml:space="preserve">Sit propoſitus maior axis
                    <var>.q.p.</var>
                  minor verò
                    <var>.e.c.</var>
                  ad angulos rectos ſe inuicem
                    <lb/>
                  ſecantes in puncto
                    <var>.o.</var>
                  deſcribatur circulus
                    <var>.q.n.p.a.</var>
                  cuius diameter ſit axis maior, in
                    <lb/>
                  quo accipiatur punctum, quod volueris, vt puta
                    <var>.u.</var>
                  à quo protrahatur
                    <var>.u.b.</var>
                  paralle-
                    <lb/>
                  la ad
                    <var>.o.c.n.</var>
                  deſignetur poſtea ſeparatim circulus
                    <var>.u.b.n.</var>
                  cuius diameter æqualis ſit ſe
                    <lb/>
                  midiametro prioris circuli, ita etiam fiat circulus
                    <var>.u.i.c.</var>
                  contingens circulum
                    <var>.u.b.n.</var>
                    <lb/>
                  in puncto
                    <var>.u.</var>
                  cuius diameter ſit
                    <var>.u.c.</var>
                  æqualis dimidio axi minori. </s>
                  <s xml:id="echoid-s3881" xml:space="preserve">accipiatur deinde in
                    <lb/>
                  circulo maximo longitudo
                    <var>.u.b.</var>
                  quæ collocetur in circulo mediocri à puncto
                    <var>.u.</var>
                  quæ
                    <lb/>
                  ſecabitur à minimo circulo in puncto
                    <var>.i.</var>
                  cum itaque longitudo
                    <var>.u.i.</var>
                  menſurata fue-
                    <lb/>
                  rit in
                    <var>.u.b.</var>
                  maximi circuli à puncto
                    <var>.u.</var>
                  habebimus propoſitum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3882" xml:space="preserve">Cuius reiratio eſt, quia
                    <var>.u.b.</var>
                  mediocris circuli diuiditur à gyro minimi in puncto
                    <lb/>
                  i. eadem proportione, qua diuiſa eſt
                    <var>.u.n.</var>
                  in puncto
                    <var>.c.</var>
                  quod manifeſtum eſt exſimi-
                    <lb/>
                  litudine triangulorum
                    <var>.u.b.n.</var>
                  et
                    <var>.u.i.c.</var>
                  imaginatæ cum fuerint duæ
                    <var>.b.n.</var>
                  et
                    <var>.i.c.</var>
                  ſed ita
                    <lb/>
                  eſſe oportet parallelas maximi circuli, quotieſcunque circunferentia ipſius ellipſis
                    <lb/>
                  tranſitura ſit per
                    <var>.c.</var>
                  vt in .51. cap. meæ gnomonicæ oſtenſum fuit.</s>
                </p>
                <figure position="here">
                  <image file="0329-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0329-01"/>
                </figure>
              </div>
              <div xml:id="echoid-div619" type="letter" level="4" n="4">
                <head xml:id="echoid-head481" style="it" xml:space="preserve">Modus deſignandi angulum, certo modo conditionatum.</head>
                <head xml:id="echoid-head482" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3883" xml:space="preserve">NVllius reuera difficultatis mihi videtur eſſe, quotieſcunque nobis propoſita
                    <lb/>
                  fuerint duo puncta
                    <var>.a.</var>
                  et
                    <var>.b.</var>
                  ſimul cum
                    <lb/>
                  angulo
                    <var>.d.</var>
                    <reg norm="necnon" type="context">necnõ</reg>
                  linea
                    <var>.g.</var>
                  ducere duas lineas
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0329-02a" xlink:href="fig-0329-02"/>
                  à dictis punctis terminatas, quæ
                    <reg norm="conſtituant" type="context">conſtituãt</reg>
                    <lb/>
                  angulum æqualem dato, & ipſæ directè
                    <reg norm="con" type="context">cõ</reg>
                    <lb/>
                  iunctæ conſtituant lineam æqualem da-
                    <lb/>
                  tæ. </s>
                  <s xml:id="echoid-s3884" xml:space="preserve">Nam ducatur linea indefinita per
                    <lb/>
                  puncta propoſita, cuius lineæ, pars illa, quę
                    <lb/>
                  intercepta fuerit inter dicta puncta, diui-
                    <lb/>
                  datur per æqualia in puncto
                    <var>.o.</var>
                  etiam & li-
                    <lb/>
                  nea data, quarum medietates accipio in
                    <lb/>
                  linea indefinitè protracta à puncto
                    <var>.o.</var>
                  me- </s>
                </p>
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