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-div622" type="section" level="3" n="25">
              <div xml:id="echoid-div622" type="letter" level="4" n="1">
                <p>
                  <s xml:id="echoid-s3892" xml:space="preserve">
                    <pb o="319" rhead="EPISTOL AE." n="331" file="0331" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0331"/>
                  liquum ſecantem æquatorem, omnes caduntin gyro elliptico, oxygonio, ſeu de-
                    <lb/>
                  fectionali, & non circulari. </s>
                  <s xml:id="echoid-s3893" xml:space="preserve">Vnde per ſupradicta tria puncta
                    <var>.n.ω.x.</var>
                  oporteret tranſi
                    <lb/>
                  re talem circunferentiam, & non
                    <reg norm="circularem" type="context">circularẽ</reg>
                  , quæ circunferentia eſſet vnius ellipſis,
                    <lb/>
                  cuius minor axis in diametro
                    <var>.b.q.</var>
                  eſſet .ab
                    <var>.ω.</var>
                  vſque ad
                    <var>.i.</var>
                  terminum ſini
                    <var>h.i.</var>
                  arcus
                    <var>.h.b.</var>
                    <lb/>
                  in analemate, maior verò axis eſſet magnitudinis
                    <var>.f.h.</var>
                  diametri paralleli, quæ
                    <reg norm="tranſiſ- ſet" type="context">trãſiſ-
                      <lb/>
                    ſet</reg>
                  per punctum
                    <var>.c.</var>
                  medium inter
                    <var>.ω.</var>
                  et
                    <var>.i.</var>
                  quę quidem circunfere ntia tota eſſet intra cir
                    <lb/>
                  culum
                    <var>.q.n.b.x.</var>
                    <reg norm="con" type="context">cõ</reg>
                    <reg norm="tiguaque" type="simple">tiguaq́;</reg>
                  gyro
                    <var>.q.n.b.x.</var>
                  in punctis
                    <var>.n.x</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s3894" xml:space="preserve">Si ergò circunferentia
                    <var>.n.ω.x.</var>
                  eſſet elliptica tunc punctum
                    <var>.u.</var>
                  in orizonte illud eſſet
                    <lb/>
                  vbi caderet ſinus altitudinis horę, et
                    <var>.t.u.</var>
                  æqualis eſſet
                    <var>.r.z.</var>
                  communi ſectioni paralle
                    <lb/>
                  li cum almicantarat ex .34. primi Euclid. et
                    <var>.u.g.</var>
                  æqualis eſſet
                    <var>.o.y.</var>
                  communi ſectioni
                    <lb/>
                  almicantarat cum meridiano, vel cum azimut illius horæ ex .4. primi, cum
                    <var>.g.t.</var>
                  æqua
                    <lb/>
                  lis ſit ipſi
                    <var>.o.r.</var>
                  et
                    <var>.t.u.</var>
                  ipſi
                    <var>.r.z.</var>
                  & angu
                    <lb/>
                    <figure xlink:label="fig-0331-01" xlink:href="fig-0331-01a" number="355">
                      <image file="0331-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0331-01"/>
                    </figure>
                  lus. t trianguli
                    <var>.g.t.u.</var>
                  rectus, quem-
                    <lb/>
                  admodum
                    <var>.r.</var>
                  qui compræhenditur
                    <lb/>
                  ab
                    <var>.z.r.</var>
                  et
                    <var>.r.o.</var>
                  vnde anguli
                    <var>.K.g.m.</var>
                    <lb/>
                  et
                    <var>.K.g.b.</var>
                  rectè ſe haberent, diſtan-
                    <lb/>
                  tia verò inter
                    <var>.K.</var>
                  et
                    <var>.g.</var>
                    <reg norm="iam" type="context">iã</reg>
                  rectè ſum-
                    <lb/>
                  pta fuit.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3895" xml:space="preserve">Sed quia punctum
                    <var>.u.</var>
                  vt
                    <reg norm="plurimum" type="context">plurimũ</reg>
                    <lb/>
                  (in gyro circulari ſumptum) extra
                    <lb/>
                  puncta interſectionum ipſius circu
                    <lb/>
                  laris gyri cum elliptico reperìtur,
                    <lb/>
                  </s>
                  <s xml:id="echoid-s3896" xml:space="preserve">propterea efficit angulos
                    <var>.K.g.m.</var>
                    <lb/>
                  et
                    <var>.K.g.b.</var>
                  falſos, & non æquales il-
                    <lb/>
                  lis, qui fiunt ab azimut horæ cum
                    <lb/>
                  verticali, & cum meridiano, quæ
                    <lb/>
                  omnia ex cap .52. meæ gnomonicę
                    <lb/>
                  facilè videre potes.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3897" xml:space="preserve">Nectacere volo quod punctum
                    <lb/>
                  u. verum, hoc eſt ellipticum, inue-
                    <lb/>
                  niri poſſet ea via quam ſcripſi in
                    <lb/>
                  eodem .52. cap. qua mediante do-
                    <lb/>
                  cui demum inuenire punctum
                    <var>.π.</var>
                    <lb/>
                  orizontis, quamuis in præſenti ca­
                    <lb/>
                  ſu
                    <var>.ω.λ.</var>
                  perpendicularis eſſet ſupra
                    <lb/>
                  minorem axem ipſius ellipſis,
                    <reg norm="quan- uis" type="context">quã-
                      <lb/>
                    uis</reg>
                  ſupra maiorem axem, quod ta-
                    <lb/>
                  men minimè mutat ordinem, imò
                    <lb/>
                  rationes eędem ſunt, tam in vna,
                    <lb/>
                  quam in alia operatione, ſed vt il-
                    <lb/>
                  licò
                    <reg norm="idipsum" type="context">idipsũ</reg>
                  habeas, fac vt
                    <var>.t.u.</var>
                  æqua
                    <lb/>
                  lis. ſit
                    <var>.r.z</var>
                  . </s>
                  <s xml:id="echoid-s3898" xml:space="preserve">& tunc punctum
                    <var>.K.</var>
                  erit
                    <lb/>
                    <reg norm="quæſitum" type="context">quæſitũ</reg>
                  , quod ego in .52. cap. meę
                    <lb/>
                  gnomonicę, ijs verbis ſignificaui.</s>
                </p>
                <quote>
                  <s xml:id="echoid-s3899" xml:space="preserve">
                    <reg norm="Itaque" type="simple">Itaq;</reg>
                  mediis binis triangulis ijs,
                    <lb/>
                    <reg norm="medioque" type="simple">medioq́;</reg>
                  azimut Solis pariter ho-
                    <lb/>
                  rologia fabricari poterunt.</s>
                </quote>
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