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-div606" type="section" level="3" n="23">
              <div xml:id="echoid-div606" type="letter" level="4" n="1">
                <pb o="311" rhead="EPISTOL AE." n="323" file="0323" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0323"/>
                <p>
                  <s xml:id="echoid-s3824" xml:space="preserve">Via triangul@rum
                    <unsure/>
                  idem facere.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3825" xml:space="preserve">Sit
                    <reg norm="exempli" type="context">exẽpli</reg>
                  gr@tia
                    <var>.q.b.</var>
                  æquator, ecliptica verò
                    <var>.q.a.</var>
                  propoſitus
                    <reg norm="autem" type="wordlist">aũt</reg>
                  orizon ſit
                    <var>.o.c.d.</var>
                    <lb/>
                  & ſtella data ſit
                    <var>.o.</var>
                  in orientali parte orizontis, circulus verò
                    <var>.a.o.</var>
                  ille ſit, qui
                    <reg norm="tranſiens" type="context">tranſiẽs</reg>
                    <lb/>
                  per polos eclipti
                    <unsure/>
                  cæ & per centrum ſtellæ terminat longitudinem ipſius ſtellæ, & in
                    <lb/>
                  ipſo ſit eius latitudo. </s>
                  <s xml:id="echoid-s3826" xml:space="preserve">Nunc propoſitum ſit inuenire arcum
                    <var>.d.q.</var>
                  eo quod illicò ſcie
                    <lb/>
                  mus punctum
                    <var>.d.</var>
                  qua propter oportet nos prius cognoſcere arcum
                    <var>.d.a.</var>
                  qui demptus,
                    <lb/>
                  vel additus arcui
                    <var>.a.q.</var>
                  prius cognito ex ſuppoſito (nam data nobis eſt longitudo, &
                    <lb/>
                  latitudo ſtellæ) dabit nobis
                    <var>.d.q</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s3827" xml:space="preserve">Cum igitur voluerimus arcum
                    <var>.d.a.</var>
                  cognoſcere, ita faciemus. </s>
                  <s xml:id="echoid-s3828" xml:space="preserve">nam
                    <var>.q.a.</var>
                  cognitus
                    <lb/>
                  nobis eſt ex ſuppoſito vt dictum eſt. </s>
                  <s xml:id="echoid-s3829" xml:space="preserve">angulus quoque
                    <var>.a.q.b.</var>
                  qui declin tionis eclipti
                    <lb/>
                  cæ ab æquatore eſt, angulus deinde
                    <var>.a.</var>
                  (trianguli
                    <var>.a.b.q.</var>
                  ) rectus eſt, ergo ex .4. primi
                    <lb/>
                  copernici cogn@tus nobis erit arcus
                    <var>.
                      <lb/>
                    a.b.</var>
                  nec non angulus
                    <var>.a.b.q.</var>
                  vnde an-
                    <lb/>
                    <figure xlink:label="fig-0323-01" xlink:href="fig-0323-01a" number="346">
                      <image file="0323-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0323-01"/>
                    </figure>
                  gulus
                    <var>.o.b.e.</var>
                  reſiduus ex duobus re-
                    <lb/>
                  ctis in duobus primis hic ſubſcriptis
                    <lb/>
                  figuris nobis itidem cognitus erit,
                    <lb/>
                  etiam & arcus
                    <var>.b.o.</var>
                  reſiduus ſiue com
                    <lb/>
                  poſitus ex ar cu
                    <var>.a.o.</var>
                  cognito ex ſup-
                    <lb/>
                  poſito
                    <reg norm="cum" type="context">cũ</reg>
                  ſit arcus latitud nis ab ecli-
                    <lb/>
                  ptica. </s>
                  <s xml:id="echoid-s3830" xml:space="preserve">Tunc
                    <unsure/>
                  in triangulo
                    <var>.o.b.e.</var>
                  co-
                    <lb/>
                  gnoſcimus latus
                    <var>.o.b.</var>
                  & angulum
                    <var>.o.
                      <lb/>
                    b.e.</var>
                  nec non angulum
                    <var>.b.e.o.</var>
                  qui eſt
                    <lb/>
                  altitudinis æquatoris ab orizonte ,
                    <lb/>
                  </s>
                  <s xml:id="echoid-s3831" xml:space="preserve">quare ex .12. dicti lib. cognitus nobis
                    <lb/>
                  erit angulus
                    <var>.b.o.e</var>
                  . </s>
                  <s xml:id="echoid-s3832" xml:space="preserve">Conſideremus
                    <lb/>
                  deinde triangulum
                    <var>.a.o.d.</var>
                  cuius angu
                    <lb/>
                  lus
                    <var>.a.</var>
                  rectus eſt, & angulus
                    <var>.a.o.d.</var>
                    <reg norm="cum" type="context">cũ</reg>
                    <lb/>
                  latere
                    <var>.a.o.</var>
                  etiam cognitus, vnde ex
                    <lb/>
                  ſupradicta .4. nobis cognitus erit ar-
                    <lb/>
                  cus
                    <var>.a.d.</var>
                  & conſequenter cognoſce-
                    <lb/>
                  mus at cum
                    <var>.d.q.</var>
                  eius reſiduum, ſeu
                    <lb/>
                  compoſitum, quem quærebamus.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3833" xml:space="preserve">Sed ſi hac via inuenire deſideras,
                    <lb/>
                  cui orizonti propoſita ſtella oriatur
                    <lb/>
                  cum eodem eclipticę puncto
                    <var>.a.</var>
                  lon-
                    <lb/>
                  gitudinis, hoc aliud nihil eſſet, quam
                    <lb/>
                  cognoſcere amplitudinem anguli
                    <var>.a.
                      <lb/>
                    b.q.</var>
                  eo quod talis orizon, idem cir-
                    <lb/>
                  culus eſſet
                    <var>.a.b.o.</var>
                  vnde cum quis ſci-
                    <lb/>
                  ret vnum illorum angulorum quem
                    <lb/>
                  æquator efficit cum orizonte, reli-
                    <lb/>
                  qua illicò ei innoteſcent, ſed dictus
                    <lb/>
                  angulus
                    <var>.b.</var>
                  iam diximus quomodo
                    <lb/>
                  cognoſcatur.</s>
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