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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IO. BAPT. BENED.
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                  <s xml:id="echoid-s3814" xml:space="preserve">Sit exempli gratia ſtella
                    <var>.o.</var>
                  ecli
                    <lb/>
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                  ptica verò
                    <var>.d.q.</var>
                  æquator autem
                    <var>.
                      <lb/>
                    p.q.</var>
                  punctus verò eclipticæ, cum
                    <lb/>
                  quo ſtella oritura ſit
                    <var>.e.</var>
                  orizon de
                    <lb/>
                    <reg norm="mum" type="context">mũ</reg>
                    <var>.o.e.</var>
                  vbi ſtella oriri poſſit
                    <reg norm="cum" type="context">cũ</reg>
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                  puncto
                    <var>.e</var>
                  . </s>
                  <s xml:id="echoid-s3815" xml:space="preserve">Nam cum ſtella pro-
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                  ponitur, datur etiam eius longi-
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                  tudo, nec non latitudo, </s>
                  <s xml:id="echoid-s3816" xml:space="preserve">quare ar-
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                  cus
                    <var>.a.q.</var>
                  & arcus
                    <var>.a.o.</var>
                  nobis cogni
                    <lb/>
                  tus erit, cum ſupponatur arcus
                    <var>.a.
                      <lb/>
                    o.</var>
                  eſſe circuli latitudinis, et
                    <var>.a.o.</var>
                    <lb/>
                  Iatitudo ipſius ſtellæ, & angulus
                    <lb/>
                  a. rectus erit, & quia punctum
                    <var>.e.</var>
                    <lb/>
                  datur, ergo arcus
                    <var>.a.o.</var>
                  & arcus
                    <var>.a.
                      <lb/>
                    e.</var>
                  ſimul
                    <reg norm="cum" type="context">cũ</reg>
                  angulo
                    <var>.a.</var>
                  recto cogni-
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                  ti ſunt, vnde ex .11. primi lib. co­
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                  pernici, angulus
                    <var>.a.e.o.</var>
                  cognoſce-
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                  tur, & angulus
                    <var>.q.e.o.</var>
                  ſimiliter, vt
                    <lb/>
                  reſiduum ex duobus rectis quo. e
                    <lb/>
                  mediante cum angulo
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                  declina
                    <lb/>
                  tionis ab æquatore,
                    <reg norm="medianteque" type="simple">medianteq́;</reg>
                    <lb/>
                  latere
                    <var>.q.e.</var>
                  cognito, cognitus quo
                    <lb/>
                  que nobis erit angnlus
                    <var>.e.t.q.</var>
                  ex
                    <lb/>
                  12. eiuſdem. </s>
                  <s xml:id="echoid-s3817" xml:space="preserve">qui quidem angulus
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                  erit altitudinis æquatoris ab ori-
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                  zonte quæſito, qui demptus à
                    <lb/>
                  90. gradibus, dabit altitudinem
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                  poli ab orizonte quæſito.</s>
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                  <s xml:id="echoid-s3818" xml:space="preserve">Inuenire poſtea gradum eclipticę, cum quo ſtella data oriatur ad orizontem pro
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                  poſitum, nullius eſt difficul@atis.</s>
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                <p>
                  <s xml:id="echoid-s3819" xml:space="preserve">Ponamus exempli gratia, aliquem ſcire velle gradum eclipticæ, cum quo canicu-
                    <lb/>
                  la oritur ad orizontem, cui polus boreus eleuatur per gradus .44. quæ canicula ſup-
                    <lb/>
                  ponatur habere gradus .19. cum min .24. </s>
                  <s xml:id="echoid-s3820" xml:space="preserve">Cancri longitudinis, & gra .16. min .10. lati-
                    <lb/>
                  tudinis meridianæ, quærere primum oportet eius declinationem ex doctrina .2. pro
                    <lb/>
                  blematis tabularum directionum Monteregij, quæ erit graduum .6. cum minutis .5.
                    <lb/>
                  ſeptentrionalis, </s>
                  <s xml:id="echoid-s3821" xml:space="preserve">deinde inuenire eius aſcenſionem rectam ex doctrina .4. problema
                    <lb/>
                  tis eiuſdem Monteregij, quæ erit gra .108. mi .42. </s>
                  <s xml:id="echoid-s3822" xml:space="preserve">deinde
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                  declinatione iam
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                  inuenta in tabulis differentiarum aſcenſionalium ſub polo .44. accipiemus differen-
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                  tiam aſcenſionum, qua differt recta ab obliqua, quæ in præſenti exemplo erit gra
                    <num value="5">.
                      <lb/>
                    5.</num>
                  min .55. quæ dempta ab aſcenſione recta ſtellæ, vt præſens exemplum exigit, relin
                    <lb/>
                  quet nobis aſcenſionem obliquam ſtellæ propoſitæ ad polum. gra .44. quæ erit gra
                    <num value="102">.
                      <lb/>
                    102.</num>
                  minu .47. qua mediante, in tabulis aſcenſionum obliquarum poli .44. habebi-
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                  mus gradum & minutum eclipticę cum quo ſtella oritur. </s>
                  <s xml:id="echoid-s3823" xml:space="preserve">quod in caſu noſtro erit
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                  gra .1. min .8. Leonis, ſed ſi tecum non fuerint tabulæ dictæ, potes eleganter omnia
                    <lb/>
                  hæc perficere via triangulorum ſphæricorum.</s>
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