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="312" rhead="IO. BAPT. BENED." n="324" file="0324" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0324"/>
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                  <s xml:id="echoid-s3834" xml:space="preserve">Ponamus nos ſcire velle
                    <reg norm="punctum" type="context">pũctum</reg>
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                    <figure xlink:label="fig-0324-01" xlink:href="fig-0324-01a" number="347">
                      <image file="0324-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0324-01"/>
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                  eclipticę, cum quo Procyon oritur
                    <lb/>
                  polo .44. o. dato, quod ſtella in gra
                    <num value="19">.
                      <lb/>
                    19.</num>
                  cum min .24. </s>
                  <s xml:id="echoid-s3835" xml:space="preserve">Cancri, reperiatur
                    <lb/>
                  diſtans ab ecliptica per gra .16. min
                    <num value="10">.
                      <lb/>
                    10.</num>
                  meridiem verſus. </s>
                  <s xml:id="echoid-s3836" xml:space="preserve">vnde
                    <reg norm="arcus" type="simple">arcꝰ</reg>
                    <var>.a.q.</var>
                    <lb/>
                  erit gra .70. min .36.
                    <reg norm="eiusque" type="simple">eiusq́;</reg>
                  ſinus par-
                    <lb/>
                  tium 94321. talium qualium totalis
                    <lb/>
                  eſt .100000. arcus verò
                    <var>.a.o.</var>
                  gra .16.
                    <lb/>
                  minut .10. ſinus erit 27845. angu-
                    <lb/>
                  lus autem
                    <var>.a.q.e.</var>
                  declinationis zodia
                    <lb/>
                  ci ab ęquatore grad .23. min .30. cu-
                    <lb/>
                  ius ſinus eſt .39875. </s>
                  <s xml:id="echoid-s3837" xml:space="preserve">Quare ex ſupra-
                    <lb/>
                  dictis rationibus angulus
                    <var>.a.b.q.</var>
                  erit
                    <lb/>
                  gra .82. mi .24. cuius
                    <reg norm="ſinus" type="simple">ſinꝰ</reg>
                  erit .99122.
                    <lb/>
                  arcus vero
                    <var>.a.b.</var>
                  gra .22. minu .17. cu-
                    <lb/>
                  ius ſinus erit .37945. </s>
                  <s xml:id="echoid-s3838" xml:space="preserve">angulus deinde
                    <lb/>
                    <var>o.e.b.</var>
                  trianguli
                    <var>.o.e.b.</var>
                  eſt gra .46. mi
                    <var>.
                      <lb/>
                    o.</var>
                  altitudinis æquatoris ab orizonte,
                    <lb/>
                  cuius ſinus eſt .71934. angulus ſimili
                    <lb/>
                  ter
                    <var>.o.b.e.</var>
                  medio coniuncti, quibus
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                  rectus perſicitur, arcus etiam
                    <var>.o.b.</var>
                  no
                    <lb/>
                  tus eſt grad .6. min .7. cuius ſinus eſt
                    <num value="10655">.
                      <lb/>
                    10655.</num>
                  cum ſit differentia inter ar-
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                  cus
                    <var>.a.b.</var>
                  et
                    <var>.a.o.</var>
                  cognitos.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3839" xml:space="preserve">Quare ex .12. iam ſupradicta an-
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                  gulus
                    <var>.e.o.b.</var>
                  hoc eſt
                    <var>.a.o.d.</var>
                  erit. grad
                    <num value="36">.
                      <lb/>
                    36.</num>
                  min .39. cuius ſinus erit .59693.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s3840" xml:space="preserve">deinde per .4. cognitus erit nobis an
                    <lb/>
                  gulus
                    <var>.a.d.o.</var>
                  gra .55. min .5. cuius
                    <reg norm="ſinus" type="simple">ſinꝰ</reg>
                    <lb/>
                  erit .81998. arcus verò
                    <var>.d.o.</var>
                  gra .19.
                    <lb/>
                  min .51. cuius ſinus erit .33957 ar-
                    <lb/>
                  cus autem gra .11. min .42. cuius
                    <reg norm="ſinus" type="simple">ſinꝰ</reg>
                    <lb/>
                  erit .20270. vnde
                    <reg norm="arcus" type="simple">arcꝰ</reg>
                    <var>.d.q.</var>
                  reſiduus
                    <lb/>
                  ex
                    <var>.a.q.</var>
                  erit gra .58. min .54. complementum
                    <reg norm="autem" type="wordlist">aũt</reg>
                  quartæ erit gra .31. mi .6. hoc eſt gra
                    <num value="1">.
                      <lb/>
                    1.</num>
                  ſigni Leonis. cum min .6.</s>
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              <div xml:id="echoid-div610" type="letter" level="4" n="2">
                <head xml:id="echoid-head471" style="it" xml:space="preserve">De ſphæroide duplæ ſpbær æ propoſit æ.</head>
                <head xml:id="echoid-head472" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3841" xml:space="preserve">MOdus autem inueniendi ſphæroidem ex dato axe, quod duplum ſit ſphæ-
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                  ra propoſita, talis eſt.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3842" xml:space="preserve">Sit exempli gratia
                    <var>.a.b.c.</var>
                  ſphæra propoſita. cuius ſemidia meter ſit
                    <var>.o.c.</var>
                  ſemiaxis
                    <lb/>
                  vero ſphæroidis ſit
                    <var>.d.x.</var>
                  cuius dimidium ſit
                    <var>.u.x.</var>
                  </s>
                  <s xml:id="echoid-s3843" xml:space="preserve">tunc ex doctrina .9. ſexti Euclid. inue
                    <lb/>
                  niatur
                    <var>.g.h.</var>
                  media proportionalis inter
                    <var>.u.x.</var>
                  et
                    <var>.c.o.</var>
                  </s>
                  <s xml:id="echoid-s3844" xml:space="preserve">deinde ſicut ſe habet
                    <var>.u.x.</var>
                  ad
                    <var>.g.h.</var>
                  </s>
                </p>
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