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-div630" type="section" level="3" n="26">
              <div xml:id="echoid-div630" type="letter" level="4" n="1">
                <pb o="326" rhead="IO. BAPT. BENED." n="338" file="0338" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0338"/>
                <p>
                  <s xml:id="echoid-s3965" xml:space="preserve">Nunc verò cum duo puncta alicuius horarię lineæ inuenta fuerint, quæ à Solis ſi-
                    <lb/>
                  tu in diuerſis parallelis efficiuntur, ſi voluerimus ipſam lineam
                    <reg norm="horariam" type="context">horariã</reg>
                  ducere, ſcien
                    <lb/>
                  dum primò eſt ipſam lineam horariam eſſe communem ſectionem circuli horarij,
                    <lb/>
                  illius horæ cum ſuperficie cyllindrica, </s>
                  <s xml:id="echoid-s3966" xml:space="preserve">& propterea ellipticam, vt oſtendit Serenus
                    <lb/>
                  in .19. primi lib. quod etiam ellicere poſſumus ab eo, quod Archimedes in .10. pro-
                    <lb/>
                  poſitione libr. de conoidalibus, ſcribit. </s>
                  <s xml:id="echoid-s3967" xml:space="preserve">Quapropter oporter nos inſtrumen-
                    <lb/>
                  tum prius componere, modo circini, ſed trium crurum, quæ omnia in eadem
                    <lb/>
                  plana ſuperficie ſint, ea tamen arte factum, vt quodlibet illorum poſſimus pro-
                    <lb/>
                  longare, necnon contrahere, ut cum duo extrema firmata fuerint, media poſ-
                    <lb/>
                  ſit circunduci circa centrum, ſeu punctum commune illarum interſectionum
                    <reg norm="ſimulque" type="simple">ſimulq́;</reg>
                    <lb/>
                  poſſit produci, necnon abbreuiari vel augeri, & diminui, vt mediante ſua extremi-
                    <lb/>
                  tate inſeriori poſſimus delineare gyrum ellipticum horarium, dum
                    <reg norm="centrum" type="context">cẽtrum</reg>
                  ipſorum
                    <lb/>
                  crurum adhæreat extremitati gnomonis, reliquæ vero extremitates ipſorum
                    <reg norm="crurum" type="context">crurũ</reg>
                    <lb/>
                  ſint ſupra puncta inuenta ipſius horæ. </s>
                  <s xml:id="echoid-s3968" xml:space="preserve">oportet etiam vt hoc inſtrumentum à tergo
                    <lb/>
                  ipſorum crurum habeat in ſuperiori parte ſuperficiem quandam
                    <reg norm="ſemicircularem" type="context">ſemicircularẽ</reg>
                  , quę
                    <lb/>
                  ſit vice vnius partis illius ſuperficiei, in qua ſupponuntur omnia crura inſtrumenti,
                    <lb/>
                  & hoc quantum fieri poteſt, quod quidem fieri debet, ne crus medium, hoc eſt mo
                    <lb/>
                  bile, exeat à tali ſuperficie, ſeu declinet ab ea, quæ ſemper ſupponitur in ſitu circuli
                    <lb/>
                  horarij talis horæ. </s>
                  <s xml:id="echoid-s3969" xml:space="preserve">oportet etiam, vt iuxta circunferentiam dimidij circuli ſint duo
                    <lb/>
                  gyri eiuſdem materiæ inter ſe parum diſtantes, ita ut crura poſſint moueri, intra hos
                    <lb/>
                  gyros, & dimidium circulum, & quod inter hos gyros locatæ ſint duæ cochleæ, ſeu
                    <lb/>
                  duo helices, vt quando voluerimus, poſſimus fir-
                    <lb/>
                  mare ipſa crura extrema, dum eorum extremitates
                    <lb/>
                    <figure xlink:label="fig-0338-01" xlink:href="fig-0338-01a" number="360">
                      <image file="0338-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0338-01"/>
                    </figure>
                  fuerint ſupra puncta inuenta illius horæ, </s>
                  <s xml:id="echoid-s3970" xml:space="preserve">deinde in
                    <lb/>
                  dorſo iſtius inſtrumenti, circa centrum coniunctio
                    <lb/>
                  nis, rectè factum erit ſi aliqua concauitas fuerit, in
                    <lb/>
                  qua, extremitas gnomonis poſſit locari, dum duce-
                    <lb/>
                  re voluerimus aliquam horariam lineam.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3971" xml:space="preserve">Tale inſtrumentum excogitaui ad fugiendum
                    <lb/>
                  tædium inueniendi dictam ellipticam ex punctis.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3972" xml:space="preserve">Nunc autem ſciendum eſt, quod vnus tantum-
                    <lb/>
                  modo gnomon ſufficiens non erit pro tota die æſti-
                    <lb/>
                  ua, neque duo, niſi valde breues fuerint reſpectu
                    <lb/>
                  ſemidiametri cyllindri, & in ſitu medio quartarum
                    <lb/>
                  meridionalium noſtro orizonti, quorum autem
                    <lb/>
                  longitudo ita inuenienda eſſet.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3973" xml:space="preserve">Sit exempli gratia circulus
                    <var>.a.b.e.u.</var>
                  cyllindri ori
                    <lb/>
                  zontis vice,
                    <reg norm="diuiſusque" type="simple">diuiſusq́;</reg>
                  à duobus diametris
                    <var>.d.e.</var>
                  et
                    <var>.c.
                      <lb/>
                    f.</var>
                  quarum
                    <var>.c.f.</var>
                  ſit pro meridiana: </s>
                  <s xml:id="echoid-s3974" xml:space="preserve">d.e. autem pro verticali,
                    <reg norm="ſitque" type="simple">ſitq́;</reg>
                  e. punctus orientalis: </s>
                  <s xml:id="echoid-s3975" xml:space="preserve">d.
                    <lb/>
                  verò
                    <reg norm="occidentalis" type="context">occidẽtalis</reg>
                    <var>.f.</var>
                  autem meridionalis. et
                    <var>.c.</var>
                  ſeptentrionalis,
                    <reg norm="computeturque" type="simple">computeturq́;</reg>
                  maxima.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s3976" xml:space="preserve">Solis amplitudo ab
                    <var>.f.</var>
                  verſus
                    <var>.e.</var>
                  quæ terminetur ab
                    <var>.q.</var>
                  ita
                    <reg norm="quodarcus" type="simple">quodarcꝰ</reg>
                    <var>.f.q.</var>
                  minor ſit
                    <reg norm="quam" type="context">quã</reg>
                    <lb/>
                  graduum .45. aliter impoſſibile eſſet duobus
                    <reg norm="tantummodo" type="context">tantũmodo</reg>
                  gnomonibus mediantibus
                    <lb/>
                  tota die æſtiua horas videre.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3977" xml:space="preserve">Quo facto ducatur ab .q:
                    <var>q.p.</var>
                  contingens circulum & à centro circuli
                    <var>.o.</var>
                  per pun-
                    <lb/>
                  ctum
                    <var>.u.</var>
                  medium quartæ ducatur
                    <var>.o.u.i.</var>
                  vſque ad contingentem
                    <var>.q.p.</var>
                  vnde
                    <var>.u.i.</var>
                  longitu
                    <lb/>
                  do erit vniuſcuiuſque gnomonis, qui gnomones infixi erunt in medio dictarum
                    <lb/>
                  quartarum.</s>
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