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-div495" type="section" level="3" n="5">
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                <pb o="231" rhead="EPISTOL AE." n="243" file="0243" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0243"/>
                <p>
                  <s xml:id="echoid-s2844" xml:space="preserve">Quod ſecundum primum ſuppoſitum finiebatur ſpacio annorum .240. qui nume
                    <lb/>
                  rus fit. ex .20. duodecies multiplicatis. </s>
                  <s xml:id="echoid-s2845" xml:space="preserve">Et quia triplicitates ſunt .4. ideo credebant
                    <lb/>
                  in ſpacio annorum .960. qui numerus fit ex .240. quater multiplicato, perfici .48.
                    <reg norm="con- iunctiones" type="context">cõ-
                      <lb/>
                    iunctiones</reg>
                  , priuſquam redirent ad ſe coniungendos in eodem loco, ubi prius iun-
                    <lb/>
                  cti fuiſſent. </s>
                  <s xml:id="echoid-s2846" xml:space="preserve">Primum autem ſuppoſitum, quod vigeſimo quoque anno
                    <reg norm="iungerentur" type="context">iũgerentur</reg>
                  ,
                    <lb/>
                  colligebant ſic ratiocinantes. </s>
                  <s xml:id="echoid-s2847" xml:space="preserve">Si Saturnus annis .30. peragit ſuum curſum per om-
                    <lb/>
                  nia ſigna Zodiaci, Iupiter autem peragit eum annis .12. Saturnus ambulauerit .4. ſi
                    <lb/>
                  gna, et .4. quintas partes ſigni, ſiue gra .24. dum Iupiter peragit integrum ambitum
                    <lb/>
                  ideſt annis .12. </s>
                  <s xml:id="echoid-s2848" xml:space="preserve">Itaque deſunt ei anni .8. ad perueniendum ad .20. quibus .8. annis Sa-
                    <lb/>
                  turnus
                    <reg norm="perambulat" type="simple">ꝑambulat</reg>
                  ſigna tria &
                    <reg norm="quintam" type="context">quintã</reg>
                    <reg norm="partem" type="context">partẽ</reg>
                  unius ſigni
                    <var>.i.</var>
                  gradus .6. qui iuncti dictis ſi
                    <lb/>
                  gnis .4. & gra .24. faciunt ſigna .8. quæ Iupiter item percurrit in annis .8. atque ita in
                    <lb/>
                  annis .20. </s>
                  <s xml:id="echoid-s2849" xml:space="preserve">Iupiter percurrit .20. ſigna
                    <reg norm="antequam" type="context">antequã</reg>
                  perueniat ad
                    <reg norm="Saturnum" type="context">Saturnũ</reg>
                  , cum Saturnus eo
                    <lb/>
                  dem tempore perfecerit curſum ſignorum .8. </s>
                  <s xml:id="echoid-s2850" xml:space="preserve">Eandem concluſionem etiam fortaſ
                    <lb/>
                  ſe collegerant ex dictis ſuppoſitis, dicentes, ſi Saturnus annis .30. ambulat .12. ſigna
                    <lb/>
                  proculdubio annis .20. ambulat .8. ſigna, quo tempore Iupiter perambulat .20. ad ra
                    <lb/>
                  tionem .12. ſignorum in annis .12.</s>
                </p>
                <p>
                  <s xml:id="echoid-s2851" xml:space="preserve">Verum hoc ſuppoſitum non eſt bonum, quoniam, ſi ita eſſet, coniunctiones
                    <reg norm="horum" type="context">horũ</reg>
                    <lb/>
                  duorum planetarum nunquam exirent ex vna triplicitate, & non modo .960.
                    <reg norm="quoque" type="simple">quoq;</reg>
                    <lb/>
                  anno, ſed etiam ſexageſimo rurſus coniungerentur in eodem puncto. </s>
                  <s xml:id="echoid-s2852" xml:space="preserve">nec coniunctio
                    <lb/>
                  nes eorum (ſemper autem intelligo de medijs) unquam egrederentur ex illis tribus
                    <lb/>
                  ſignis Zodiaci.</s>
                </p>
                <p>
                  <s xml:id="echoid-s2853" xml:space="preserve">Sed periodus æqualis Saturni, eſt dierum circiter .10740. atque ita minor an .30.
                    <lb/>
                  atque etiam .29. cum dimidio periodus autem æqualis Iouis, eſt circiter .4328. vt
                    <lb/>
                  ego eam comperio, quidquid alij
                    <reg norm="dicant" type="context">dicãt</reg>
                  ,
                    <reg norm="vtque" type="simple">vtq́;</reg>
                  planius alias oſtendam. </s>
                  <s xml:id="echoid-s2854" xml:space="preserve">
                    <reg norm="Itaque" type="simple">Itaq;</reg>
                  hæc per
                    <lb/>
                  iodus Iouis, etiam minor eſt ann .12. prætermittendo in ſupputatione
                    <reg norm="tam" type="context">tã</reg>
                  Saturni
                    <reg norm="quam" type="context">quã</reg>
                    <lb/>
                  Iouis quaſdam minutias horarum & earum partium, quæ hac in re pto nihilo habe-
                    <lb/>
                  ri poſſunt. </s>
                  <s xml:id="echoid-s2855" xml:space="preserve">Atque his duabus periodis eccentricorum duorum planetarum poſſu-
                    <lb/>
                  mus cognoſcere interuallum quod erit inter vtramque mediam coniunctionem, hoc
                    <lb/>
                  modo agendo, & ratiocinando.</s>
                </p>
                <p>
                  <s xml:id="echoid-s2856" xml:space="preserve">Si Saturnus diebus .10740. circuit gradus .360. diebus .4328. qui ſunt periodus
                    <lb/>
                  Iouis, conficiet gradus .145. & min .4. ideſt min .8704. & eadem regula inueniemus
                    <lb/>
                    <reg norm="quod" type="simple">ꝙ</reg>
                  Saturnus .30.
                    <reg norm="quibuſque" type="simple">quibuſq́;</reg>
                  diebus, conſiciet min .60. & ſecunda .20. </s>
                  <s xml:id="echoid-s2857" xml:space="preserve">Iupiter autem ſin-
                    <lb/>
                  gulis .30. diebus, conficiet min .149. & ſecunda .43. vnde ſubtrahendo minuta Satur-
                    <lb/>
                  ni à minutis Iouis, ſupererunt min .89. cum ſecun .23. </s>
                  <s xml:id="echoid-s2858" xml:space="preserve">
                    <reg norm="Itaque" type="simple">Itaq;</reg>
                  Iupiter .30.
                    <reg norm="quibuſque" type="simple">quibuſq́;</reg>
                  die-
                    <lb/>
                  bus velocitate curſus, ſuperabit Saturnum minutis .89. cum ſecundis .23. </s>
                  <s xml:id="echoid-s2859" xml:space="preserve">
                    <reg norm="Atque" type="simple">Atq;</reg>
                  dicen-
                    <lb/>
                  do, ſi minuta .89. cum ſecundis .23 dant nobis dies .30. ſupradicta, minuta .8704. da-
                    <lb/>
                  bunt nobis dies .2921. quibus iunctis cum diebus .4328. periodi Iouis, efficientur dies
                    <lb/>
                  7249. ideſt anni Aegiptij .19. cum diebus .314. & hæc erit æqua periodus temporis
                    <lb/>
                  inter vtranque coniunctionem horum duorum Altiorum planetarum. </s>
                  <s xml:id="echoid-s2860" xml:space="preserve">Vt autem pla
                    <lb/>
                  nius oſtendatur hanc operationem rectam eſſe (nam demonſtrationem
                    <reg norm="ſpeculatiuam" type="context">ſpeculatiuã</reg>
                    <lb/>
                  huius operationis in .113. Theoremate noſtræ Arithmeticę
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                  videre licet) fieri
                    <lb/>
                  poteſt his alijs calculis.</s>
                </p>
                <p>
                  <s xml:id="echoid-s2861" xml:space="preserve">Si Saturnus diebus .10740. tranſit per gra .360. in ſpacio dierum .2921. tranſibit
                    <lb/>
                  per gradus .97. min .54. quibus iunctis cum gra .145. min .4. ſupra notatis, efticientur
                    <lb/>
                  gra .242. min .58. </s>
                  <s xml:id="echoid-s2862" xml:space="preserve">Deinde, ſi Iupiter ſpatio dierum .4328. tranſit per gra .360. igitur
                    <lb/>
                  ſpatio .2921. per eandem regulam inueniemus eum tranſire gradus .242. mi .58. qui
                    <lb/>
                  numerus par eſt illi Saturni. </s>
                  <s xml:id="echoid-s2863" xml:space="preserve">Cum ergo Iupiter confecerit vnum ambitum poſt con­ </s>
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