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-div780" type="section" level="3" n="51">
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                <p>
                  <s xml:id="echoid-s5140" xml:space="preserve">
                    <pb o="424" rhead="IO. BAPT. BENED." n="436" file="0436" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0436"/>
                  tium. </s>
                  <s xml:id="echoid-s5141" xml:space="preserve">Exempli gratia, ſi prima Rota conſtaret ex .36. dentibus, dicendum eſſet, ſi
                    <lb/>
                  4. conuenit cum .36. cum quibus conuenient .3. & inueniemus .27. cum quo numero
                    <lb/>
                  dicta ſecunda Rota circunuolueretur eodem tempore à ſuo colino trium dentium,
                    <lb/>
                  quo prima à ſuo quatuor dentium, </s>
                  <s xml:id="echoid-s5142" xml:space="preserve">quare duplicando .27. haberemus .54. pro nume-
                    <lb/>
                  ro dentium dictę ſecundæ Rotæ, vt duplo temporis circunuoluatur quo prima. </s>
                  <s xml:id="echoid-s5143" xml:space="preserve">Sed
                    <lb/>
                  ſi primus colinus conſtaret ex .6. dentibus, exiſtente ſua Rota ex .36.
                    <reg norm="vellemusque" type="simple">vellemusq́;</reg>
                    <reg norm="quod" type="simple">ꝙ</reg>
                    <lb/>
                  ſecundus exiſteret ex .4. </s>
                  <s xml:id="echoid-s5144" xml:space="preserve">tunc ſuam Rotam oporteret habere dentes .48. ex dicta re-
                    <lb/>
                  gula. </s>
                  <s xml:id="echoid-s5145" xml:space="preserve">Si autem primus colinus conſtaret ex numero impari, nihil referret, dummo-
                    <lb/>
                  do huiuſmodi numerus impar, ſeu par, exiſteret pars propria numeri dentium, vel
                    <lb/>
                  ipſius dupli primæ Rotę, hoc eſt, eſſet pars aliquota numeri dentium ipſius primæ
                    <lb/>
                  Rotæ vel ipſius dupli. </s>
                  <s xml:id="echoid-s5146" xml:space="preserve">In ijs verò horologiis in quibus duplum numeri dentium di-
                    <lb/>
                  ctę primę Rotę non erit multiplex numero dentium primi colini, hoc fieri non pote
                    <lb/>
                  rit. </s>
                  <s xml:id="echoid-s5147" xml:space="preserve">Ratio enim tam clarè, tibi conſideranti, patebit, vt nullis verbis indigeat cum
                    <lb/>
                  ſemper numerus dentium ſecundę Rotę multiplex eſſe debeat numero dentium ſe-
                    <lb/>
                  cundi colini. </s>
                  <s xml:id="echoid-s5148" xml:space="preserve">Idem autem non dico de prima Rota cum ſuo colino, hoc eſt, vt nu-
                    <lb/>
                  merus primę multiplex ſit numero ſui colini, nam hoc neceſſarium non eſt. </s>
                  <s xml:id="echoid-s5149" xml:space="preserve">Pona-
                    <lb/>
                  mus exempli gratia primum colinum conſtare ſex dentibus, ſuam vero Rotam den-
                    <lb/>
                  tibus .21. cuius quidem numeri, 6. non eſt pars aliquota, ſed dupli ipſius .21. ipſe .6.
                    <lb/>
                  eſt pars aliquota. </s>
                  <s xml:id="echoid-s5150" xml:space="preserve">Nunc verò ſi voluerimus numerum dentium ſecundæ Rotę inue-
                    <lb/>
                  nire, cuius colinus ex quinque dentibus exiſtat (ſuppoſito primo ex .6. conſtare) </s>
                  <s xml:id="echoid-s5151" xml:space="preserve">tunc
                    <lb/>
                  ex regula de tribus, diuiſo producto, quod fit ex .21. in .5. per .6. exibit .17. cum di-
                    <lb/>
                  midio, cuius duplum eſſet .35. qui multiplex eſt ipſi quinque. </s>
                  <s xml:id="echoid-s5152" xml:space="preserve">Reperto igitur nume
                    <lb/>
                  ro ſecundę Rotę, cum numero ipſius colini, oportet nunc ſcire modum compoſitio-
                    <lb/>
                  nis, ſeu coniunctionis harum rerum, hoc eſt duorum colinorum
                    <reg norm="concentricorum" type="context">concentricorũ</reg>
                  (ſed
                    <lb/>
                  de ijs ſatis iam ſuperius dictum fuit) duarum Rotarum concentricarum cum Tabula,
                    <lb/>
                  cum Zodiaco, & cum indice, ſeu Oſtenſore, cuius quidem Oſtenſoris medietas tan
                    <lb/>
                  tummodo nobis ſufficiet. </s>
                  <s xml:id="echoid-s5153" xml:space="preserve">Sciendum igitur nunc eſt quod cum primus colinus re-
                    <lb/>
                  uoluat totam primam Rotam, ſpacio temporis .12. horarum, oportet vt eius axis, ſeu
                    <lb/>
                  arbor voluat oſtenſorem,
                    <reg norm="Zodiacumque" type="simple">Zodiacumq́;</reg>
                  , eodem temporis ſpacio, & quia Rota hęc
                    <lb/>
                  inalterabis eſt, propter eius coniunctionem cum ſuo colino, & nos oporteat indicem
                    <lb/>
                    <reg norm="Zodiacumque" type="simple">Zodiacumq́;</reg>
                  , quotidie ferè, dirigere,
                    <reg norm="ſuisque" type="simple">ſuisq́;</reg>
                  locis collocare, ideo nos oportet, indi
                    <lb/>
                  cem, Zodiacum, & primam Rotam, ita cum axe, ſeu arbore coniungere, vt poſſimus
                    <lb/>
                  dicta omnia efficere. </s>
                  <s xml:id="echoid-s5154" xml:space="preserve">Pars igitur Arboris, ſeu axis dicti, quæ ingredi debet in prima
                    <lb/>
                  Rota, ſit rotunda, & contigua ipſi Rotæ, non autem continua, vel cum Rota conſoli-
                    <lb/>
                  data. </s>
                  <s xml:id="echoid-s5155" xml:space="preserve">Pars verò quę per foramen Zodiaci, ſeu Araneę tranſibit, ſit quadrata vſque
                    <lb/>
                  ad
                    <reg norm="ſummitatem" type="context">ſummitatẽ</reg>
                  ipſius axis (tali ſpiſſitudine, vt in claui ipſius horologij ingredi poſ-
                    <lb/>
                  ſit) & ita foramen ipſius Araneę, quadratum ſit, Oſtenſor autem circa axem, com
                    <lb/>
                  poſitus ſit tali ordine, vt circa paruum circulum volui poſſit, qui paruus circulus ha-
                    <lb/>
                  beat quadratum foramen, per quod tranſeat axis, qui axis aliquantulum emineat
                    <lb/>
                  ſupra
                    <reg norm="oſtenſorem" type="context">oſtenſorẽ</reg>
                  . </s>
                  <s xml:id="echoid-s5156" xml:space="preserve">Sub Aranea vero vel Zodiaco, locata erit Tabula, vt
                    <reg norm="nunc" type="context">nũc</reg>
                  dicemus,
                    <lb/>
                  ſed ſciendum eſt prius, quod inter Tabulam, & ſuam ſecundam Rotam, aliam lami-
                    <lb/>
                  nam immobilem interpoſitam eſſe oportet, quę circulare foramen habeat, per
                    <reg norm="quod" type="wordlist">qđ</reg>
                    <lb/>
                  quędam breuis fiſtula tranſeat circundans axem & coniungens
                    <reg norm="Tabulam" type="context">Tabulã</reg>
                  cum ſua Ro-
                    <lb/>
                  ta, cuius quidem fiſtulæ ſuperficies concaua, rotunda ſit, ſuperficies verò extrinſe-
                    <lb/>
                  ca, nontota, niſi ea pars, quę ſecundam Rotam ingreditur, vt in rotundo foramine
                    <lb/>
                  ipſius Rotę, dicta fiſtula volui poſſit, pars vero extrinſeca quę Tabulam ingredi de-
                    <lb/>
                  bet, ſit quadrata. </s>
                  <s xml:id="echoid-s5157" xml:space="preserve">Tabula vero quatuor paruiſſima foramina habeat in extremitati- </s>
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