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-div776" type="section" level="3" n="50">
              <div xml:id="echoid-div778" type="letter" level="4" n="3">
                <pb o="423" rhead="EPISTOL AE." n="435" file="0435" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0435"/>
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            <div xml:id="echoid-div780" type="section" level="3" n="51">
              <div xml:id="echoid-div780" type="letter" level="4" n="1">
                <head xml:id="echoid-head592" xml:space="preserve">NOVA INVENTIO COMPONENDI ASTROLABIA
                  <lb/>
                cum Horologijs artificialibus.</head>
                <head xml:id="echoid-head593" style="it" xml:space="preserve">Facobo Mayeto Ingenioſißimo Horologiorum Serenißimi
                  <lb/>
                Sabaudiæ Ducis Artifici.</head>
                <p>
                  <s xml:id="echoid-s5130" xml:space="preserve">
                    <emph style="sc">NOnnvnqvam</emph>
                  conſideraui mirabilem pulchritudinem, ſimul cum vtili-
                    <lb/>
                  tate coniunctam, illorum horologiorum, quæin Germania conſtruuntur
                    <lb/>
                    <reg norm="cum" type="context">cũ</reg>
                  mobili Rete, ſeu Aranea Aſtrolabij
                    <reg norm="ſuper" type="simple">ſuꝑ</reg>
                    <reg norm="Tabulam" type="context">Tabulã</reg>
                  regionis, in
                    <reg norm="quibus" type="simple">ꝗbus</reg>
                    <reg norm="conti" type="context">cõti</reg>
                    <lb/>
                  nuo
                    <reg norm="videntur" type="simple">vident̃</reg>
                  oriri,
                    <reg norm="occidereque" type="simple">occidereq́;</reg>
                  cæleſtia ſigna, cælum mediare ſupra orizon
                    <lb/>
                    <reg norm="tem" type="context">tẽ</reg>
                    <unsure/>
                  , necnon ſub eo, & vt vno verbo dicam, continuo erecta videtur tota coelifigura.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s5131" xml:space="preserve">Sed quia talia horologia omnia eorum limbum diſtinctum habent in .24. horas, qua
                    <lb/>
                  propter diametrum limbi, minorem duobus palmis, ſeu ſemipede eſſe non oportet
                    <lb/>
                  neinterſtitia horarum iuſtò breuiora ſeu anguſtiora efficiantur, etiam ne interualla
                    <lb/>
                  dentium rotæ indicis nimis anguſta ſint. </s>
                  <s xml:id="echoid-s5132" xml:space="preserve">Sed quia talis magnitudo vt plurimum in-
                    <lb/>
                  commoda exiſtit. </s>
                  <s xml:id="echoid-s5133" xml:space="preserve">Ideo non inutile fore cogitaui, ſi modus aliquis inuentus fuerit,
                    <lb/>
                  vt ea omnia efficiantur in limbo diuiſo tantummodo in .12. horas æquales,
                    <reg norm="ipſumque" type="simple">ipſumq́;</reg>
                    <lb/>
                  inueni, qui quidem erit, efficiendo vt Tabula (in qua deſignantur cęleſtes domus,
                    <lb/>
                  cum almicantarat, atque azimut) Reti ſubiectæ, mobilis ſit, tardior tamen ipſo Re-
                    <lb/>
                  te cum indice, pro duplo temporis, hoc eſt, quod eo tempore, quo Aranea cum in
                    <lb/>
                  dice circunuoluetur ſpacio .12. horarum vno gyro perfecto, ipſa Tabula efficiat tan
                    <lb/>
                  tummodo ſexinterſtitia horarum. </s>
                  <s xml:id="echoid-s5134" xml:space="preserve">Ideſt dum Tabula dicta eſſicit vnam integram re
                    <lb/>
                  uolutionem, Aranea, ſeu Zodiacus cum indice, duas efficiat reuolutiones. </s>
                  <s xml:id="echoid-s5135" xml:space="preserve">Ita quod
                    <lb/>
                  Aranea cum indice perficiet vnam reuolutionem ſpaci o temporis .12. horarum, Ta-
                    <lb/>
                  bula verò perficiet eam ſpacio temporis .24. horarum. </s>
                  <s xml:id="echoid-s5136" xml:space="preserve">Vnde ſequetur quod Ara-
                    <lb/>
                  nea ſeu Zodiacus cum indice, ſpacio .24. horarum perfectè circunuoluetur ſupra Ta-
                    <lb/>
                  bulam, & ita huiuſmodi horologia, in hoc nihil differrent ab illis ſupradictis. </s>
                  <s xml:id="echoid-s5137" xml:space="preserve">Vt au
                    <lb/>
                  tem facias dictam tabulam tardiorem duplo temporis Araneæ cum indice, quamuis
                    <lb/>
                  diuerſis modis hoc fieri poſſit, pręſtantiorem tamen iudico, ſi cum Rota indicis,
                    <reg norm="aliam" type="context">aliã</reg>
                    <lb/>
                  Rotam
                    <reg norm="concentricam" type="context">concentricã</reg>
                  coniunxeris, ita tamen, vt
                    <reg norm="vnaquęque" type="simple">vnaquęq;</reg>
                  liberè poſſit volui, ſimiliter
                    <lb/>
                  ſi cum ea horologii particula (quę
                    <reg norm="circumagit" type="context">circũagit</reg>
                  Rotam indicis, quæ Italicè
                    <emph style="sc">rochetto</emph>
                    <lb/>
                  Germanicè verò
                    <emph style="sc">trib</emph>
                  vocatur, Latinè
                    <reg norm="autem" type="wordlist">aũt</reg>
                  ipſum vocabo,
                    <emph style="sc">colinvm</emph>
                  , qui ſubro-
                    <lb/>
                  ta fuſi reperitur) coniunxeris alium colinum quem, ſecundum vocabo,
                    <reg norm="concentricum" type="context">concentricũ</reg>
                    <lb/>
                  verò cum primo, cum
                    <reg norm="eoque" type="simple">eoq́;</reg>
                  conſolidato, numerum verò dentium, tam Rotę adiunctę
                    <lb/>
                  quam ſecundi colini, varijs modis poteris inuenire, quorum primus erit, vt numerus
                    <lb/>
                  dentium ſecundæ Rotę duplus exiſtat numero dentium primę, efficiendo ſecundum
                    <lb/>
                  colinum eiuſdem numeri dentium quo primum, ſed quia interualla dentium huiuſ-
                    <lb/>
                  modi Rotę, nimis anguſta fortaſſe reſultabunt, </s>
                  <s xml:id="echoid-s5138" xml:space="preserve">propterea alios etiam modos inue-
                    <lb/>
                  ni, quorum vnus erit (dum numerus dentium primi colini par fuerit)
                    <reg norm="efficiendo" type="context">efficiẽdo</reg>
                  ſecun
                    <lb/>
                  dam
                    <reg norm="Rotam" type="context">Rotã</reg>
                    <reg norm="eiuſdem" type="context">eiuſdẽ</reg>
                  numeri
                    <reg norm="dentium" type="context">dentiũ</reg>
                  cuius eſt prima.
                    <reg norm="ſecundum" type="context context">ſecũdũ</reg>
                  vero colinum, medietatis
                    <lb/>
                  numeri dentium cuius erit primus. </s>
                  <s xml:id="echoid-s5139" xml:space="preserve">Attamen ſi primus colinus eſſet .4. dentium, ſecun
                    <lb/>
                  dum oporteret eſſe duorum dentium, vnde motus ſecundę Rotę non eſſet ita conti-
                    <lb/>
                  nuus. </s>
                  <s xml:id="echoid-s5140" xml:space="preserve">Quapropter alium etiam mòdum excogitaui, hoc eſt, cupiendo vt ſecundus
                    <lb/>
                  colinus, extribus dentibus exiſtat, ſi primus ex .4. repertus fuerit, oportebit prius ex
                    <lb/>
                  regula de tribus, numerum quendam inuenire quo inuento ipſum duplicare, & hunc
                    <lb/>
                  duplicatum numerum conueniet ſecundam Rotam habere, vt ipſa poſſit ab illo co-
                    <lb/>
                  lino
                    <reg norm="trium" type="context">triũ</reg>
                    <reg norm="dentium" type="context">dentiũ</reg>
                  circunuolui in duplo temporis, quo prima à ſuo colino quatuor den­ </s>
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