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">
              <div xml:id="echoid-div495" type="letter" level="4" n="1">
                <p>
                  <s xml:id="echoid-s3123" xml:space="preserve">
                    <pb o="248" rhead="IO. BAPT. BENED." n="260" file="0260" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0260"/>
                  cum epicycli, cum ipſa proportio nullo modo alteratur exiſtente epicyclo vbi volue
                    <lb/>
                  ris ipſius circunferentiæ eccentrici, ſed angulus in centro mundi, cui ſubiacet dictus
                    <lb/>
                  diameter epicycli, bene alteratur, propter inæqualem diſtantiam centri epicycli
                    <lb/>
                  ab ipſo centro mundi. </s>
                  <s xml:id="echoid-s3124" xml:space="preserve">At ſi de tali angulo inferre voluiſſet, iam probaui ipſum
                    <reg norm="con- tinere" type="context">cõ-
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                    tinere</reg>
                  ſolum gra .66. minu .28. exiſtente centro epicycli in longitudinibus medijs &
                    <lb/>
                  non gra .79. vt ipſe dicit.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3125" xml:space="preserve">Omitto poſtea, quod vbi mentionem facit coniunctionum Solis cum Marte au-
                    <lb/>
                  gium & earum oppoſitorum, non explicat an intelligat de veris an de medijs. </s>
                  <s xml:id="echoid-s3126" xml:space="preserve">Nam
                    <lb/>
                  ſi ex eius modo loquendi accipiatur eum loqui de veris multum erraret.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3127" xml:space="preserve">Sed quia iam tibi moleſtum eſſe inciperet ſi diutius te detinerem in his conten-
                    <lb/>
                  tionibus aſtronomicis, vlterius non diſputabo. </s>
                  <s xml:id="echoid-s3128" xml:space="preserve">Satis enim hactenus explicaui
                    <reg norm="ſenten- tiam" type="context">ſentẽ-
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                    tiam</reg>
                  meam, vt oſtendiſſe videor quam mihi iucundum ſit tibi
                    <reg norm="morem" type="context">morẽ</reg>
                  gerere. </s>
                  <s xml:id="echoid-s3129" xml:space="preserve">In quo
                    <lb/>
                  etiam hnmanitati tuæ gratiam habebo,
                    <reg norm="quum" type="context">quũ</reg>
                  petitione tua occaſionem mihi de deris
                    <lb/>
                  efficiendi, vt tum amici tui (amant enim te omnia ſublimia ingenia) tum alij, ſi
                    <reg norm="quam" type="context">quã</reg>
                    <lb/>
                  falſam opinionem ex huius Benedicti Altæuillæ ſcriptis ſumpſiſſent,
                    <reg norm="eam" type="context">eã</reg>
                  relinquant,
                    <lb/>
                  & per te hoc beneficium à me conſequantur, & huiuſmodi occaſionem, & iuuandi
                    <lb/>
                  hominum ſtudia & tibi gratum faciendi, honorificum, & per gratum mihi fuiſſe in-
                    <lb/>
                  telligant. </s>
                  <s xml:id="echoid-s3130" xml:space="preserve">Vale & me vt ſoles ama.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3131" xml:space="preserve">Taurini pridie Kal. </s>
                  <s xml:id="echoid-s3132" xml:space="preserve">Octobris .1581.</s>
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              <div xml:id="echoid-div500" type="letter" level="4" n="2">
                <head xml:id="echoid-head374" style="it" xml:space="preserve">De probatione diuiſionis numerorum.</head>
                <head xml:id="echoid-head375" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3133" xml:space="preserve">INter alia quæ à me ſcire cupis, vir doctiſſime, hoc vnum eſt, vt ex literis tuis ac-
                    <lb/>
                  cepi, vnde ſit vt priſci noſtri probatione numeri nouenarij potius quam ſepte-
                    <lb/>
                  narij vſi fuerint, & qua ratione non idem proueniat ex probatione numerorum
                    <lb/>
                  octonarij, ſenarij, vel quinarij, aut cuiuslibet alterius: </s>
                  <s xml:id="echoid-s3134" xml:space="preserve">Vnde pariter oriatur quod in
                    <lb/>
                  partitionis probatione neceſſum ſit probationum euentus multiplicare cum proba-
                    <lb/>
                  tione diuiſoris, ac eam quæ eſt producti poſtea cum probatione fractionis in ſum-
                    <lb/>
                  mam colligere, & c. </s>
                  <s xml:id="echoid-s3135" xml:space="preserve">Ad hæc in primis reſpondeo, cum aliquoties accidere poſſit ta
                    <lb/>
                  les probationes nos fallere poſſe,
                    <reg norm="idque" type="simple">idq́;</reg>
                  fi in tali ſumma ſimilis numerus, ut puta ſe-
                    <lb/>
                  ptem, aut nouem, plus vel minus æquo iuſtouè poſitus fuerit, attamen per raro eueni
                    <lb/>
                  re poteſt, vt quis per nouenarium potius quam per ſeptenarium decipiatur. </s>
                  <s xml:id="echoid-s3136" xml:space="preserve">Exem-
                    <lb/>
                  pli gratia, ponamus ſummam eſſe .100. quam numerus nouenarius vndecies ſolum
                    <lb/>
                  ingreditur, at ſeptenarius quatuordecies, vnde quis
                    <reg norm="ſępius" type="simple">ſępiꝰ</reg>
                  ex ſeptenario, hacratione,
                    <lb/>
                  quam ex nouenario numero ſe poſſe errare facile depræhendet, efſi ex probatione
                    <lb/>
                  nouenarij magis quam ſeptenarij, vt practici ſcribunt, duabus de cauſis errare poſſi-
                    <lb/>
                  mus. </s>
                  <s xml:id="echoid-s3137" xml:space="preserve">Alia tamen ratio mihi ſuppetit, ob quam credibile eſt ipſos potius nouena-
                    <lb/>
                  rio adiutos fuiſſe, quam ſeptenario, quæ eſt ob ſui cum velocitatem tum
                    <reg norm="facilitatem" type="context">facilitatẽ</reg>
                  ,
                    <lb/>
                    <reg norm="neque" type="simple">neq;</reg>
                  enim in ſeptenario eſt adeo facilis. </s>
                  <s xml:id="echoid-s3138" xml:space="preserve">
                    <reg norm="Nam" type="context">Nã</reg>
                  quamuis, tam vna quam altera aliud
                    <lb/>
                  non ſit, quam numerorum ordines diuidere (ſi de ſummis primo loquamur) aut è
                    <lb/>
                  ſumma ſuperſluum ordinum colligere, & videre an idemmet ſuperfluum ex eadem
                    <lb/>
                  ſumma emanet, attamen cum modus, qui in hoc adhiberi poteſt in nouenario
                    <reg norm="quam" type="context">quã</reg>
                    <lb/>
                  in ſeptenario velocior ſit, & ob id probationem nouenarij ſeligunt potius quam
                    <lb/>
                  ſeptenarij.</s>
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