Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres

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          <pb o="107" file="119" n="119" rhead=""/>
          <p style="it">
            <s xml:id="echoid-s3960" xml:space="preserve">_QVONIAM_ vero Sinus totus (hoc eſt, ſemidiameter cuiusuis circuli) intelligi-
              <lb/>
            tur ab Aſtronomis diuiſus in aliquot partes æquales, vt ratione barum partium om-
              <lb/>
              <note position="right" xlink:label="note-119-01" xlink:href="note-119-01a" xml:space="preserve">Omnes ſi-
                <lb/>
              nus expri-
                <lb/>
              muntur in
                <lb/>
              partibus,
                <lb/>
              in quas ſi
                <lb/>
              nus totus
                <lb/>
              concipitut
                <lb/>
              eſſe diui-
                <lb/>
              ſus.</note>
            nes alios ſinus metiantur, proportiones ve omnium ſinuum ad ſinum totum, ſiue ad ſe-
              <lb/>
            midiametrum in numeris exprimant; </s>
            <s xml:id="echoid-s3961" xml:space="preserve">ex plicãdum paucis erit, in quot partes ſemidia-
              <lb/>
            metrum diſtribuerint: </s>
            <s xml:id="echoid-s3962" xml:space="preserve">Neque enim omnes eodem modo eam ſunt partiti. </s>
            <s xml:id="echoid-s3963" xml:space="preserve">Ptolemæus
              <lb/>
            namque ſemidiametrum ſecatin _60._ </s>
            <s xml:id="echoid-s3964" xml:space="preserve">partes æquales, totam vero diametrum in 120.
              <lb/>
            </s>
            <s xml:id="echoid-s3965" xml:space="preserve">Quamlibet deinde partem concipit diuiſam eſſe in _60._ </s>
            <s xml:id="echoid-s3966" xml:space="preserve">Minuta, & </s>
            <s xml:id="echoid-s3967" xml:space="preserve">quoduis Minutum
              <lb/>
            in 60. </s>
            <s xml:id="echoid-s3968" xml:space="preserve">Secunda. </s>
            <s xml:id="echoid-s3969" xml:space="preserve">Hanc diuiſionem omnes fermè antiqui, & </s>
            <s xml:id="echoid-s3970" xml:space="preserve">nonnulli ex recentioribus,
              <lb/>
            inter quoseſt Orontius, ſecuti ſunt. </s>
            <s xml:id="echoid-s3971" xml:space="preserve">Supputauit autem Ptolemæus lib. </s>
            <s xml:id="echoid-s3972" xml:space="preserve">I. </s>
            <s xml:id="echoid-s3973" xml:space="preserve">Almageſti ta-
              <lb/>
              <note position="right" xlink:label="note-119-02" xlink:href="note-119-02a" xml:space="preserve">Semidiame
                <lb/>
              ter circult
                <lb/>
              in quot par
                <lb/>
              tes ſecetur
                <lb/>
              à Ptolemęo
                <lb/>
              & Arzahe-
                <lb/>
              le.</note>
            bulam omnium chordarum, quæarcubus ſemicirculi dimidiato gradu ſeſe ordine ſu-
              <lb/>
            perantibus, initio facto ab arcu _30._ </s>
            <s xml:id="echoid-s3974" xml:space="preserve">Minutorum, reſpondẽt, in partibus, quarum 120.
              <lb/>
            </s>
            <s xml:id="echoid-s3975" xml:space="preserve">tota diameter continet. </s>
            <s xml:id="echoid-s3976" xml:space="preserve">Orontius vero tabulam condidit omnium ſinuum, qui arcu-
              <lb/>
            bus quadrantis vno Minuto ſeſe ordine ſuperantibus, initio facto ab arcu I. </s>
            <s xml:id="echoid-s3977" xml:space="preserve">Minuti,
              <lb/>
            reſpondent, in partibus, quarum _60._ </s>
            <s xml:id="echoid-s3978" xml:space="preserve">ſemidiameter, ſeu ſinus totus continet. </s>
            <s xml:id="echoid-s3979" xml:space="preserve">Ar Zahel
              <lb/>
            vero Arabs conſtituit ſemidiametrum partium 150. </s>
            <s xml:id="echoid-s3980" xml:space="preserve">ac proinde totam diametrum
              <lb/>
            partium 300. </s>
            <s xml:id="echoid-s3981" xml:space="preserve">quas quidem partes rurſus diſtribuit in Minuta, & </s>
            <s xml:id="echoid-s3982" xml:space="preserve">Secunda, vt Pto-
              <lb/>
            lemæus. </s>
            <s xml:id="echoid-s3983" xml:space="preserve">Sed vtrouis modo ſemidiameter, siue diameter diuidatur, permoleſtum eſt,
              <lb/>
            alios omnes ſinus ſiue chordas in eiusmodi partibus inueſtigare, cum ſemper multi-
              <lb/>
            plicatio, diuiſio, extractioq́; </s>
            <s xml:id="echoid-s3984" xml:space="preserve">radicum per fractiones Aſtronomicas in ſtituenda ſit; </s>
            <s xml:id="echoid-s3985" xml:space="preserve">Vel
              <lb/>
            certe Partes in Minuta, ac Secunda conuertendæ, & </s>
            <s xml:id="echoid-s3986" xml:space="preserve">contra, Minuta ac Secunda in
              <lb/>
            Partes: </s>
            <s xml:id="echoid-s3987" xml:space="preserve">quæres valde laborioſa eſt non ſolum parum exercitatis in Arithmeticis, ve-
              <lb/>
            rum etiam peritißimis.</s>
            <s xml:id="echoid-s3988" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3989" xml:space="preserve">_QVAMOBREM_ alij Aſtronomi, inter quos eſt Georgius Purbachius, Ioan-
              <lb/>
            nes Regiomontanus. </s>
            <s xml:id="echoid-s3990" xml:space="preserve">Petrus Appianus, ſemidiametrum, hoc eſt, sinum totum, in multo
              <lb/>
              <note position="right" xlink:label="note-119-03" xlink:href="note-119-03a" xml:space="preserve">Cõmodiot
                <lb/>
              eſt diuiſio
                <lb/>
              ſemidiame
                <lb/>
              tr i, vel ſin
                <lb/>
              totius in
                <lb/>
              particulas
                <lb/>
              10000000.
                <lb/>
              vel _100000._
                <lb/>
              quàm in
                <lb/>
              60.</note>
            plures particulas æquales partiti ſunt, vtpote in partes _10000000._ </s>
            <s xml:id="echoid-s3991" xml:space="preserve">vel _100000._
              <lb/>
            </s>
            <s xml:id="echoid-s3992" xml:space="preserve">Ita enim opus non erit partes has in Minuta, ac Secunda diſtribuere; </s>
            <s xml:id="echoid-s3993" xml:space="preserve">cum vna ha-
              <lb/>
            rum partium sit vel multo minor, quàm vnum Secũdum ſemidiametri in partes _60._ </s>
            <s xml:id="echoid-s3994" xml:space="preserve">
              <lb/>
            ſecundum Ptolemæum diuiſæ, vel certe non multo maior. </s>
            <s xml:id="echoid-s3995" xml:space="preserve">Nam vnum Secundum eſt
              <lb/>
            {1/216000} totius ſemidiametri diuiſæ in 60. </s>
            <s xml:id="echoid-s3996" xml:space="preserve">partes, cum 60. </s>
            <s xml:id="echoid-s3997" xml:space="preserve">partes contineant
              <lb/>
            _216000._ </s>
            <s xml:id="echoid-s3998" xml:space="preserve">Secunda: </s>
            <s xml:id="echoid-s3999" xml:space="preserve">At vna particula ſemidiametridiuiſæ in partes _10000000._ </s>
            <s xml:id="echoid-s4000" xml:space="preserve">vel
              <lb/>
            _100000._ </s>
            <s xml:id="echoid-s4001" xml:space="preserve">eſt {1/10000000}. </s>
            <s xml:id="echoid-s4002" xml:space="preserve">vel {1/100000}. </s>
            <s xml:id="echoid-s4003" xml:space="preserve">totius ſemidiametri. </s>
            <s xml:id="echoid-s4004" xml:space="preserve">Con
              <lb/>
            ſtat autẽ minutiã hãc {1/10000000}. </s>
            <s xml:id="echoid-s4005" xml:space="preserve">eſſe multo minorẽilla {1/216000}. </s>
            <s xml:id="echoid-s4006" xml:space="preserve">
              <lb/>
            hanc vero {1/100000}. </s>
            <s xml:id="echoid-s4007" xml:space="preserve">non eſſe multo maiorẽ illa eadem {1/216000}. </s>
            <s xml:id="echoid-s4008" xml:space="preserve">Ita-
              <lb/>
            que etiã si in sinu aliquo negligatur interdum vna ferme particula ex _10000000._ </s>
            <s xml:id="echoid-s4009" xml:space="preserve">
              <lb/>
            particulis sinus totius, multò tamen minor error committetur, quàm si negligatur
              <lb/>
            vnum ferè ſecundum ex _216000._ </s>
            <s xml:id="echoid-s4010" xml:space="preserve">Secundis, in quæ sinus totus intelligitur eſſe diui-
              <lb/>
            ſus: </s>
            <s xml:id="echoid-s4011" xml:space="preserve">Si vero negligatur vna ferè particula ex _100000._ </s>
            <s xml:id="echoid-s4012" xml:space="preserve">particulis sinus totius, non
              <lb/>
            multò maior error cõmittetur, quàm ſinegligatur vnum fere ſecundum ex _216000._ </s>
            <s xml:id="echoid-s4013" xml:space="preserve">
              <lb/>
            ſecundis, in quæ sinus totus diſtribuitur.</s>
            <s xml:id="echoid-s4014" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Quantue
            <lb/>
          ſit ſinus to-
            <lb/>
          tus ſecun-
            <lb/>
          dum com-
            <lb/>
          munem v-
            <lb/>
          ſum, & quã
            <lb/>
          tus ab au-
            <lb/>
          ctore ſta -
            <lb/>
          tuatur.</note>
          <p style="it">
            <s xml:id="echoid-s4015" xml:space="preserve">_SVNT_ etiam, qui diſtribuant sinum totum in partes _6000000._ </s>
            <s xml:id="echoid-s4016" xml:space="preserve">vel _60000._
              <lb/>
            </s>
            <s xml:id="echoid-s4017" xml:space="preserve">extantq́ tabulæ sinuũ à Ioan. </s>
            <s xml:id="echoid-s4018" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s4019" xml:space="preserve">compositæ, in quibus sinus totus tot particu-
              <lb/>
            las ponitur continere: </s>
            <s xml:id="echoid-s4020" xml:space="preserve">ſed magis in vſu eſt apud Aſtronomos diuisio sinus totius in
              <lb/>
            particulas _10000000._ </s>
            <s xml:id="echoid-s4021" xml:space="preserve">vel _100000._ </s>
            <s xml:id="echoid-s4022" xml:space="preserve">Immo communis fere vſus omnium obtinuit, vt
              <lb/>
            in ſupputationibus, quæ ex sinubus depromuntur, sinus totus ſtatuatur particula-
              <lb/>
            rum _100000._ </s>
            <s xml:id="echoid-s4023" xml:space="preserve">qualem & </s>
            <s xml:id="echoid-s4024" xml:space="preserve">nos tam in ſphæra, quàm in Gnomonica alijsque operibus
              <lb/>
            conſtituimus: </s>
            <s xml:id="echoid-s4025" xml:space="preserve">quamuis, quo maior fuerit sinus totus, eo etiam accuratior ſupputatio
              <lb/>
              <note position="right" xlink:label="note-119-05" xlink:href="note-119-05a" xml:space="preserve">Item eo fie
                <lb/>
              ri calculũ</note>
            atque calculus reddatur. </s>
            <s xml:id="echoid-s4026" xml:space="preserve">Conſtruxit porrò Ioan. </s>
            <s xml:id="echoid-s4027" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s4028" xml:space="preserve">tabulam omnium </s>
          </p>
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