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

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          <p style="it">
            <s xml:id="echoid-s4028" xml:space="preserve">
              <pb o="108" file="120" n="120" rhead=""/>
            qui arcubus quadrantis vno Minuto ſeſe ordine ſuperantibus reſpondent, in parti-
              <lb/>
              <note position="left" xlink:label="note-120-01" xlink:href="note-120-01a" xml:space="preserve">accuratio
                <lb/>
              tem, quo
                <lb/>
              maior fue-
                <lb/>
              eit ſinus to
                <lb/>
              tus.</note>
            bus sinus totius in partes _10000000_ diuisi, initio facto ab arcu 1. </s>
            <s xml:id="echoid-s4029" xml:space="preserve">Minuti: </s>
            <s xml:id="echoid-s4030" xml:space="preserve">quam nos
              <lb/>
            ſumma cura, ac diligentia exam inauimus, & </s>
            <s xml:id="echoid-s4031" xml:space="preserve">in quibuſdam locis correximus; </s>
            <s xml:id="echoid-s4032" xml:space="preserve">quo-
              <lb/>
            niam propter typographorum incuriam mendis omnino non carebat. </s>
            <s xml:id="echoid-s4033" xml:space="preserve">Hanc tabulam
              <lb/>
            emendatam infra ſubijciemus, si prius demonſtrationes ex Ioanne Regiomontano po-
              <lb/>
            tißimum decerpt as exponamus, qu bus omnium arcuum sinus numeris exprimi poßint
              <lb/>
            in partibus sinus totius in quotuis partes diſtributi. </s>
            <s xml:id="echoid-s4034" xml:space="preserve">Poſt tabulæ vero vſumſubijcie
              <lb/>
            mus quoque Ptolemæi & </s>
            <s xml:id="echoid-s4035" xml:space="preserve">aliorum demonſtrationes, quibus omnium arcuum chordæ
              <lb/>
            numeris exprimantur, ex quibus rurſus facili negotio tabula sinuũ conſtrui poteſt.</s>
            <s xml:id="echoid-s4036" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4037" xml:space="preserve">_ATQVE_ in primis, si in plano aliquo Quadrans tantæ magnitudinis conſtrue-
              <lb/>
            retur, vt eius arcus commode in _90._ </s>
            <s xml:id="echoid-s4038" xml:space="preserve">gradus, & </s>
            <s xml:id="echoid-s4039" xml:space="preserve">singuli gradus in _60._ </s>
            <s xml:id="echoid-s4040" xml:space="preserve">Minuta; </s>
            <s xml:id="echoid-s4041" xml:space="preserve">item-
              <lb/>
            que vtraque eius ſemidiameter, siue sinus totus, in _10000000._ </s>
            <s xml:id="echoid-s4042" xml:space="preserve">partes æquales, vel
              <lb/>
            etiam in plures, pauciores ve diuidi poſſet, facili negotio sine vlla ſupputationis mole-
              <lb/>
            ſtia, aut labore, omniũ ſinuũ magnitudines cognoſcerẽtur, si ex singulis arcus Minu-
              <lb/>
            tis rectæ ad vtramque ſemidiametrũ perpendiculares ducerentur. </s>
            <s xml:id="echoid-s4043" xml:space="preserve">Vt in quadrãte hoc
              <lb/>
            _ABC,_ si arcus _
              <emph style="sc">B</emph>
            C,_ in Gradus, ac Minuta ſecetur; </s>
            <s xml:id="echoid-s4044" xml:space="preserve">(Nos ob ſpatij anguſtias eum in
              <lb/>
              <note position="left" xlink:label="note-120-02" xlink:href="note-120-02a" xml:space="preserve">Quo pacto
                <lb/>
              omnes ſi-
                <lb/>
              nus poſsint
                <lb/>
              cognoſci in
                <lb/>
              maximo a-
                <lb/>
              liquo qua-
                <lb/>
              drante, ſine
                <lb/>
              vllo ſuppu-
                <lb/>
              tationis la-
                <lb/>
              bore, aut
                <lb/>
              moleſtia.</note>
              <figure xlink:label="fig-120-01" xlink:href="fig-120-01a" number="117">
                <image file="120-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/120-01"/>
              </figure>
            nouem partes ſecuimus, vt sin
              <lb/>
            gulæ denos complectãtur gra
              <lb/>
            dus.) </s>
            <s xml:id="echoid-s4045" xml:space="preserve">Item vtraque ſemidia-
              <lb/>
            meter in _10000000._ </s>
            <s xml:id="echoid-s4046" xml:space="preserve">particu-
              <lb/>
            las, vel in plures, pauciores ve
              <lb/>
            diſtribuatur, atque ad vtram
              <lb/>
            que ſemidiametrum perpendi-
              <lb/>
            culares ducantur: </s>
            <s xml:id="echoid-s4047" xml:space="preserve">erunt per-
              <lb/>
            pendiculares ad ſemidiame-
              <lb/>
            trum _AB,_ ductæ, sinus recti
              <lb/>
            arcuum quadrantis à puncto
              <lb/>
            B, incipientium; </s>
            <s xml:id="echoid-s4048" xml:space="preserve">quibus æqua
              <lb/>
              <note position="left" xlink:label="note-120-03" xlink:href="note-120-03a" xml:space="preserve">34. primi.</note>
            les ſunt portiones ſemidiame
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            tri _AC,_ inter punctum _A,_ & </s>
            <s xml:id="echoid-s4049" xml:space="preserve">
              <lb/>
            perpẽdiculares ad ſemidiame
              <lb/>
            trum _AC,_ ductas. </s>
            <s xml:id="echoid-s4050" xml:space="preserve">Quot ergo
              <lb/>
            particulas cõtinebunt hæ por
              <lb/>
            tiones ex illis _10000000._ </s>
            <s xml:id="echoid-s4051" xml:space="preserve">tot
              <lb/>
            particularũ erunt sinus recti
              <lb/>
            arcũ quadrantis. </s>
            <s xml:id="echoid-s4052" xml:space="preserve">Eodem modo
              <lb/>
            tam sinus complementorum arcuum eorundem, quàm sinus versi cognoſcentur. </s>
            <s xml:id="echoid-s4053" xml:space="preserve">Per-
              <lb/>
            pendiculares enim ad ſemidiametrum _AC,_ demiſſæ ſunt sinus complementorum, qui-
              <lb/>
            bus æquales ſunt portiones ſemidiametri _AB,_ inter punctum _A,_ & </s>
            <s xml:id="echoid-s4054" xml:space="preserve">perpendiculares
              <lb/>
              <note position="left" xlink:label="note-120-04" xlink:href="note-120-04a" xml:space="preserve">34. primi.</note>
            ad ſemidiametrum _AB,_ ductas: </s>
            <s xml:id="echoid-s4055" xml:space="preserve">Portiones vero eiuſdem ſemidiam etri _AB,_ inter pun-
              <lb/>
            ctum _B,_ & </s>
            <s xml:id="echoid-s4056" xml:space="preserve">dictas perpendiculares ſunt sinus versi eorundem arcuum à puncto _B,_
              <lb/>
            incipientium. </s>
            <s xml:id="echoid-s4057" xml:space="preserve">Sed quoniam fieri non poteſt, vt Quadrans tantæ magnitudinis repe-
              <lb/>
            riatur, qui commode tot diuisiones recipiat, inueſtigabimus sinuum magnitudines
              <lb/>
            per demonſtr ationes Geometricas, posito sinu to to quotcunq; </s>
            <s xml:id="echoid-s4058" xml:space="preserve">particularum, ſequen-
              <lb/>
            tibus propoſitionibus. </s>
            <s xml:id="echoid-s4059" xml:space="preserve">Satis autem erit, ſinus rectos omnium arcuum inquiramus: </s>
            <s xml:id="echoid-s4060" xml:space="preserve">ex
              <lb/>
            his enim cognitis & </s>
            <s xml:id="echoid-s4061" xml:space="preserve">ſinus complementorum, & </s>
            <s xml:id="echoid-s4062" xml:space="preserve">verſi eorundem arcuum pateſient,
              <lb/>
            @@ in vſutabulæ Sinuum exponemus.</s>
            <s xml:id="echoid-s4063" xml:space="preserve"/>
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