Apian, Petrus, Instrvmentvm Sinvvm, sev primi mobilis
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        <div xml:id="echoid-div9" type="section" level="1" n="7">
          <pb file="0026" n="26" rhead="GENVINVS VSVS"/>
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        <div xml:id="echoid-div11" type="section" level="1" n="8">
          <head xml:id="echoid-head10" xml:space="preserve">Sequuntur nunc canones uſum ſiue ingreſſum iſtarum
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          tabularum lucidiſsime declarantes.</head>
          <p>
            <s xml:id="echoid-s598" xml:space="preserve">QVando arcus propoſiti ſinum ex tabulis ſupputare deſideras, primo conſidera an
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            maior aut minor quadrãte exiſtat. </s>
            <s xml:id="echoid-s599" xml:space="preserve">fit interdum ut arcus quarta circuli parte ſit mi
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              <note position="left" xlink:label="note-0026-01" xlink:href="note-0026-01a" xml:space="preserve">
                <emph style="it">Cuiuslibet</emph>
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                <emph style="it">arcus qud-</emph>
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                <emph style="it">drãte mino</emph>
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                <emph style="it">ris ſinũ ut</emph>
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                <emph style="it">inuenias.</emph>
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            nor, aliquando maior, & </s>
            <s xml:id="echoid-s600" xml:space="preserve">tamen ſemicirculo minor, hoc eſt gra. </s>
            <s xml:id="echoid-s601" xml:space="preserve">180. </s>
            <s xml:id="echoid-s602" xml:space="preserve">nonnunquam etiam
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            maior illo, & </s>
            <s xml:id="echoid-s603" xml:space="preserve">adhuc minor gradibus 270. </s>
            <s xml:id="echoid-s604" xml:space="preserve">quæ tres quartæ ſunt circuli unius, quibus etiã
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            arcus dari poteſt maior, & </s>
            <s xml:id="echoid-s605" xml:space="preserve">tamẽ toto circulo minor. </s>
            <s xml:id="echoid-s606" xml:space="preserve">Quicquid aũt ſit, facile huiuſmo
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            di arcus ſinum inuenire poteris in hunc modum. </s>
            <s xml:id="echoid-s607" xml:space="preserve">Si arcus 90. </s>
            <s xml:id="echoid-s608" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s609" xml:space="preserve">fuerit minor, tabulam
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              <note position="left" xlink:label="note-0026-02" xlink:href="note-0026-02a" xml:space="preserve">
                <emph style="it">Propoſiti</emph>
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                <emph style="it">arcus qud-</emph>
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                <emph style="it">drãte maio-</emph>
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                <emph style="it">ris, nec non</emph>
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                <emph style="it">ſemiãr culo</emph>
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                <emph style="it">minoris</emph>
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                <emph style="it">quõ ſinus</emph>
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                <emph style="it">quærẽdg ſit</emph>
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                <emph style="it">Vbi ſing nu</emph>
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                <emph style="it">merũ ſupat</emph>
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                <emph style="it">100000. ue</emph>
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                <emph style="it">luti arcg eig</emph>
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                <emph style="it">ſit inuenicn</emph>
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                <emph style="it">dus.</emph>
              </note>
            præſcriptam ingredere, in eius capite quære gradus cum minutisiuxta lineam primam
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            manus ſiniſtræ deſcendẽdo, & </s>
            <s xml:id="echoid-s610" xml:space="preserve">inuenies in angulo communi ſinũ arcus propoſiti. </s>
            <s xml:id="echoid-s611" xml:space="preserve">Sin
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            autẽ arcus gra. </s>
            <s xml:id="echoid-s612" xml:space="preserve">90. </s>
            <s xml:id="echoid-s613" xml:space="preserve">maior fuerit, & </s>
            <s xml:id="echoid-s614" xml:space="preserve">tamen adhuc minor gradibus 180. </s>
            <s xml:id="echoid-s615" xml:space="preserve">ſubtrahe hinc 90.
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            </s>
            <s xml:id="echoid-s616" xml:space="preserve">& </s>
            <s xml:id="echoid-s617" xml:space="preserve">cum reſiduo tabulam ingreſſus, inuenies etiã ſinum arcus quem quærebas. </s>
            <s xml:id="echoid-s618" xml:space="preserve">Si porrò
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            arcus maior fuerit gradibus 180. </s>
            <s xml:id="echoid-s619" xml:space="preserve">& </s>
            <s xml:id="echoid-s620" xml:space="preserve">tamen 270. </s>
            <s xml:id="echoid-s621" xml:space="preserve">minor, ſubtractis inde 180. </s>
            <s xml:id="echoid-s622" xml:space="preserve">ingredere
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            tabulam cũ reſiduo, & </s>
            <s xml:id="echoid-s623" xml:space="preserve">inuenies quod optas. </s>
            <s xml:id="echoid-s624" xml:space="preserve">Similiter operare quum arcus maior eſt
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            gra. </s>
            <s xml:id="echoid-s625" xml:space="preserve">270. </s>
            <s xml:id="echoid-s626" xml:space="preserve">& </s>
            <s xml:id="echoid-s627" xml:space="preserve">tamen minor 360. </s>
            <s xml:id="echoid-s628" xml:space="preserve">Quando & </s>
            <s xml:id="echoid-s629" xml:space="preserve">hoc fit nõ raro, ut dati ſinus recti arcũ ſcire
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            cupias, tunc ita  ſinum illum quære in tabulis præſcriptis in area aliqua, ſi non præciſe
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            attamen quàm potes rectiſsime proximum illum accipiendo, qui nec magnus, nec nimi
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            um ſit paruus, & </s>
            <s xml:id="echoid-s630" xml:space="preserve">tunc ab iſto digitum directe ad ſiniſtram educendo, inuenies in prima
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            linea numeros minutorum, & </s>
            <s xml:id="echoid-s631" xml:space="preserve">ſi directe ſurſum ab eo ſinu tendas, inuenies in capite ta-
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            bulæ etiam gradus, quos ubi minutis coniunxeris, habebis arcũ quæſitum. </s>
            <s xml:id="echoid-s632" xml:space="preserve">Quid ſi au
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            tem tot fuerint ſinus ij, ut in tabula inuenire nequeant? </s>
            <s xml:id="echoid-s633" xml:space="preserve">tunc ſanè ſubtrahe ab eo ſinu
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            100000. </s>
            <s xml:id="echoid-s634" xml:space="preserve">& </s>
            <s xml:id="echoid-s635" xml:space="preserve">cum reſiduo quære arcum ut ſupra. </s>
            <s xml:id="echoid-s636" xml:space="preserve">Quod ſi arcus propoſiti ſinũ uerſum
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              <note position="left" xlink:label="note-0026-03" xlink:href="note-0026-03a" xml:space="preserve">
                <emph style="it">Vt inuenia</emph>
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                <emph style="it">tur ſing uer</emph>
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                <emph style="it">ſus ꝓ ppoſiti</emph>
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                <emph style="it">arcus.</emph>
              </note>
            inueſtigare uolueris, & </s>
            <s xml:id="echoid-s637" xml:space="preserve">hic minor fuerit 90. </s>
            <s xml:id="echoid-s638" xml:space="preserve">cuius reſidui ſinum ſtatim rectum inquire, ip
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            ſum´ à ſinu toto ubi ſubtraxeris, remanebit ſinus uerſus quem quæſiſti. </s>
            <s xml:id="echoid-s639" xml:space="preserve">Sin aũt arcus 90
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            maior fuerit, & </s>
            <s xml:id="echoid-s640" xml:space="preserve">minor 180. </s>
            <s xml:id="echoid-s641" xml:space="preserve">ſubtrahe inde 90. </s>
            <s xml:id="echoid-s642" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s643" xml:space="preserve">& </s>
            <s xml:id="echoid-s644" xml:space="preserve">cum reſiduo quære ſinũ rectũ, eũ ad-
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            de ad 100000. </s>
            <s xml:id="echoid-s645" xml:space="preserve">& </s>
            <s xml:id="echoid-s646" xml:space="preserve">habebis ſinũ uerſum arcus ꝓpoſiti. </s>
            <s xml:id="echoid-s647" xml:space="preserve">Siuero habueris ſinũ uerſum, & </s>
            <s xml:id="echoid-s648" xml:space="preserve">uis
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              <note position="left" xlink:label="note-0026-04" xlink:href="note-0026-04a" xml:space="preserve">
                <emph style="it">Habito ſinu</emph>
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                <emph style="it">uerſu quõ</emph>
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                <emph style="it">arcus eiuſdê</emph>
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                <emph style="it">agnoſ@tur.</emph>
              </note>
            indagare arcum illius, conſidera ſi minor fuerit 100000. </s>
            <s xml:id="echoid-s649" xml:space="preserve">ſubtrahe eum â 100000. </s>
            <s xml:id="echoid-s650" xml:space="preserve">cũ eius
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            reſiduiſinu quærere arcũ illum, ſi ſubtraxeris à 90. </s>
            <s xml:id="echoid-s651" xml:space="preserve">remanebit arcus optatus. </s>
            <s xml:id="echoid-s652" xml:space="preserve">Sin uero
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            fuerit maior ſinu perſecto, inquiſiturus ſic quo arcum, ſubtrahe de ſinu uerſo 100000.
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            </s>
            <s xml:id="echoid-s653" xml:space="preserve">eius reſidui quære arcum non ſecus ac ſi ſinus rectus eſſet. </s>
            <s xml:id="echoid-s654" xml:space="preserve">arcum illum adde ad grad. </s>
            <s xml:id="echoid-s655" xml:space="preserve">90. </s>
            <s xml:id="echoid-s656" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0026-05" xlink:href="note-0026-05a" xml:space="preserve">
                <emph style="it">Chordã ꝓ-</emph>
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                <emph style="it">poſiti arcus</emph>
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                <emph style="it">ueluti de-</emph>
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                <emph style="it">prehendas.</emph>
              </note>
            & </s>
            <s xml:id="echoid-s657" xml:space="preserve">tunc habebis arcũ ſinus quẽ quærebas. </s>
            <s xml:id="echoid-s658" xml:space="preserve">Si uero arcus propoſiti chordam inuenire
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            uolueris, eodem modo operare, ut inquirendo ſinum, niſi quòd arcum illum medium tan
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            tum accipere debes, eius arcus inuentus & </s>
            <s xml:id="echoid-s659" xml:space="preserve">duplicatus ſinus, chordam monſtrat quæſitã.
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            </s>
            <s xml:id="echoid-s660" xml:space="preserve">ſiquidẽ cũ Sinus, quod principio cõmemorauimus, nihil aliud eſt quàm arcus dati chor
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              <note position="left" xlink:label="note-0026-06" xlink:href="note-0026-06a" xml:space="preserve">
                <emph style="it">Ad propo-</emph>
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                <emph style="it">ſitam chor-</emph>
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                <emph style="it">dam arcum</emph>
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                <emph style="it">ut ſdas</emph>
              .</note>
            da media. </s>
            <s xml:id="echoid-s661" xml:space="preserve">Chordæ uero propoſitæ arcũ inuenies facillime, modo chordam mediaris,
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            & </s>
            <s xml:id="echoid-s662" xml:space="preserve">medij illius arcum quæſieris ex præmiſsis, arcum quo iſtum dehinc duplicaris, tunc
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            enim ſinum habebis quæſitum.</s>
            <s xml:id="echoid-s663" xml:space="preserve"/>
          </p>
          <figure number="7">
            <image file="0026-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0026-01"/>
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