Apian, Petrus, Instrvmentvm Sinvvm, sev primi mobilis

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    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div9" type="section" level="1" n="7">
          <pb file="0015" n="15" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
          <p>
            <s xml:id="echoid-s467" xml:space="preserve">SEd ut nõnihil degenerali huius inſtrumẽti uſu dicamus, retulerit plurimũ, imò neceſ
              <lb/>
            ſariũ fuerit p̃mittere quædã, puta, ꝗd ſit Diameter, quid Chorda, quid etiã Sinus rect 9
              <lb/>
              <note position="right" xlink:label="note-0015-01" xlink:href="note-0015-01a" xml:space="preserve">
                <emph style="it">Diameter</emph>
                <lb/>
                <emph style="it">quid.</emph>
              </note>
            & </s>
            <s xml:id="echoid-s468" xml:space="preserve">quid ſituerſus. </s>
            <s xml:id="echoid-s469" xml:space="preserve">?</s>
            <s xml:id="echoid-s470" xml:space="preserve">?Diameter ſiue dimetiẽs circuli, eſt linea recta ꝑ eius umbilicum
              <lb/>
            trãſiens, illum´ in duo æqualia diuidens. </s>
            <s xml:id="echoid-s471" xml:space="preserve">?</s>
            <s xml:id="echoid-s472" xml:space="preserve">?Arcus eſt cuiuslibet circuli ſeu periferiæ
              <lb/>
              <note position="right" xlink:label="note-0015-02" xlink:href="note-0015-02a" xml:space="preserve">
                <emph style="it">Arcus.</emph>
              </note>
            portio. </s>
            <s xml:id="echoid-s473" xml:space="preserve">?</s>
            <s xml:id="echoid-s474" xml:space="preserve">?Chorda eſt linea recta ſecãs circulũ in duas portiones inæquales. </s>
            <s xml:id="echoid-s475" xml:space="preserve">?</s>
            <s xml:id="echoid-s476" xml:space="preserve">?Sinus
              <lb/>
              <note position="right" xlink:label="note-0015-03" xlink:href="note-0015-03a" xml:space="preserve">
                <emph style="it">Chorda.</emph>
              </note>
            eſt linea recta, diametro circuli lõgitudine uel potẽtia cõmenſurabilis. </s>
            <s xml:id="echoid-s477" xml:space="preserve">?</s>
            <s xml:id="echoid-s478" xml:space="preserve">?Sinus totus
              <lb/>
              <note position="right" xlink:label="note-0015-04" xlink:href="note-0015-04a" xml:space="preserve">
                <emph style="it">Sinus.</emph>
              </note>
            ſiue ꝑfectus eſt circuli ſemidiameter in aliquas ꝑtes diuiſa. </s>
            <s xml:id="echoid-s479" xml:space="preserve">?</s>
            <s xml:id="echoid-s480" xml:space="preserve">?Sinus diuiditur in Sinum
              <lb/>
              <note position="right" xlink:label="note-0015-05" xlink:href="note-0015-05a" xml:space="preserve">
                <emph style="it">Sinus totus</emph>
                <lb/>
                <emph style="it">ſiue perfe-</emph>
                <lb/>
                <emph style="it">ctus quid.</emph>
              </note>
            rectũ ac uerſum. </s>
            <s xml:id="echoid-s481" xml:space="preserve">?</s>
            <s xml:id="echoid-s482" xml:space="preserve">?Sinus rectus ſubdiuidit̃ in primũ & </s>
            <s xml:id="echoid-s483" xml:space="preserve">ſecũdũ. </s>
            <s xml:id="echoid-s484" xml:space="preserve">?</s>
            <s xml:id="echoid-s485" xml:space="preserve">?Sinus rectus pri-
              <lb/>
            mus eſt medietas chordæ arcus dupli ad arcũ, cuius eſt ſinus, ſiue dimidiũ chordæ reſpe-
              <lb/>
            ctu totius arcus. </s>
            <s xml:id="echoid-s486" xml:space="preserve">?</s>
            <s xml:id="echoid-s487" xml:space="preserve">?Sinus uerſus eſt portio diametri à ſinu recto ad periferiã cõprehen
              <lb/>
              <note position="right" xlink:label="note-0015-06" xlink:href="note-0015-06a" xml:space="preserve">
                <emph style="it">Sinus rect
                  <emph style="sub">9</emph>
                </emph>
                <lb/>
                <emph style="it">dupliater</emph>
                <lb/>
                <emph style="it">diuiditur.</emph>
              </note>
            ſi, utpote ſagitta arcus. </s>
            <s xml:id="echoid-s488" xml:space="preserve">?</s>
            <s xml:id="echoid-s489" xml:space="preserve">?Sinus rectus ſecũdus eſt reſiduũ cuiuslibet arc9 ſubtracti ex
              <lb/>
            90. </s>
            <s xml:id="echoid-s490" xml:space="preserve">ſiue arcus ꝗ reſtat uſ ad cõplementũ quartæ circuli, is ſemper eſt æqualis ꝑti dime
              <lb/>
            tientis, quæ à cẽtro circuli ad ſinũ rectũ primũ terminatur. </s>
            <s xml:id="echoid-s491" xml:space="preserve">?</s>
            <s xml:id="echoid-s492" xml:space="preserve">?Sector circuli eſt figura
              <lb/>
              <note position="right" xlink:label="note-0015-07" xlink:href="note-0015-07a" xml:space="preserve">
                <emph style="it">Sinus uerſ
                  <emph style="sub">9</emph>
                </emph>
                <lb/>
                <emph style="it">quid.</emph>
              </note>
            q̃ continetur à duabus lineis recte à centro ad circumferentiã ductis, necnon ab arcu qui
              <lb/>
              <note position="right" xlink:label="note-0015-08" xlink:href="note-0015-08a" xml:space="preserve">
                <emph style="it">Sinus rect
                  <emph style="sub">9</emph>
                </emph>
                <lb/>
                <emph style="it">ſecundus.</emph>
              </note>
            inter illos comprehẽditur. </s>
            <s xml:id="echoid-s493" xml:space="preserve">Verum hic quo teiſtud celare nolo, ꝙ inſtrumentũ hoc
              <lb/>
            oportet eſſe ſatis magnũ, omnino enim q̊ amplius fuerit, eò certius per illud operari pote
              <lb/>
              <note position="right" xlink:label="note-0015-09" xlink:href="note-0015-09a" xml:space="preserve">
                <emph style="it">Sector cir-</emph>
                <lb/>
                <emph style="it">culi.</emph>
              </note>
            ris. </s>
            <s xml:id="echoid-s494" xml:space="preserve">Quamuis ſi uoles, poteris q̊cũ alio numero ad hoc uti, alijs tamẽ cõmodiores ſunt
              <lb/>
            numeri, qui unitatẽ habent cũ aliquot nullis 000 &</s>
            <s xml:id="echoid-s495" xml:space="preserve">c. </s>
            <s xml:id="echoid-s496" xml:space="preserve">quales ſunt 10. </s>
            <s xml:id="echoid-s497" xml:space="preserve">100. </s>
            <s xml:id="echoid-s498" xml:space="preserve">1000. </s>
            <s xml:id="echoid-s499" xml:space="preserve">10000.
              <lb/>
            </s>
            <s xml:id="echoid-s500" xml:space="preserve">100000 &</s>
            <s xml:id="echoid-s501" xml:space="preserve">c. </s>
            <s xml:id="echoid-s502" xml:space="preserve">ſiquidẽ per iſtos operatio nõ paulo redditur facilior in multiplicando pari
              <lb/>
            ter & </s>
            <s xml:id="echoid-s503" xml:space="preserve">diuidẽdo. </s>
            <s xml:id="echoid-s504" xml:space="preserve">Diuiſa igitur linea A B in hũc modũ, porrò circinũ altero pede repone
              <lb/>
            in A, alte℞ uero extẽde ad ſingula illa pũcta, extẽdens hoc pacto circinũ uſ ad ſemicir
              <lb/>
            culũ A F B, omnibus deinde illis in eũ circulũ ſinuũ redactis, numeros adſcribe incipien
              <lb/>
            do in B ꝑ F uſ ad A, ea´ dicentur puncta ſinus uerſi, quamobrẽ & </s>
            <s xml:id="echoid-s505" xml:space="preserve">ſemicirculus ille cir
              <lb/>
            culus appellabitur ſinus uerſi. </s>
            <s xml:id="echoid-s506" xml:space="preserve">Deinceps adductis iam punctis iſtis à linea A B uſ in cir
              <lb/>
              <note position="right" xlink:label="note-0015-10" xlink:href="note-0015-10a" xml:space="preserve">
                <emph style="it">Vſus huius</emph>
                <lb/>
                <emph style="it">ſemiarculi.</emph>
              </note>
            culũ A F B, remoueri omnino aut deleri debet linea A B. </s>
            <s xml:id="echoid-s507" xml:space="preserve">uniuerſa aũt operatio illa ſatis
              <lb/>
            patebit ex ſubiecta figura. </s>
            <s xml:id="echoid-s508" xml:space="preserve">?</s>
            <s xml:id="echoid-s509" xml:space="preserve">?Seꝗtur ita uſus huius ſemicirculi in hunc modum: </s>
            <s xml:id="echoid-s510" xml:space="preserve">Si
              <lb/>
              <figure xlink:label="fig-0015-01" xlink:href="fig-0015-01a" number="4">
                <image file="0015-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0015-01"/>
              </figure>
            quando ſinũ uerſum ſcire cupis cuiuslibet arcus, filũ in centro A adfixũ
              <lb/>
            repone ſuper illũ gradum, & </s>
            <s xml:id="echoid-s511" xml:space="preserve">ſtatim ubicun filum iſtud ſemicirculum
              <lb/>
            AFB attingit, ibi uidebis numerũ unà cũ punctis ſinus illius uerſi. </s>
            <s xml:id="echoid-s512" xml:space="preserve">Vi
              <lb/>
            ciſsim cum antea habes puncta ſinus uerſi, & </s>
            <s xml:id="echoid-s513" xml:space="preserve">hinc deſideras arcum eius
              <lb/>
            cognoſcere, Age filum colloca ſuper illa puncta ſinus uerſi in ſemicir-
              <lb/>
            culo AFB, & </s>
            <s xml:id="echoid-s514" xml:space="preserve">eo quo filum tanget circulũ AC, ſcilicet limbum exteri
              <lb/>
            orem, ibi noris eſſe arcũ illorũ punctorũ ſinus uerſi propoſiti. </s>
            <s xml:id="echoid-s515" xml:space="preserve">Quod
              <lb/>
            ſi & </s>
            <s xml:id="echoid-s516" xml:space="preserve">alte℞ ſemicirculũ AFC cupis in pũcta ſinus recti diuidere, ſemper
              <lb/>
            tibi ꝓpone 10. </s>
            <s xml:id="echoid-s517" xml:space="preserve">aut 100 &</s>
            <s xml:id="echoid-s518" xml:space="preserve">c. </s>
            <s xml:id="echoid-s519" xml:space="preserve">ſecũdũ q̊d plura puncta habes in ſinu per-
              <lb/>
            fecto, hoc eſt in tota ſemidiametro AB. </s>
            <s xml:id="echoid-s520" xml:space="preserve">Vt ſi iã lineã AB in 100000.
              <lb/>
            </s>
            <s xml:id="echoid-s521" xml:space="preserve">partes habes diuiſam (nõ ꝙ totidẽ pũcta poſsis in ea conſignare, q̊rũ quodlibet ſignificet
              <lb/>
            unũ, ſed hoc ſatis eſt, ſi unũquod punctũ deſignet 100. </s>
            <s xml:id="echoid-s522" xml:space="preserve">aut 10. </s>
            <s xml:id="echoid-s523" xml:space="preserve">aut 5.) </s>
            <s xml:id="echoid-s524" xml:space="preserve">& </s>
            <s xml:id="echoid-s525" xml:space="preserve">porrò ſinũ re-
              <lb/>
            ctum 100000. </s>
            <s xml:id="echoid-s526" xml:space="preserve">punctorũ uis in circulũ AFC conſcribere, & </s>
            <s xml:id="echoid-s527" xml:space="preserve">cõprehendere in 100. </s>
            <s xml:id="echoid-s528" xml:space="preserve">pun-
              <lb/>
            ctis, ita, ꝙ unaquæ diuiſio cõprehendit 1000. </s>
            <s xml:id="echoid-s529" xml:space="preserve">tũc ſanè ſubtrahe 1000. </s>
            <s xml:id="echoid-s530" xml:space="preserve">à toto ſinu qui in
              <lb/>
            hoc exemplo eſſe debet 100000. </s>
            <s xml:id="echoid-s531" xml:space="preserve">& </s>
            <s xml:id="echoid-s532" xml:space="preserve">remanebũt 99000. </s>
            <s xml:id="echoid-s533" xml:space="preserve">qui ſinus erit uerſus, cuius ſi arcũ
              <lb/>
            ex ſupra dictis quæras, inuenies 88. </s>
            <s xml:id="echoid-s534" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s535" xml:space="preserve">26. </s>
            <s xml:id="echoid-s536" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s537" xml:space="preserve">ea ſubtrahe à 90. </s>
            <s xml:id="echoid-s538" xml:space="preserve">& </s>
            <s xml:id="echoid-s539" xml:space="preserve">reſidui erũt o. </s>
            <s xml:id="echoid-s540" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s541" xml:space="preserve">34. </s>
            <s xml:id="echoid-s542" xml:space="preserve">
              <lb/>
            minut. </s>
            <s xml:id="echoid-s543" xml:space="preserve">Iam uero filũ repone ſuper o. </s>
            <s xml:id="echoid-s544" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s545" xml:space="preserve">& </s>
            <s xml:id="echoid-s546" xml:space="preserve">34. </s>
            <s xml:id="echoid-s547" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s548" xml:space="preserve">numerãdo à Buerſus C, & </s>
            <s xml:id="echoid-s549" xml:space="preserve">in eũ locũ
              <lb/>
            quo tanget circulũ AFC, adponito punctũ 1000. </s>
            <s xml:id="echoid-s550" xml:space="preserve">puncta ſinus recti deſignans ex illis
              <lb/>
            100000. </s>
            <s xml:id="echoid-s551" xml:space="preserve">pũctis. </s>
            <s xml:id="echoid-s552" xml:space="preserve">Quod ſi aũt ſinus totus ſiue perfectus fuerit 10000. </s>
            <s xml:id="echoid-s553" xml:space="preserve">tũc punctũ illud ſi-
              <lb/>
            gnificat 100. </s>
            <s xml:id="echoid-s554" xml:space="preserve">rurſus ſi ſit ſinus perfectus 1000. </s>
            <s xml:id="echoid-s555" xml:space="preserve">punctũ hoc deſignabit 10. </s>
            <s xml:id="echoid-s556" xml:space="preserve">& </s>
            <s xml:id="echoid-s557" xml:space="preserve">ſi fuerit ſinus
              <lb/>
            perfectus 100. </s>
            <s xml:id="echoid-s558" xml:space="preserve">punctũ iſtud ſignabit unũ tantũ. </s>
            <s xml:id="echoid-s559" xml:space="preserve">At eo modo operaberis cum ſingulis
              <lb/>
            numeris prædictis, qñ locũ eius in ſemicirculo AFC quæris & </s>
            <s xml:id="echoid-s560" xml:space="preserve">ſcire deſideras. </s>
            <s xml:id="echoid-s561" xml:space="preserve">Mihi au
              <lb/>
            tem conſultiſsimũ eſſe uidetur, ſi ſemicirculũ illũ diuidas in 100. </s>
            <s xml:id="echoid-s562" xml:space="preserve">partes, ſicut hic ſeꝗtur. </s>
            <s xml:id="echoid-s563" xml:space="preserve">
              <lb/>
            Principio ſemidiametrũ AB diuide in 100. </s>
            <s xml:id="echoid-s564" xml:space="preserve">partes æquales, adſcribe etiã numeros ſingu
              <lb/>
            larũ partiũ occulte ꝑ quinarios uel denarios retrorſum à B in A at ea pũcta erunt ſinus
              <lb/>
            uerſi, q̃ deinde, modo quo ſupra diximus, transfer cũ circino in ſemicirculũ AFB, adſcri
              <lb/>
            bendo numeros q̊ pari modo ſicut in ſemidiametro AB feciſti. </s>
            <s xml:id="echoid-s565" xml:space="preserve">Mox pũcta ſimul & </s>
            <s xml:id="echoid-s566" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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