Apian, Petrus, Instrvmentvm Sinvvm, sev primi mobilis
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        <div xml:id="echoid-div61" type="section" level="1" n="35">
          <p>
            <s xml:id="echoid-s2118" xml:space="preserve">
              <pb file="0043" n="43" rhead="TABVLARVM SINVVM."/>
            arcus eſt ipſe arcus horizontis inter punctũ Solis aſcendentis & </s>
            <s xml:id="echoid-s2119" xml:space="preserve">ortum æ quinoctialem.
              <lb/>
            </s>
            <s xml:id="echoid-s2120" xml:space="preserve">?</s>
            <s xml:id="echoid-s2121" xml:space="preserve">? Exemplum ſit hoc tibi, in die intronizationis eſto, ut obſeruarit quis altitudinem So-
              <lb/>
              <note position="right" xlink:label="note-0043-01" xlink:href="note-0043-01a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
              E
                <emph style="it">piſoo
                  <unsure/>
                pi.</emph>
              </note>
            lis in circulo uerticali, ea fuit 28. </s>
            <s xml:id="echoid-s2122" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2123" xml:space="preserve">24. </s>
            <s xml:id="echoid-s2124" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2125" xml:space="preserve">ſinum illius 47564. </s>
            <s xml:id="echoid-s2126" xml:space="preserve">duxerit in ſinum totum,
              <lb/>
            productum diuiſerit in ſinum complementi altitudinis poli 66913. </s>
            <s xml:id="echoid-s2127" xml:space="preserve">in quotiente proue-
              <lb/>
            nerũt 71083. </s>
            <s xml:id="echoid-s2128" xml:space="preserve">ex eo quadrato, hoc eſt in ſe ducto, ꝓdijt numer
              <emph style="sub">9</emph>
            ille q̃dratus 5052792889
              <lb/>
            deinde ſimili modo quadrato etiam ſinum altitudinis uerticalis, prouenit 2262334096.
              <lb/>
            </s>
            <s xml:id="echoid-s2129" xml:space="preserve">eo ſubtracto à ſuperiori, remanſit 2790458793. </s>
            <s xml:id="echoid-s2130" xml:space="preserve">radix illius numeri quadrata eſt 52825. </s>
            <s xml:id="echoid-s2131" xml:space="preserve">
              <lb/>
            arcus eius 31. </s>
            <s xml:id="echoid-s2132" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2133" xml:space="preserve">53. </s>
            <s xml:id="echoid-s2134" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2135" xml:space="preserve">amplitudo illa Solis ad diem intronizationis, quam pronuncia-
              <lb/>
            to 12. </s>
            <s xml:id="echoid-s2136" xml:space="preserve">diuerſo modo docuimus inuenire.</s>
            <s xml:id="echoid-s2137" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div63" type="section" level="1" n="36">
          <head xml:id="echoid-head40" xml:space="preserve">PRONVNCIATVM XXIIII.</head>
          <p>
            <s xml:id="echoid-s2138" xml:space="preserve">Ex altitudine Solis in circulo uerticali, & </s>
            <s xml:id="echoid-s2139" xml:space="preserve">ex amplitudine Solis eiuſdem di
              <lb/>
            ei altitudinem poli expedite inueſtigare, etiam ſi neſcias gradum Solis ſimul
              <lb/>
            & </s>
            <s xml:id="echoid-s2140" xml:space="preserve">declinationem illius.</s>
            <s xml:id="echoid-s2141" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2142" xml:space="preserve">Per hoc q̊d iam docebimus. </s>
            <s xml:id="echoid-s2143" xml:space="preserve">poteſt ꝗs quotidie tota æſtate mane altitudinem poli ob-
              <lb/>
            ſeruare, nõ cognito gradu & </s>
            <s xml:id="echoid-s2144" xml:space="preserve">declinatione Solis, ſi modo ꝑ inſtrumentũ aliq̊d amplitudi
              <lb/>
            nem Solis ortiuã & </s>
            <s xml:id="echoid-s2145" xml:space="preserve">occiduã obſeruarit (quicꝗd em̃ hic de amplitudine ortiua dicimus ſi-
              <lb/>
            mul & </s>
            <s xml:id="echoid-s2146" xml:space="preserve">de altitudine uerticali, idẽ etiã de amplitudine occidua & </s>
            <s xml:id="echoid-s2147" xml:space="preserve">altitudine Solis in circu
              <lb/>
            lo uerticali occiduo intelligi debet) parit’ & </s>
            <s xml:id="echoid-s2148" xml:space="preserve">altitudinẽ Solis in circulo uerticali exiſten-
              <lb/>
            tis, ſtatim duc ſinũ amplitudinis in ſe ꝗ̃drate, deinde etiã ſinũ altitudinis uerticalis, utrũ
              <lb/>
            hũc nume℞ quadratũ in unã ſummã cõponito, ex ea rurſus quære radicem quadratã, & </s>
            <s xml:id="echoid-s2149" xml:space="preserve">il
              <lb/>
              <note position="right" xlink:label="note-0043-02" xlink:href="note-0043-02a" xml:space="preserve">
                <emph style="it">Lateraliter</emph>
                <lb/>
                <emph style="it">idem inue-</emph>
                <lb/>
                <emph style="it">nies.</emph>
              </note>
            lam propone in regulã philoſopho℞ primo loco, ſecũdo ſinũ altitudinis Solis in circulo
              <lb/>
            uerticali, tertio ſinũ totũ. </s>
            <s xml:id="echoid-s2150" xml:space="preserve">Et iuxta regulã numerũ ultimũ duc in mediũ, ꝓductũ in primũ
              <lb/>
            diuide, & </s>
            <s xml:id="echoid-s2151" xml:space="preserve">arcus q̊tientis ex quadra circuli ſubtractus, oſtendet tibi altitudinem poli quæ-
              <lb/>
              <note position="right" xlink:label="note-0043-03" xlink:href="note-0043-03a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
              E
                <emph style="it">piſoo
                  <unsure/>
                pi.</emph>
              </note>
            ſitam. </s>
            <s xml:id="echoid-s2152" xml:space="preserve">?</s>
            <s xml:id="echoid-s2153" xml:space="preserve">?Sed obſcurius paulò hoc tibiuidetur, en exemplo ſit dilucidius. </s>
            <s xml:id="echoid-s2154" xml:space="preserve">Altitudo So
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            lis in circulo uerticali in die intronizationis fuit 28. </s>
            <s xml:id="echoid-s2155" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2156" xml:space="preserve">24. </s>
            <s xml:id="echoid-s2157" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2158" xml:space="preserve">ſinus eius 47564. </s>
            <s xml:id="echoid-s2159" xml:space="preserve">amplitu
              <lb/>
            do q̊ ortiua ꝑ in ſtrumentũ inuenta eſt 31. </s>
            <s xml:id="echoid-s2160" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2161" xml:space="preserve">53. </s>
            <s xml:id="echoid-s2162" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2163" xml:space="preserve">ſinus ipſius 52825. </s>
            <s xml:id="echoid-s2164" xml:space="preserve">quadratũ illi-
              <lb/>
            us 2790458793. </s>
            <s xml:id="echoid-s2165" xml:space="preserve">quadratũ aũt ſinus altitudinis 2262334096. </s>
            <s xml:id="echoid-s2166" xml:space="preserve">utrun quadratũ hoc con
              <lb/>
            iunctũ in una ſumma, facit 5052792889. </s>
            <s xml:id="echoid-s2167" xml:space="preserve">radix eius quadrata eſt 71083. </s>
            <s xml:id="echoid-s2168" xml:space="preserve">Si ergo in regu-
              <lb/>
            lam proportionũ cõpoſuero hoc modo 71083. </s>
            <s xml:id="echoid-s2169" xml:space="preserve">dant mihi 47564. </s>
            <s xml:id="echoid-s2170" xml:space="preserve">Quid ita ex toto pro
              <lb/>
            ueniet ſinu@ Inueniam uti ex operatione regulæ huius 66913. </s>
            <s xml:id="echoid-s2171" xml:space="preserve">Arcus eius 42. </s>
            <s xml:id="echoid-s2172" xml:space="preserve">ex circuli
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            quadra ſubtra ctus, reliquã faciet altitudinem poli 48. </s>
            <s xml:id="echoid-s2173" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2174" xml:space="preserve">quæſitã ad locũ obſeruationis.</s>
            <s xml:id="echoid-s2175" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div65" type="section" level="1" n="37">
          <head xml:id="echoid-head41" xml:space="preserve">PRONVNCIATVM XXV.</head>
          <p>
            <s xml:id="echoid-s2176" xml:space="preserve">Quocun tempore, ſiue qualibet hora, gradum eclypticæ, quimeridia,
              <lb/>
            num tangit, ex ſphærica ſupputatione colligere.</s>
            <s xml:id="echoid-s2177" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2178" xml:space="preserve">Si quando mediũ cœli in eclyptica noſſe cupis, uel ante uel poſt meridiem: </s>
            <s xml:id="echoid-s2179" xml:space="preserve">ꝓpone tibi
              <lb/>
            diſtantiã Solis à meridie, & </s>
            <s xml:id="echoid-s2180" xml:space="preserve">reſolue eã in gradus, deinde adſume etiã aſcenſionem rectam
              <lb/>
            gradus Solis ꝑ pronunciatũ 7. </s>
            <s xml:id="echoid-s2181" xml:space="preserve">Quòd ſi tempus operationis huius fuerit antemeridianũ,
              <lb/>
            tũc ſubtrahe gradus diſtãtiæ à meridiano: </s>
            <s xml:id="echoid-s2182" xml:space="preserve">ſin aũt pomeridianũ fuerit, addenda tibi erit di
              <lb/>
            ſtantia horaria in gradus cõuerſa ad aſcenſionem rectã gradus Solis. </s>
            <s xml:id="echoid-s2183" xml:space="preserve">Ex additiõe uel ſub
              <lb/>
            tractione huiuſmodi quicquid prouenerituel reliquũ manſerit, aſcenſio recta dicet̃ me-
              <lb/>
            dij cœli. </s>
            <s xml:id="echoid-s2184" xml:space="preserve">Hinc ſi adhuc ſcire deſideras gradũ eclypticæ eo ipſo momento tangentem me-
              <lb/>
            ridianũ, is ſanè eſt, qui cum eo in ſphæra recta aſcendit, quære eũ ex pronunciato 8.
              <lb/>
            </s>
            <s xml:id="echoid-s2185" xml:space="preserve">& </s>
            <s xml:id="echoid-s2186" xml:space="preserve">habebis punctum eclypticæ, qui mediat cœlum tempore propoſito. </s>
            <s xml:id="echoid-s2187" xml:space="preserve">?</s>
            <s xml:id="echoid-s2188" xml:space="preserve">?Et ſit eius rei
              <lb/>
              <note position="right" xlink:label="note-0043-04" xlink:href="note-0043-04a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
              E
                <emph style="it">piſoo
                  <unsure/>
                pi.</emph>
              </note>
            exemplum tale. </s>
            <s xml:id="echoid-s2189" xml:space="preserve">Scire for ſitan cupio ad ipſam horã intronizationis, quid tunc mediũ cœ
              <lb/>
            li habuerit, quando intronizatio facta eſt hora 9. </s>
            <s xml:id="echoid-s2190" xml:space="preserve">ante meridiem: </s>
            <s xml:id="echoid-s2191" xml:space="preserve">diſtantia uti horaria
              <lb/>
            eſt 3. </s>
            <s xml:id="echoid-s2192" xml:space="preserve">graduũ, quoniã à 9. </s>
            <s xml:id="echoid-s2193" xml:space="preserve">uſad 12. </s>
            <s xml:id="echoid-s2194" xml:space="preserve">horæ tres ſunt: </s>
            <s xml:id="echoid-s2195" xml:space="preserve">in reſolutione ergo ſemper 15. </s>
            <s xml:id="echoid-s2196" xml:space="preserve">gradus
              <lb/>
            pro hora cõnumerando, faciũt horæ tres gradus 45. </s>
            <s xml:id="echoid-s2197" xml:space="preserve">eos ſubtraho ab aſcenſione gradus
              <lb/>
            Solis, quem ſupra in pronũciato 7. </s>
            <s xml:id="echoid-s2198" xml:space="preserve">inueni: </s>
            <s xml:id="echoid-s2199" xml:space="preserve">ſiquidem tũc Sol ſuit in 2. </s>
            <s xml:id="echoid-s2200" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2201" xml:space="preserve">26. </s>
            <s xml:id="echoid-s2202" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2203" xml:space="preserve">II. </s>
            <s xml:id="echoid-s2204" xml:space="preserve">aſcen
              <lb/>
            ſio eius eſt 60. </s>
            <s xml:id="echoid-s2205" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2206" xml:space="preserve">21. </s>
            <s xml:id="echoid-s2207" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2208" xml:space="preserve">unde ſubtraho 45. </s>
            <s xml:id="echoid-s2209" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2210" xml:space="preserve">& </s>
            <s xml:id="echoid-s2211" xml:space="preserve">remanent 6. </s>
            <s xml:id="echoid-s2212" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s2213" xml:space="preserve">21. </s>
            <s xml:id="echoid-s2214" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s2215" xml:space="preserve">æquatoris,
              <lb/>
            quæ tangunt medium cœli ipſa hora intronizationis. </s>
            <s xml:id="echoid-s2216" xml:space="preserve">Si igitur iuxta pronuhciatum 8.</s>
            <s xml:id="echoid-s2217" xml:space="preserve"/>
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