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-div30" type="section" level="1" n="19">
          <pb file="0035" n="35" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
        </div>
        <div xml:id="echoid-div32" type="section" level="1" n="20">
          <head xml:id="echoid-head24" xml:space="preserve">PRONVNCIATVM VIII.</head>
          <p>
            <s xml:id="echoid-s1192" xml:space="preserve">Habita iam aſcenſione recta in æquinoctiali, arcum ipſius eclypticæ cum
              <lb/>
            eo aſcendentem in ſphæra recta cognoſcere.</s>
            <s xml:id="echoid-s1193" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1194" xml:space="preserve">Pronunciatũ hoc quo inuertit quod ſuperior docuerat, at ideo qñ multũ cõueniũt
              <lb/>
            ambæ illæ, diutius hic nõ immorabimur oſtendẽdo, quõ aſcenſio recta debeat intelligi,
              <lb/>
            ſed prætermiſsis amba gibus & </s>
            <s xml:id="echoid-s1195" xml:space="preserve">inuolutis uerbis, ad ipſam ſtatim operationẽ uenia mus.
              <lb/>
            </s>
            <s xml:id="echoid-s1196" xml:space="preserve">Vbi iam noris, qualis declinatio eclypticæ fit penes arcũ æquinoctialis, ex ſuperiori ꝓ-
              <lb/>
            poſitiõe aſcenſionẽ eclypticæ cũ æquino ctiali facile inuenies hoc modo. </s>
            <s xml:id="echoid-s1197" xml:space="preserve">Si multiplices
              <lb/>
              <note position="right" xlink:label="note-0035-01" xlink:href="note-0035-01a" xml:space="preserve">
                <emph style="it">Primũ in-</emph>
                <lb/>
                <emph style="it">uenies m-</emph>
                <lb/>
                <emph style="it">greſſu late</emph>
                <lb/>
                <emph style="it">rali, ſecũdũ</emph>
                <lb/>
                <emph style="it">uero per a-</emph>
                <lb/>
                <emph style="it">realem.</emph>
              </note>
            ſinum declinatiõis cũ toto ſinu, & </s>
            <s xml:id="echoid-s1198" xml:space="preserve">ꝓductũ diuidas cum ſinu maximæ declinatiõis ☉(sun), ar
              <lb/>
            cus quotientis mõſtrabit tibi arcũ eclypticæ, qui cũ arcu æquatoris aſcẽdit in ſphæra re
              <lb/>
            cta. </s>
            <s xml:id="echoid-s1199" xml:space="preserve">Habe eius rei hoc tibi exemplũ. </s>
            <s xml:id="echoid-s1200" xml:space="preserve">Sit arcus æquatoris à principio æquinoctialis 60.
              <lb/>
            </s>
            <s xml:id="echoid-s1201" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1202" xml:space="preserve">21. </s>
            <s xml:id="echoid-s1203" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1204" xml:space="preserve">declinatio aũt eclypticæ in eoloco 20. </s>
            <s xml:id="echoid-s1205" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1206" xml:space="preserve">42. </s>
            <s xml:id="echoid-s1207" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1208" xml:space="preserve">ſinus eius 35347. </s>
            <s xml:id="echoid-s1209" xml:space="preserve">ſinũ hũc
              <lb/>
            ubi duxeris in totũ ſinũ ꝓductũ inde diuiſeris in ſinũ rectũ maximæ declinatiõis ☉(sun), puta
              <lb/>
            39874. </s>
            <s xml:id="echoid-s1210" xml:space="preserve">ꝓuenient in quotiẽte 88647. </s>
            <s xml:id="echoid-s1211" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s1212" xml:space="preserve">ij gradus ſunt 62. </s>
            <s xml:id="echoid-s1213" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1214" xml:space="preserve">26. </s>
            <s xml:id="echoid-s1215" xml:space="preserve">hoc ipſum ſi numerem à
              <lb/>
              <note position="right" xlink:label="note-0035-02" xlink:href="note-0035-02a" xml:space="preserve">
                <emph style="it">Hoc areali</emph>
                <lb/>
                <emph style="it">introitu</emph>
                <lb/>
                <emph style="it">quœrenti</emph>
                <lb/>
                <emph style="it">apparet.</emph>
              </note>
            principio ♈, deſinet numerus in 2. </s>
            <s xml:id="echoid-s1216" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1217" xml:space="preserve">26. </s>
            <s xml:id="echoid-s1218" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1219" xml:space="preserve">II. </s>
            <s xml:id="echoid-s1220" xml:space="preserve">ubi Sol fuit hora intronizationis. </s>
            <s xml:id="echoid-s1221" xml:space="preserve">Etſi
              <lb/>
            aũt modus ille non ſit uerus ac ſolidus, quũ uſurpari nequeat in arcu æquatoris, ſed ad de
              <lb/>
            clinationẽ tantũ, nolui tamẽ, & </s>
            <s xml:id="echoid-s1222" xml:space="preserve">hũc ipſum te latere, ne ꝗd haberes ambiguum in ijs quæ
              <lb/>
            obiter tibi circa hãc rem poſſent offerri & </s>
            <s xml:id="echoid-s1223" xml:space="preserve">incidere. </s>
            <s xml:id="echoid-s1224" xml:space="preserve">Alia etea quidẽ aptiſsima operatio
              <lb/>
            hæc eſt, propoſitum habes arcũ æquatoris, iam´ cupis inuenire arcum ſuum coaſcẽden
              <lb/>
            tem in eclyptica, multiplica principio ſinum cõplementi arcus æquinoctialis propoſiti,
              <lb/>
            ſi ſaltem ſit quadrante minor, cũ ſinu maximæ declinationis, ꝓductũ inde diuide per ſinũ
              <lb/>
              <note position="right" xlink:label="note-0035-03" xlink:href="note-0035-03a" xml:space="preserve">
                <emph style="it">Hoc reſp♉-</emph>
                <lb/>
                <emph style="it">det laterali</emph>
                <lb/>
                <emph style="it">ingreſſu.</emph>
              </note>
            totũ & </s>
            <s xml:id="echoid-s1225" xml:space="preserve">ſubtracto quotientis arcu à 90. </s>
            <s xml:id="echoid-s1226" xml:space="preserve">ſinũ reſidui tibi ꝓpone, ſimul´ ſinũ arcus propoſi
              <lb/>
            ti æquatoris, uter eorũ fuerit minor, multiplicandus erit cũ toto ſinu, ꝓductum´ diui-
              <lb/>
            dendum in ſinũ maiorem, & </s>
            <s xml:id="echoid-s1227" xml:space="preserve">tunc arcus quotientis monſtrabit tibi arcũ eclypticæ, qui cũ
              <lb/>
            arcu æquatoris propoſito aſcendit in ſphæra recta. </s>
            <s xml:id="echoid-s1228" xml:space="preserve">lam autẽ fixo hic pede priuſ̈ ulteri-
              <lb/>
            us in regula progrediamur, lubet exemplo rem apertius declarare, quando adhuc opera
              <lb/>
            tio in recenti memoria hæret. </s>
            <s xml:id="echoid-s1229" xml:space="preserve">?</s>
            <s xml:id="echoid-s1230" xml:space="preserve">? Eſto ut hora intronizationis Solis in aſcenſione recta
              <lb/>
              <note position="right" xlink:label="note-0035-04" xlink:href="note-0035-04a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
                <emph style="it">Epiſoo
                  <unsure/>
                pi.</emph>
              </note>
            contigerit 60. </s>
            <s xml:id="echoid-s1231" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1232" xml:space="preserve">21. </s>
            <s xml:id="echoid-s1233" xml:space="preserve">mi ego aũt cupiã ſcire gradũ Solis in eclyptica, eum facile cogno
              <lb/>
            ſcam ſi quæſiero arcũ eclypticæ, qui cũ arcu æquatoris aſcẽdit in ſphæra recta: </s>
            <s xml:id="echoid-s1234" xml:space="preserve">ita quũ
              <lb/>
            duco ſinũ cõplementi arcus propoſiti æquatoris. </s>
            <s xml:id="echoid-s1235" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s1236" xml:space="preserve">29. </s>
            <s xml:id="echoid-s1237" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1238" xml:space="preserve">39. </s>
            <s xml:id="echoid-s1239" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1240" xml:space="preserve">49471. </s>
            <s xml:id="echoid-s1241" xml:space="preserve">in ſinũ maxi-
              <lb/>
            mæ declinatiõis Solis, puta 39874. </s>
            <s xml:id="echoid-s1242" xml:space="preserve">productũ diuido cũ ſinu toto, prodibunt in quotiẽte
              <lb/>
            19726. </s>
            <s xml:id="echoid-s1243" xml:space="preserve">arcus eius eſt 11. </s>
            <s xml:id="echoid-s1244" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1245" xml:space="preserve">23. </s>
            <s xml:id="echoid-s1246" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1247" xml:space="preserve">Cõplementũ uero 78. </s>
            <s xml:id="echoid-s1248" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1249" xml:space="preserve">37. </s>
            <s xml:id="echoid-s1250" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1251" xml:space="preserve">habet in ſinu pro-
              <lb/>
            poſiti arcus æquatoris 86906. </s>
            <s xml:id="echoid-s1252" xml:space="preserve">ſinum illum (quãdo minimus eſt) multiplico cũ toto, pro-
              <lb/>
            ductum diuido in maiorem, & </s>
            <s xml:id="echoid-s1253" xml:space="preserve">prouenient in quotiente 88647. </s>
            <s xml:id="echoid-s1254" xml:space="preserve">arcus eius eſt 62. </s>
            <s xml:id="echoid-s1255" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1256" xml:space="preserve">26
              <lb/>
            mi. </s>
            <s xml:id="echoid-s1257" xml:space="preserve">at is eſt arcus eclypticæ ſimul aſcendens cum arcu æquatoris propoſito in ſphæ-
              <lb/>
            ra recta, tunc ſi reijciam 60. </s>
            <s xml:id="echoid-s1258" xml:space="preserve">hoc eſt 2 ſigna remanebunt 2. </s>
            <s xml:id="echoid-s1259" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1260" xml:space="preserve">26. </s>
            <s xml:id="echoid-s1261" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1262" xml:space="preserve">II. </s>
            <s xml:id="echoid-s1263" xml:space="preserve">Quod ſi autem
              <lb/>
            arcus propoſitus æquatoris maior ſit ̈ 90. </s>
            <s xml:id="echoid-s1264" xml:space="preserve">& </s>
            <s xml:id="echoid-s1265" xml:space="preserve">tamẽ minor ̈ 180. </s>
            <s xml:id="echoid-s1266" xml:space="preserve">ſubduc eum à ſemicir
              <lb/>
            culo, & </s>
            <s xml:id="echoid-s1267" xml:space="preserve">deinde cum reſiduo operare modo prædicto. </s>
            <s xml:id="echoid-s1268" xml:space="preserve">atqui numerus poſtremo inuentus
              <lb/>
            uerus nõ eſt, niſi eũ à ſemicirculo ſubtrahes, tunc tandem manebit arcus quælitus, quem
              <lb/>
            ſemper numerabis à principio ♈. </s>
            <s xml:id="echoid-s1269" xml:space="preserve">Quid uero ſi arcus propoſitus æquatoris fuerit ſemi-
              <lb/>
            circulo maior @ tunc ſane ſubtrahe ſemicir culum gra. </s>
            <s xml:id="echoid-s1270" xml:space="preserve">180. </s>
            <s xml:id="echoid-s1271" xml:space="preserve">& </s>
            <s xml:id="echoid-s1272" xml:space="preserve">cum eo, quod reliquũ ma-
              <lb/>
            net, operare ſicut edoctus es antea. </s>
            <s xml:id="echoid-s1273" xml:space="preserve">At extremũ quũ omnia iam perfeceris, adhuc adde
              <lb/>
            180. </s>
            <s xml:id="echoid-s1274" xml:space="preserve">& </s>
            <s xml:id="echoid-s1275" xml:space="preserve">ſic demum habebis arcum eclypticæ, quem tam operoſe hactenus inquirebas.</s>
            <s xml:id="echoid-s1276" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div34" type="section" level="1" n="21">
          <head xml:id="echoid-head25" xml:space="preserve">PRONVNCIATVM IX.</head>
          <p>
            <s xml:id="echoid-s1277" xml:space="preserve">Quum arcum aliquẽ eclypticæ cognoſcere cupis, cum quo æqualis arcus
              <lb/>
            æquatoris aſcẽdit in ſphæra recta, iam´ principiũ ſiue terminus illius arcus
              <lb/>
            tibi innotuit, alterum quo terminũ ex artificioſa ſupputatione colligere.</s>
            <s xml:id="echoid-s1278" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1279" xml:space="preserve">Arcũ hic eclypticæ intellige inter duo ſigna cardinalia intercluſum, ut inter ♈ & </s>
            <s xml:id="echoid-s1280" xml:space="preserve">pri
              <lb/>
            mũ mi. </s>
            <s xml:id="echoid-s1281" xml:space="preserve">♋, inter primũ pũctũ ♋ & </s>
            <s xml:id="echoid-s1282" xml:space="preserve">primũ mi. </s>
            <s xml:id="echoid-s1283" xml:space="preserve">♎, ſimiliter inter ♎ & </s>
            <s xml:id="echoid-s1284" xml:space="preserve">♑ & </s>
            <s xml:id="echoid-s1285" xml:space="preserve">♑ & </s>
            <s xml:id="echoid-s1286" xml:space="preserve">♈, tbi ſa
              <lb/>
            nè talis erit operatio. </s>
            <s xml:id="echoid-s1287" xml:space="preserve">Eius termini ſiue principij tandẽ ſiue finis tibi cogniti quære de
              <lb/>
            clinationẽ per ꝓpoſitionẽ 5. </s>
            <s xml:id="echoid-s1288" xml:space="preserve">declinationis illius ſinũ cõplementi tibi propone, ſimul´ </s>
          </p>
        </div>
      </text>
    </echo>
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