Apian, Petrus, Instrvmentvm Sinvvm, sev primi mobilis

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        <div xml:id="echoid-div28" type="section" level="1" n="18">
          <p>
            <s xml:id="echoid-s1088" xml:space="preserve">
              <pb file="0034" n="34" rhead="GENVINVS VSVS"/>
            pticæ ab una & </s>
            <s xml:id="echoid-s1089" xml:space="preserve">proxima interſectione eclypticæ & </s>
            <s xml:id="echoid-s1090" xml:space="preserve">æꝗnoctialis ?</s>
            <s xml:id="echoid-s1091" xml:space="preserve">? Exẽplores tibi fiet
              <lb/>
            apertior& </s>
            <s xml:id="echoid-s1092" xml:space="preserve">dilucidior. </s>
            <s xml:id="echoid-s1093" xml:space="preserve">Sit ꝓpoſita tibi declinatio gradus, in q̊ ☉(sun) fuit ea hora qua intro-
              <lb/>
            nizatus eſt Reuerendiſs. </s>
            <s xml:id="echoid-s1094" xml:space="preserve">pater Epiſcopus Auguſtenſis, ſicut in priori propoſitione com-
              <lb/>
              <note position="left" xlink:label="note-0034-01" xlink:href="note-0034-01a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
                <emph style="it">Epiſoo
                  <unsure/>
                pi.</emph>
              </note>
            memorauimus, gradus autem Solis non conſtet, ſed hoc tantum, quòd declinatio ſit 20.
              <lb/>
            </s>
            <s xml:id="echoid-s1095" xml:space="preserve">graduum, 42. </s>
            <s xml:id="echoid-s1096" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1097" xml:space="preserve">Iam ad inueniendum gradum Solis eo ipſo die & </s>
            <s xml:id="echoid-s1098" xml:space="preserve">hora intronizatio-
              <lb/>
            nis, multiplica ſinũ huius declinationis 35347. </s>
            <s xml:id="echoid-s1099" xml:space="preserve">cũ toto ſinu, & </s>
            <s xml:id="echoid-s1100" xml:space="preserve">prouenient 3534700000
              <lb/>
            idipſum ſi diuidas in ſinum maximæ declinationis 39874, emanabũt in quotiente 88647
              <lb/>
            eius ſinus arcus 62. </s>
            <s xml:id="echoid-s1101" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1102" xml:space="preserve">26. </s>
            <s xml:id="echoid-s1103" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1104" xml:space="preserve">diſtantia illa iuſta eſt quam quærebas. </s>
            <s xml:id="echoid-s1105" xml:space="preserve">Et quia introniza
              <lb/>
            tio huiuſmodi facta in Maio, diſtantia hæc à principio ♈ numerari debet, & </s>
            <s xml:id="echoid-s1106" xml:space="preserve">cadet ſuꝑ
              <lb/>
            2. </s>
            <s xml:id="echoid-s1107" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1108" xml:space="preserve">26. </s>
            <s xml:id="echoid-s1109" xml:space="preserve">mi II, at hoc erat quod intendebatur.</s>
            <s xml:id="echoid-s1110" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div30" type="section" level="1" n="19">
          <head xml:id="echoid-head23" xml:space="preserve">PRONVNCIATVM VII.</head>
          <p>
            <s xml:id="echoid-s1111" xml:space="preserve">Cuiuslibet arcus eclypticæ, quiprincipium ſuum ab æquinoctiali & </s>
            <s xml:id="echoid-s1112" xml:space="preserve">in-
              <lb/>
            terſectione cum eclyptica capit, a cenſionem in ſphæra recta addiſcere.</s>
            <s xml:id="echoid-s1113" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1114" xml:space="preserve">Per hanc aſcenſionẽ rectã intelligi debet arcus æꝗnoctialis interceptus inter ipſum
              <lb/>
            eclypticæ & </s>
            <s xml:id="echoid-s1115" xml:space="preserve">æꝗnoctialis interſectionẽ, ſimul at circulũ illũ maiorem, qui à polo mundi
              <lb/>
            per punctũ iſtum eclypticæ ꝓpoſitũ (cuius aſcenſionẽ ſcire deſideras) uſ ad æquinocti
              <lb/>
            alem ad angulos rectos ſphærales eſt ductus. </s>
            <s xml:id="echoid-s1116" xml:space="preserve">Et quũ zodiacus in 4. </s>
            <s xml:id="echoid-s1117" xml:space="preserve">quadrantes per 4. </s>
            <s xml:id="echoid-s1118" xml:space="preserve">ſi-
              <lb/>
            gna cardinalia ♈ ♋ ♎ & </s>
            <s xml:id="echoid-s1119" xml:space="preserve">♑, per quæ etiã circuli maiores 4. </s>
            <s xml:id="echoid-s1120" xml:space="preserve">ex polis mũdi protẽſi ſunt,
              <lb/>
            diuidatur, æquinoctialis etiã in 4. </s>
            <s xml:id="echoid-s1121" xml:space="preserve">quadrantes, partiendus eſt, nõ quidẽ per ſigna, ſed pri-
              <lb/>
            ma quarta à principio æquinoctialis uſ in 90. </s>
            <s xml:id="echoid-s1122" xml:space="preserve">gradus, reſpõdet primo gradu ♋ ſupra
              <lb/>
            horizontẽ ſphæræ rectæ, & </s>
            <s xml:id="echoid-s1123" xml:space="preserve">180. </s>
            <s xml:id="echoid-s1124" xml:space="preserve">gradus æquinoctialis, hoc eſt media pars æquinoctialis
              <lb/>
            reſpõdet etiã mediæ eclypticæ, primus enim gradus ♎ (quæ interſectio eſt æquinoctia-
              <lb/>
            lis cũ eclyptica) eſt gradus 180. </s>
            <s xml:id="echoid-s1125" xml:space="preserve">â primo gradu ♈. </s>
            <s xml:id="echoid-s1126" xml:space="preserve">Et quia utrun principiũ æꝗnoctialis
              <lb/>
            & </s>
            <s xml:id="echoid-s1127" xml:space="preserve">eclypticæ apud primũ minutũ ♈ initiũ habet, etiã inde numerari debẽt quartæ & </s>
            <s xml:id="echoid-s1128" xml:space="preserve">me
              <lb/>
            diæ partes circulorũ. </s>
            <s xml:id="echoid-s1129" xml:space="preserve">Quum´ cõſtet 4. </s>
            <s xml:id="echoid-s1130" xml:space="preserve">quartas æquinoctialis cũ 4. </s>
            <s xml:id="echoid-s1131" xml:space="preserve">quartis eclypticæ, ſin
              <lb/>
            gulas cũ adia centibus ſibi, æqualiter aſcẽdere in ſphæra recta, & </s>
            <s xml:id="echoid-s1132" xml:space="preserve">tamẽ inter principiũ et
              <lb/>
            finẽ cuiuslibet quartæ nullus alioquin gradus, ne punctũ æquali numero cũ adiacẽte
              <lb/>
            quarta in aſcenſione cõuenit, neceſſariũ eſt cõſcenſionẽ iſtã per ſupputationẽ ſphæricã
              <lb/>
            internoſcere, id´ ꝑ hãc regulã. </s>
            <s xml:id="echoid-s1133" xml:space="preserve">Si arcus eclypticæ minor fuerit ̈ 90. </s>
            <s xml:id="echoid-s1134" xml:space="preserve">erit ille planè ac-
              <lb/>
            commodus inueniendæ huic aſcenſioni, at is primus modus eſto. </s>
            <s xml:id="echoid-s1135" xml:space="preserve">Sin aũt maior fuerit
              <lb/>
            ̈ 90. </s>
            <s xml:id="echoid-s1136" xml:space="preserve">ſubtrahito eum ab 180. </s>
            <s xml:id="echoid-s1137" xml:space="preserve">ipſo nimi℞ ſemicirculo, & </s>
            <s xml:id="echoid-s1138" xml:space="preserve">ꝗcquid reliquũ manſerit, id aptũ
              <lb/>
            erit cognoſcẽdæ aſcẽſioni rectæ, & </s>
            <s xml:id="echoid-s1139" xml:space="preserve">hæc altera ſit ratio inueniendæ aſcenſionis. </s>
            <s xml:id="echoid-s1140" xml:space="preserve">Sicut au
              <lb/>
            tem ex media parte eclypticæ duos modos oſtendimus, ita reliquã partẽ nedũ â princi-
              <lb/>
            pio ♎ uſ ad finẽ κ identidẽ diuides in duas uias ſeu rationes inueniendi aſcenſionem.
              <lb/>
            </s>
            <s xml:id="echoid-s1141" xml:space="preserve">Quod ſi numerũ cõueniẽtẽ ex primo modo iã inuentũ habes, hoc eſt, ſi arcus eclypticæ
              <lb/>
            minor fuerit ̈ 90. </s>
            <s xml:id="echoid-s1142" xml:space="preserve">tũc ſubtrahe eũ à 90. </s>
            <s xml:id="echoid-s1143" xml:space="preserve">reſiduũ uo cabit̃ cõplementũ ipſius, tũc etiã com
              <lb/>
            plementũ aſſume declinationis, ultimi pũcti ꝓpoſiti arcus eclypticæ, & </s>
            <s xml:id="echoid-s1144" xml:space="preserve">ſinũ minimi cõ-
              <lb/>
            plemẽti duc in totũ ſinũ, ꝓductũ diuide in ſinũ cõplementi maioris, hinc ſubtracto arcu
              <lb/>
            q̊tiẽtis à 90. </s>
            <s xml:id="echoid-s1145" xml:space="preserve">manebit aſcenſio recta arcus ꝓpoſiti. </s>
            <s xml:id="echoid-s1146" xml:space="preserve">Quod ſi aũt nume℞ cõuenientẽ altero
              <lb/>
            modo inueniſti, iã nõ opus habebis ultima ſubtractiõe â 90. </s>
            <s xml:id="echoid-s1147" xml:space="preserve">ſed tũc addes inſuper gradus
              <lb/>
              <note position="left" xlink:label="note-0034-02" xlink:href="note-0034-02a" xml:space="preserve">
                <emph style="it">Operatio</emph>
                <lb/>
                <emph style="it">arealis.</emph>
              </note>
            90. </s>
            <s xml:id="echoid-s1148" xml:space="preserve">& </s>
            <s xml:id="echoid-s1149" xml:space="preserve">ſic q̊ habebis arcũ æꝗnoctialis cũ ꝓpoſito arcu coaſcendentem in ſphæra recta.
              <lb/>
            </s>
            <s xml:id="echoid-s1150" xml:space="preserve">Cæterũ ſi tibi ꝓponas arcũ zodiaci â principio ♎ cõputando uſ ad finẽ κ, ubicun il
              <lb/>
            le deſierit, inter hoc ſpacium, aſcenſionem eius quære eo planè modo q̊ iam edoctus es,
              <lb/>
            niſi ꝙ ad extremũ addes gradus 180. </s>
            <s xml:id="echoid-s1151" xml:space="preserve">Primus em̃ gradus ♎ habet gradus 180. </s>
            <s xml:id="echoid-s1152" xml:space="preserve">æꝗnoctia
              <lb/>
            lis in ſua aſcẽſione, ſicut antea docuimus. </s>
            <s xml:id="echoid-s1153" xml:space="preserve">?</s>
            <s xml:id="echoid-s1154" xml:space="preserve">? lam uero exemplis rem demonſtremus ad
              <lb/>
              <note position="left" xlink:label="note-0034-03" xlink:href="note-0034-03a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
                <emph style="it">Epiſoo
                  <unsure/>
                pi.</emph>
              </note>
            oculũ. </s>
            <s xml:id="echoid-s1155" xml:space="preserve">Adſumo ecce 2. </s>
            <s xml:id="echoid-s1156" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1157" xml:space="preserve">62. </s>
            <s xml:id="echoid-s1158" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1159" xml:space="preserve">II, in q̊ ☉(sun) fuit tꝑe & </s>
            <s xml:id="echoid-s1160" xml:space="preserve">hora intronizationis, nunc ſinu
              <lb/>
            merauero arcũ à principio ♈, inueniã uti 62. </s>
            <s xml:id="echoid-s1161" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1162" xml:space="preserve">26. </s>
            <s xml:id="echoid-s1163" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1164" xml:space="preserve">cõplemẽtũ eius eſt 27. </s>
            <s xml:id="echoid-s1165" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1166" xml:space="preserve">34
              <lb/>
            mi. </s>
            <s xml:id="echoid-s1167" xml:space="preserve">ſinus aũt cõplementi 46278. </s>
            <s xml:id="echoid-s1168" xml:space="preserve">declinationẽ puncti terminantis, arcũ iam inueni ꝓpo
              <lb/>
            ſitione 5. </s>
            <s xml:id="echoid-s1169" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1170" xml:space="preserve">20. </s>
            <s xml:id="echoid-s1171" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1172" xml:space="preserve">42. </s>
            <s xml:id="echoid-s1173" xml:space="preserve">cõplementũ declinatiõis eſt 69. </s>
            <s xml:id="echoid-s1174" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1175" xml:space="preserve">18. </s>
            <s xml:id="echoid-s1176" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1177" xml:space="preserve">ſinus uero cõplemen
              <lb/>
            ti iſtius 93544. </s>
            <s xml:id="echoid-s1178" xml:space="preserve">Iam ita duco ſinum minorem 46278. </s>
            <s xml:id="echoid-s1179" xml:space="preserve">in totũ ſinum, & </s>
            <s xml:id="echoid-s1180" xml:space="preserve">productum diui
              <lb/>
            do in ſinum maiorem, ſcilicet 93544. </s>
            <s xml:id="echoid-s1181" xml:space="preserve">at in quotiente prouenient 49471. </s>
            <s xml:id="echoid-s1182" xml:space="preserve">arcus erit 29.
              <lb/>
            </s>
            <s xml:id="echoid-s1183" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1184" xml:space="preserve">39. </s>
            <s xml:id="echoid-s1185" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s1186" xml:space="preserve">eum ſi ſubtraxero à 90. </s>
            <s xml:id="echoid-s1187" xml:space="preserve">remanebit aſcenſio recta quæſita 60. </s>
            <s xml:id="echoid-s1188" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s1189" xml:space="preserve">29. </s>
            <s xml:id="echoid-s1190" xml:space="preserve">minut.</s>
            <s xml:id="echoid-s1191" xml:space="preserve"/>
          </p>
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