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-div173" type="section" level="1" n="90">
          <p>
            <s xml:id="echoid-s6017" xml:space="preserve">
              <pb file="0075" n="75" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
            declinationis in ſinum diſtantiæ à meridiano, ꝓductũ diuide in totum, arcus quotientis
              <lb/>
              <note position="right" xlink:label="note-0075-01" xlink:href="note-0075-01a" xml:space="preserve">
                <emph style="it">Inuentum</emph>
                <lb/>
                <emph style="it">primum</emph>
                <lb/>
                <emph style="it">ex lateri in</emph>
                <lb/>
                <emph style="it">greſſu de-</emph>
                <lb/>
                <emph style="it">prehẽſum.</emph>
              </note>
            dicetur inuentũ primũ. </s>
            <s xml:id="echoid-s6018" xml:space="preserve">Mox duc & </s>
            <s xml:id="echoid-s6019" xml:space="preserve">ſinũ minorẽ ex ſinu cõplementi huius primi inuenti
              <lb/>
            & </s>
            <s xml:id="echoid-s6020" xml:space="preserve">ſinu declinationis ſtellæ uel propoſiti in totũ, ꝓductũ diuide in maiorẽ, & </s>
            <s xml:id="echoid-s6021" xml:space="preserve">arcũ quoti-
              <lb/>
            entis ſubtrahe de 90. </s>
            <s xml:id="echoid-s6022" xml:space="preserve">reliquũ adde ad altitudinem poli tuæ regiõis, & </s>
            <s xml:id="echoid-s6023" xml:space="preserve">habebis inuentũ ſe
              <lb/>
            cundũ. </s>
            <s xml:id="echoid-s6024" xml:space="preserve">Deinde ducito ſinus utriuſ cõplementi in ſe, ꝓductũ diuide in totũ, arcum quoti
              <lb/>
              <note position="right" xlink:label="note-0075-02" xlink:href="note-0075-02a" xml:space="preserve">
                <emph style="it">Inuentum</emph>
                <lb/>
                <emph style="it">ſecundum,</emph>
                <lb/>
                <emph style="it">ſecũdũ are-</emph>
                <lb/>
                <emph style="it">am aſſeque</emph>
                <lb/>
                <emph style="it">ris.</emph>
              </note>
            entis ſubduc de 90. </s>
            <s xml:id="echoid-s6025" xml:space="preserve">& </s>
            <s xml:id="echoid-s6026" xml:space="preserve">ſi ſecundũ inuentũ ſit minus ̈ 90. </s>
            <s xml:id="echoid-s6027" xml:space="preserve">remanebit tibi inuentũ tertium,
              <lb/>
            ſi aũt plus 90. </s>
            <s xml:id="echoid-s6028" xml:space="preserve">fuerit, adhuc adde arcũ quotientis, & </s>
            <s xml:id="echoid-s6029" xml:space="preserve">habebis inuentũ tertium. </s>
            <s xml:id="echoid-s6030" xml:space="preserve">Porrò ad-
              <lb/>
            huc ꝓpone tibi ſinũ inuentorũ primi & </s>
            <s xml:id="echoid-s6031" xml:space="preserve">tertij, minorẽ exijs duc in totum, & </s>
            <s xml:id="echoid-s6032" xml:space="preserve">productũ di-
              <lb/>
            uide in maiorem, arcus q̊tientis dabit portionẽ circuli uerticalis inter uerticẽ capitis & </s>
            <s xml:id="echoid-s6033" xml:space="preserve">
              <lb/>
            circulum poſitionis interceptũ quẽ quærebas. </s>
            <s xml:id="echoid-s6034" xml:space="preserve">Sed ſi diſtantia puncti ꝓpoſiti uel ſtellæ à
              <lb/>
              <note position="right" xlink:label="note-0075-03" xlink:href="note-0075-03a" xml:space="preserve">
                <emph style="it">Inuentum</emph>
                <lb/>
                <emph style="it">tertium ex</emph>
                <lb/>
                <emph style="it">lateribus</emph>
                <lb/>
                <emph style="it">patet.</emph>
              </note>
            meridiano præciſe fuerit 90. </s>
            <s xml:id="echoid-s6035" xml:space="preserve">graduũ, tunc cõplementũ declinationis erit inuentũ primũ,
              <lb/>
            & </s>
            <s xml:id="echoid-s6036" xml:space="preserve">latitudo regionis inuentũ ſecundũ, tertiũ uero inuenies ut antea, ſimiliter & </s>
            <s xml:id="echoid-s6037" xml:space="preserve">arcũ quæ-
              <lb/>
            ſitum. </s>
            <s xml:id="echoid-s6038" xml:space="preserve">Quod ſi qũt diſtantia à meridiano maior fuerit ̈ 90. </s>
            <s xml:id="echoid-s6039" xml:space="preserve">ſubtrahe eam de ſemicirculo
              <lb/>
            ſinum quo cõplementi duc in ſinum cõplementi declinationis, ꝓductũ diuide in ſinum
              <lb/>
              <note position="right" xlink:label="note-0075-04" xlink:href="note-0075-04a" xml:space="preserve">
                <emph style="it">Introitus d</emph>
                <lb/>
                <emph style="it">realis quæ</emph>
                <lb/>
                <emph style="it">ſitum oſten</emph>
                <lb/>
                <emph style="it">dit.</emph>
              </note>
            totũ, & </s>
            <s xml:id="echoid-s6040" xml:space="preserve">quotiens dabit inuentũ primũ, cuius cõplementũ ſimul & </s>
            <s xml:id="echoid-s6041" xml:space="preserve">ſinũ declinationis ſtel-
              <lb/>
            læ ſi tibi proponas, minorem uero nume℞ ducas in totum, diuidas aũt ꝓductum in maio
              <lb/>
            rem, & </s>
            <s xml:id="echoid-s6042" xml:space="preserve">arcum quotientis ſubtrahas de 90. </s>
            <s xml:id="echoid-s6043" xml:space="preserve">ſimiliter & </s>
            <s xml:id="echoid-s6044" xml:space="preserve">reſiduũ de latitudine regiõis, rema-
              <lb/>
            nebit inuentũ ſecundũ. </s>
            <s xml:id="echoid-s6045" xml:space="preserve">Mox ꝓcede hic, ut antea edoctus es, quãdo diſtãtia ſtellæ minor
              <lb/>
              <note position="right" xlink:label="note-0075-05" xlink:href="note-0075-05a" xml:space="preserve">
                <emph style="it">Inucntum</emph>
                <lb/>
                <emph style="it">primum ꝑ</emph>
                <lb/>
                <emph style="it">latera ad-</emph>
                <lb/>
                <emph style="it">diſces.</emph>
              </note>
            erat ̈ 90. </s>
            <s xml:id="echoid-s6046" xml:space="preserve">Operæpreciũ q̊ eſt ſcire, ꝙ qñ inuentũ ſecundũ maius eſt ̈ 90. </s>
            <s xml:id="echoid-s6047" xml:space="preserve">tunc etiã ter-
              <lb/>
            tium erit amplius eo, at ſi ita contingat, tũc ſubtrahe inuentũ tertiũ de ſemicirculo, & </s>
            <s xml:id="echoid-s6048" xml:space="preserve">
              <lb/>
            inuentũ primũ etiã paulò diligẽtius cõſidera, numerũ´ minorẽ duc in totũ, & </s>
            <s xml:id="echoid-s6049" xml:space="preserve">productũ
              <lb/>
              <note position="right" xlink:label="note-0075-06" xlink:href="note-0075-06a" xml:space="preserve">
                <emph style="it">Inuentum</emph>
                <lb/>
                <emph style="it">ſecundum</emph>
                <lb/>
                <emph style="it">areatim de</emph>
                <lb/>
                <emph style="it">prebendis.</emph>
                <lb/>
                <emph style="it">Operatio</emph>
                <lb/>
                <emph style="it">arcalis.</emph>
              </note>
            diuide in maiorẽ, arcus quotientis dabit arcũ circuli uerticalis quæſitũ. </s>
            <s xml:id="echoid-s6050" xml:space="preserve">Fieri etiã poteſt, ut
              <lb/>
            inuentũ ſecundũ ſit quadra circuli, & </s>
            <s xml:id="echoid-s6051" xml:space="preserve">tũc quo inuentũ tertiũ erit quadra circuli, at ſic
              <lb/>
            inuento primo habito, nõ eſt ꝙ amplius oꝑeris, ſiquidẽ illud ipſum inuentũ primũ eſt ar-
              <lb/>
            cus circuli uerticalis quæſitus. </s>
            <s xml:id="echoid-s6052" xml:space="preserve">Ethactenus ꝗdem diſſeruimus de ſtellis & </s>
            <s xml:id="echoid-s6053" xml:space="preserve">punctis, quæ
              <lb/>
            declinationẽ habent ſeptentrionalẽ, nunc reliquũ eſt & </s>
            <s xml:id="echoid-s6054" xml:space="preserve">de ijsdicere quæ meridionalem
              <lb/>
            habent declinationẽ, ibi tu duc ſinum declinationis ſtellæ in ſinũ diſtantiæ ſtellæ à meri-
              <lb/>
              <note position="right" xlink:label="note-0075-07" xlink:href="note-0075-07a" xml:space="preserve">
                <emph style="it">De ſtellis et</emph>
                <lb/>
                <emph style="it">punctis ha</emph>
                <lb/>
                <emph style="it">bentibus de</emph>
                <lb/>
                <emph style="it">clinationẽ</emph>
                <lb/>
                <emph style="it">meridionæ</emph>
                <lb/>
                <emph style="it">lem.</emph>
              </note>
            diano, productũ diuide in ſinũ ꝑfectũ, arcus q̊tientis erit inuentũ primũ. </s>
            <s xml:id="echoid-s6055" xml:space="preserve">Deinde uter ſi-
              <lb/>
            nus fuerit maior ex cõplemento huius inuenti & </s>
            <s xml:id="echoid-s6056" xml:space="preserve">declinationis, ducatur in totum, & </s>
            <s xml:id="echoid-s6057" xml:space="preserve">diui
              <lb/>
            datur in alte℞. </s>
            <s xml:id="echoid-s6058" xml:space="preserve">A cõplemẽto quotientis huius ſubtrahe latitudinẽ regiõis, & </s>
            <s xml:id="echoid-s6059" xml:space="preserve">manebit in-
              <lb/>
            uentum ſecundũ. </s>
            <s xml:id="echoid-s6060" xml:space="preserve">Vtriuſ huius inuẽti cõplementa duc in ſe, ꝓductũ in totũ ſinũ diuide,
              <lb/>
            & </s>
            <s xml:id="echoid-s6061" xml:space="preserve">cõplementũ huius quotientis oſtendit inuentũ tertiũ, ſi iam minorẽ ſinũ primi inuen-
              <lb/>
            ti & </s>
            <s xml:id="echoid-s6062" xml:space="preserve">tertij ducas in totum, ꝓductũ uero diuidas in maiorẽ, arcus quotientis oſtendet arcũ
              <lb/>
              <note position="right" xlink:label="note-0075-08" xlink:href="note-0075-08a" xml:space="preserve">
                <emph style="it">Inuentum</emph>
                <lb/>
                <emph style="it">primum ꝑ</emph>
                <lb/>
                <emph style="it">areã inſpie</emph>
                <lb/>
                <emph style="it">ads.</emph>
              </note>
            circuli uerticalis optatũ, & </s>
            <s xml:id="echoid-s6063" xml:space="preserve">hactenus tam operoſe quæſitum. </s>
            <s xml:id="echoid-s6064" xml:space="preserve">Si aũt declinatio nulla eſt
              <lb/>
            ſtellæ uel puncti ab æquinoctiali, tunc inuentũ primũ ſit tibi diſtantia ſtellæ uel puncti à
              <lb/>
            meridiano, & </s>
            <s xml:id="echoid-s6065" xml:space="preserve">inuentum ſecundũ erit cõplementũ altitudinis poli, tertium uero acquires,
              <lb/>
            ſi ſinum altitudinis poli ducas in ſinũ cõplementi diſtantiæ à meridiano, diuidas aũt in ſi-
              <lb/>
              <note position="right" xlink:label="note-0075-09" xlink:href="note-0075-09a" xml:space="preserve">
                <emph style="it">Inuentũ ſe@</emph>
                <lb/>
                <emph style="it">cundum.</emph>
              </note>
            num ꝑfectũ, tunc tibi cõplementũ q̊tientis dabit inuentũ tertiũ. </s>
            <s xml:id="echoid-s6066" xml:space="preserve">Iam ſi minorem nurr e℞
              <lb/>
              <note position="right" xlink:label="note-0075-10" xlink:href="note-0075-10a" xml:space="preserve">
                <emph style="it">Inuentum</emph>
                <lb/>
                <emph style="it">tertim.</emph>
              </note>
            ex inuento tertio & </s>
            <s xml:id="echoid-s6067" xml:space="preserve">diſtãtia à meridiano ducas in totũ, & </s>
            <s xml:id="echoid-s6068" xml:space="preserve">diuidas in maiorem, tunc arcus
              <lb/>
            quotientis ꝓducet arcũ circuli uerticalis inter zenith & </s>
            <s xml:id="echoid-s6069" xml:space="preserve">circulũ poſitionis, qui tranſit per
              <lb/>
              <note position="right" xlink:label="note-0075-11" xlink:href="note-0075-11a" xml:space="preserve">
                <emph style="it">De ſtellis ſi</emph>
                <lb/>
                <emph style="it">ue punctis</emph>
                <lb/>
                <emph style="it">declinatio-</emph>
                <lb/>
                <emph style="it">nem ab æꝗ</emph>
                <lb/>
                <emph style="it">noctiali nõ</emph>
                <lb/>
                <emph style="it">habẽtibus.</emph>
              </note>
            locum ſtellæ. </s>
            <s xml:id="echoid-s6070" xml:space="preserve">?</s>
            <s xml:id="echoid-s6071" xml:space="preserve">?Exempli loco quæram ecce in ipſo loco intronizatiõis arcum circuli
              <lb/>
            uerticalis inter zenith ſiue polum horizontis & </s>
            <s xml:id="echoid-s6072" xml:space="preserve">circulum poſitiõis, qui per locũ Solis du
              <lb/>
            citur, ad horã intronizatiõis, quæ ꝗa facta eſt hora 9 ante meridiẽ ſatis fœliciter, Sol tũc
              <lb/>
            fuit in 2. </s>
            <s xml:id="echoid-s6073" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6074" xml:space="preserve">26. </s>
            <s xml:id="echoid-s6075" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6076" xml:space="preserve">II, duco igit̃ ſinum cõplementi declinatiõis loci ☉(sun). </s>
            <s xml:id="echoid-s6077" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s6078" xml:space="preserve">93544. </s>
            <s xml:id="echoid-s6079" xml:space="preserve">in ſinũ
              <lb/>
            diſtãtiæ ☉(sun) à meridie. </s>
            <s xml:id="echoid-s6080" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s6081" xml:space="preserve">70710. </s>
            <s xml:id="echoid-s6082" xml:space="preserve">ꝓductũ in totũ diuiſo, remanẽt 66145. </s>
            <s xml:id="echoid-s6083" xml:space="preserve">inuentũ illud pri-
              <lb/>
            mũ, cuius cõplementũ eſt 48. </s>
            <s xml:id="echoid-s6084" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6085" xml:space="preserve">35. </s>
            <s xml:id="echoid-s6086" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6087" xml:space="preserve">ſinus uero 74991. </s>
            <s xml:id="echoid-s6088" xml:space="preserve">Nunciã duco ſinũ declinatio
              <lb/>
              <note position="right" xlink:label="note-0075-12" xlink:href="note-0075-12a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
                <emph style="it">de loco So</emph>
                <lb/>
                <emph style="it">lis introni-</emph>
                <lb/>
                <emph style="it">zationis</emph>
                <lb/>
                <emph style="it">hora.</emph>
              </note>
            nis 35347. </s>
            <s xml:id="echoid-s6089" xml:space="preserve">ꝗa minorẽ in totũ, & </s>
            <s xml:id="echoid-s6090" xml:space="preserve">ꝓductum diuido in linũ cõplementi primi inuenti, ꝓue-
              <lb/>
            nient in q̊tiente 47135. </s>
            <s xml:id="echoid-s6091" xml:space="preserve">arcus eius eſt 28. </s>
            <s xml:id="echoid-s6092" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6093" xml:space="preserve">8. </s>
            <s xml:id="echoid-s6094" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6095" xml:space="preserve">is de 90. </s>
            <s xml:id="echoid-s6096" xml:space="preserve">ſubductus, relinꝗt 61. </s>
            <s xml:id="echoid-s6097" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6098" xml:space="preserve">52
              <lb/>
            mi. </s>
            <s xml:id="echoid-s6099" xml:space="preserve">ijs addo altitudinem poli.</s>
            <s xml:id="echoid-s6100" xml:space="preserve">ſ.</s>
            <s xml:id="echoid-s6101" xml:space="preserve">48. </s>
            <s xml:id="echoid-s6102" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6103" xml:space="preserve">20. </s>
            <s xml:id="echoid-s6104" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6105" xml:space="preserve">& </s>
            <s xml:id="echoid-s6106" xml:space="preserve">erit ſumma 110. </s>
            <s xml:id="echoid-s6107" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6108" xml:space="preserve">12. </s>
            <s xml:id="echoid-s6109" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6110" xml:space="preserve">dicetur´ in-
              <lb/>
            uentum ſecundum, q̊d ꝗa maius eſt ̈ 90. </s>
            <s xml:id="echoid-s6111" xml:space="preserve">ſubtraho de ſemicirculo, & </s>
            <s xml:id="echoid-s6112" xml:space="preserve">remanent 69. </s>
            <s xml:id="echoid-s6113" xml:space="preserve">gra.
              <lb/>
            </s>
            <s xml:id="echoid-s6114" xml:space="preserve">48. </s>
            <s xml:id="echoid-s6115" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6116" xml:space="preserve">Cõplementũ eſt 20. </s>
            <s xml:id="echoid-s6117" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6118" xml:space="preserve">12. </s>
            <s xml:id="echoid-s6119" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6120" xml:space="preserve">cuius ſinum 34529. </s>
            <s xml:id="echoid-s6121" xml:space="preserve">duco in ſinum cõplementi in-
              <lb/>
            uenti primi 48. </s>
            <s xml:id="echoid-s6122" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6123" xml:space="preserve">35. </s>
            <s xml:id="echoid-s6124" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s6125" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s6126" xml:space="preserve">74991. </s>
            <s xml:id="echoid-s6127" xml:space="preserve">ꝓductum diuido in totum, & </s>
            <s xml:id="echoid-s6128" xml:space="preserve">in q̊tiente, pdeũt 25904
              <lb/>
            arcus eius eſt 15. </s>
            <s xml:id="echoid-s6129" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s6130" xml:space="preserve">cue addo 90. </s>
            <s xml:id="echoid-s6131" xml:space="preserve">gradus(eo ꝙ inuentũ ſecundũ quadrãte maius eſt) </s>
          </p>
        </div>
      </text>
    </echo>
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