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        <div xml:id="echoid-div166" type="section" level="1" n="87">
          <p>
            <s xml:id="echoid-s5626" xml:space="preserve">
              <pb file="0072" n="72" rhead="GENVINVS VSVS"/>
            tudinis huius ſecundiloci tibi propones, ſimiliter & </s>
            <s xml:id="echoid-s5627" xml:space="preserve">ſinum intercapedinis, minorem ex
              <lb/>
            ijs duces in totum, productum diuides in minorem, & </s>
            <s xml:id="echoid-s5628" xml:space="preserve">arcus quotientis dabit differenti-
              <lb/>
            am longitudinis, at iſtud ip ſum in hac re te celare noluimus.</s>
            <s xml:id="echoid-s5629" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div168" type="section" level="1" n="88">
          <head xml:id="echoid-head92" xml:space="preserve">PRONVNCIATVM LXXVI.</head>
          <p>
            <s xml:id="echoid-s5630" xml:space="preserve">Cognita tantum unius loci propoſiti eleuatione polari ſimul & </s>
            <s xml:id="echoid-s5631" xml:space="preserve">alterius,
              <lb/>
            at hinc etiam intercapedine habita inter utran, differentiam adhuc longi
              <lb/>
            tudinum & </s>
            <s xml:id="echoid-s5632" xml:space="preserve">angulum poſitionis ab altero ad alterum inuenire.</s>
            <s xml:id="echoid-s5633" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5634" xml:space="preserve">Primũ oĩm hic tibi ꝓpone gradus & </s>
            <s xml:id="echoid-s5635" xml:space="preserve">ſinus cõplemento℞ utriuſ eleuationis poli, gra-
              <lb/>
            dus etiã & </s>
            <s xml:id="echoid-s5636" xml:space="preserve">ſinus diſtãtiæ ſiue intercapedinis inter utrũ locum, ſiquidem certum eſt quũ
              <lb/>
              <note position="left" xlink:label="note-0072-01" xlink:href="note-0072-01a" xml:space="preserve">
                <emph style="it">Meteoroſco</emph>
                <lb/>
                <emph style="it">piũ abſolu-</emph>
                <lb/>
                <emph style="it">tißimum in</emph>
                <lb/>
                <emph style="it">Aſtronomi</emph>
                <lb/>
                <emph style="it">co Cæſareo</emph>
                <lb/>
                <emph style="it">ſimiliter in</emph>
                <lb/>
                <emph style="it">Coſmogra-</emph>
                <lb/>
                <emph style="it">phia. Com-</emph>
                <lb/>
                <emph style="it">poſitiones</emph>
                <lb/>
                <emph style="it">uero eiuſdẽ</emph>
                <lb/>
                <emph style="it">in Plani-</emph>
                <lb/>
                <emph style="it">ſphærio, li-</emph>
                <lb/>
                <emph style="it">bris à nobis</emph>
                <lb/>
                <emph style="it">æditis.</emph>
              </note>
            intercapedo ad 90. </s>
            <s xml:id="echoid-s5637" xml:space="preserve">gradus nõ adſurgat, cõplemẽtũ alte℞ latitudinis oportere eſſe maius
              <lb/>
            intercapedine, ne eſt q̊d in hoc uſu ulterius requiras, plura aũt ſuꝑ hac re inuenies in
              <lb/>
            Mereoroſcopijs noſtris, ſiquidẽ duo cõſcripſimus, alte℞ ſpeculare uocauimus, alterũ recti
              <lb/>
            linearũ, nũc porrò quæ cœpimus ſic proſequemur. </s>
            <s xml:id="echoid-s5638" xml:space="preserve">Numeros illos tres, puta utrun cõ-
              <lb/>
            plementũ latitudinũ & </s>
            <s xml:id="echoid-s5639" xml:space="preserve">intercapedinis arcũ ita diſpone, ut unũ colloces ſuꝑ alterũ, & </s>
            <s xml:id="echoid-s5640" xml:space="preserve">ma
              <lb/>
            iorem quidẽ ſupremo loco, in medio aũt mediũ, & </s>
            <s xml:id="echoid-s5641" xml:space="preserve">minimũ inſimo loco, hinc ſubtrahe me
              <lb/>
            dium à maximo, & </s>
            <s xml:id="echoid-s5642" xml:space="preserve">reſiduũ dicet̃ differentia prima. </s>
            <s xml:id="echoid-s5643" xml:space="preserve">Mox ſubtrahe etiã minorẽ de 90. </s>
            <s xml:id="echoid-s5644" xml:space="preserve">qđ
              <lb/>
            relinquetur, appellabitur differentia ſecunda. </s>
            <s xml:id="echoid-s5645" xml:space="preserve">Poſthæc ꝓpone tibi & </s>
            <s xml:id="echoid-s5646" xml:space="preserve">ſinum cõplementi
              <lb/>
            primæ differentiæ, & </s>
            <s xml:id="echoid-s5647" xml:space="preserve">inde ſubtrahe ſinum differentiæ ſecundæ, reſiduũ duc in ſinũ cõple-
              <lb/>
            menti maioris arcus, ꝓductũ diuide in ſinũ maioris, & </s>
            <s xml:id="echoid-s5648" xml:space="preserve">q̊tientẽ adde ad ſinũ arcus primæ
              <lb/>
            differentiæ, ſummã illã quadrato, ſimiliter & </s>
            <s xml:id="echoid-s5649" xml:space="preserve">ſinũ differentiæ ſecundæ, at hinc illa duo
              <lb/>
            quadrata ſimul adde in unã ſummã, ex ea quære radicẽ quadratã, arcus deinceps huius ra
              <lb/>
            dicis ſubtractus de 90. </s>
            <s xml:id="echoid-s5650" xml:space="preserve">relinquit argumentum operationis. </s>
            <s xml:id="echoid-s5651" xml:space="preserve">Iuxta ſinũ illius argumenti re
              <lb/>
            pone & </s>
            <s xml:id="echoid-s5652" xml:space="preserve">ſinũ cõplementi maioris latitudinis, minorẽ duc in totum, & </s>
            <s xml:id="echoid-s5653" xml:space="preserve">ꝓductũ diuide in
              <lb/>
              <note position="left" xlink:label="note-0072-02" xlink:href="note-0072-02a" xml:space="preserve">
                <emph style="it">Per latera-</emph>
                <lb/>
                <emph style="it">lem introi-</emph>
                <lb/>
                <emph style="it">tum ſimile</emph>
                <lb/>
                <emph style="it">aſſequeris.</emph>
              </note>
            maiorem, ſic arcus q̊tientis ꝓducet differentiam longitudinis quã primo quærebam. </s>
            <s xml:id="echoid-s5654" xml:space="preserve">Ad
              <lb/>
            hæc ducito & </s>
            <s xml:id="echoid-s5655" xml:space="preserve">ſinũ cõplementi latitudinis minoris in ſinũ differentiæ lõgitudinis, produ-
              <lb/>
            ctum diuide in ſinũ totũ, & </s>
            <s xml:id="echoid-s5656" xml:space="preserve">quotientem rurſus ſepone in aliquẽ locũ, ei´ adiunge ſinum
              <lb/>
            intercapedinis minorem duc in totũ, & </s>
            <s xml:id="echoid-s5657" xml:space="preserve">ꝓductũ diuide cũ maiori, hinc arcus q̊tientis mon
              <lb/>
            ſtrat angulum poſitiõis quæſitúm. </s>
            <s xml:id="echoid-s5658" xml:space="preserve">At hæc ita demũ ueritatẽ obtinent, ſi locus ſecũdus
              <lb/>
            Auſtralior extiterit, qui ſi ſit Borealior ̈ primus & </s>
            <s xml:id="echoid-s5659" xml:space="preserve">datus locus, iuxta quem angulus po
              <lb/>
            ſitionis accipitur, tunc quære angulũ poſitionis hoc modo. </s>
            <s xml:id="echoid-s5660" xml:space="preserve">Fac tibi proponas ſinũ argu-
              <lb/>
              <note position="left" xlink:label="note-0072-03" xlink:href="note-0072-03a" xml:space="preserve">
                <emph style="it">Arealis in-</emph>
                <lb/>
                <emph style="it">troitus.</emph>
              </note>
            menti operationis ſuperius inuentũ, & </s>
            <s xml:id="echoid-s5661" xml:space="preserve">ſintercapedinis minorũ duc in totum, & </s>
            <s xml:id="echoid-s5662" xml:space="preserve">ꝓdu-
              <lb/>
            cto in maiorem diuiſo, arcus quotientis angulũ dabit poſitionis à ſeptentrione adortum,
              <lb/>
            ſi tamen locus ſecundus ſuerit orientalior, is ſi ſit occidẽtalior, numerandus erit tibi angu-
              <lb/>
              <note position="left" xlink:label="note-0072-04" xlink:href="note-0072-04a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
                <emph style="it">diſtãtiæ in-</emph>
                <lb/>
                <emph style="it">ter Augu-</emph>
                <lb/>
                <emph style="it">ſtã &</emph>
              Hie
                <lb/>
                <emph style="it">ruſalem.</emph>
              </note>
            lus ille à meridiano ſeptentrionali ad occaſum. </s>
            <s xml:id="echoid-s5663" xml:space="preserve">?</s>
            <s xml:id="echoid-s5664" xml:space="preserve">?Sed iã opus eſt rem exemplo plenius
              <lb/>
            excutere. </s>
            <s xml:id="echoid-s5665" xml:space="preserve">Age igitur Auguſta in latitudine habet 48. </s>
            <s xml:id="echoid-s5666" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5667" xml:space="preserve">20. </s>
            <s xml:id="echoid-s5668" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5669" xml:space="preserve">Hieruſalem aũt 31. </s>
            <s xml:id="echoid-s5670" xml:space="preserve">gra.
              <lb/>
            </s>
            <s xml:id="echoid-s5671" xml:space="preserve">40. </s>
            <s xml:id="echoid-s5672" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5673" xml:space="preserve">ab Auguſta etiã uſ in Hieruſalem ſunt 491. </s>
            <s xml:id="echoid-s5674" xml:space="preserve">miliaria, quæ faciunt 32. </s>
            <s xml:id="echoid-s5675" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5676" xml:space="preserve">44. </s>
            <s xml:id="echoid-s5677" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5678" xml:space="preserve">
              <lb/>
            nunc aſſumo numeros illos tres, cõplementum minoris latitudinis, at is numerus erit
              <lb/>
            maior, complementum latitudinis maioris medium tenebit, & </s>
            <s xml:id="echoid-s5679" xml:space="preserve">intercapedo infimum lo-
              <lb/>
            cum, quia minor. </s>
            <s xml:id="echoid-s5680" xml:space="preserve">Medium porrò ſubtraho à maiori, & </s>
            <s xml:id="echoid-s5681" xml:space="preserve">remanet differentia prima, mi-
              <lb/>
            norem uero à 90. </s>
            <s xml:id="echoid-s5682" xml:space="preserve">& </s>
            <s xml:id="echoid-s5683" xml:space="preserve">relinquitur differentia ſecunda, diſponuntur hoc modo.</s>
            <s xml:id="echoid-s5684" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5685" xml:space="preserve">Numerus maior 58. </s>
            <s xml:id="echoid-s5686" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5687" xml:space="preserve">20. </s>
            <s xml:id="echoid-s5688" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5689" xml:space="preserve">complementum minoris latitudinis.</s>
            <s xml:id="echoid-s5690" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5691" xml:space="preserve">Mediuserit 41. </s>
            <s xml:id="echoid-s5692" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5693" xml:space="preserve">49. </s>
            <s xml:id="echoid-s5694" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5695" xml:space="preserve">complementum maioris latitudinis.</s>
            <s xml:id="echoid-s5696" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5697" xml:space="preserve">Numerus minor 32. </s>
            <s xml:id="echoid-s5698" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5699" xml:space="preserve">44. </s>
            <s xml:id="echoid-s5700" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5701" xml:space="preserve">diſtantia locorum.</s>
            <s xml:id="echoid-s5702" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5703" xml:space="preserve">Differentia prima 16. </s>
            <s xml:id="echoid-s5704" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5705" xml:space="preserve">40. </s>
            <s xml:id="echoid-s5706" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5707" xml:space="preserve">ſcilicet complementorum latitud.</s>
            <s xml:id="echoid-s5708" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5709" xml:space="preserve">Differentia ſecunda 57. </s>
            <s xml:id="echoid-s5710" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5711" xml:space="preserve">16. </s>
            <s xml:id="echoid-s5712" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5713" xml:space="preserve">hoc eſt complementum diſtantiæ.</s>
            <s xml:id="echoid-s5714" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5715" xml:space="preserve">Iam ꝓpono mihi ſinũ cõplemẽti primæ differentiæ. </s>
            <s xml:id="echoid-s5716" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5717" xml:space="preserve">95798. </s>
            <s xml:id="echoid-s5718" xml:space="preserve">inde ſubtraho ſinũ ſecundæ
              <lb/>
            differentiæ, puta 84119. </s>
            <s xml:id="echoid-s5719" xml:space="preserve">& </s>
            <s xml:id="echoid-s5720" xml:space="preserve">remanent 11679. </s>
            <s xml:id="echoid-s5721" xml:space="preserve">quẽ numerũ duco in ſinũ cõplementi maio-
              <lb/>
            ris. </s>
            <s xml:id="echoid-s5722" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5723" xml:space="preserve">52497. </s>
            <s xml:id="echoid-s5724" xml:space="preserve">ꝓductũ diuido cũ ſinu maioris. </s>
            <s xml:id="echoid-s5725" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5726" xml:space="preserve">85111. </s>
            <s xml:id="echoid-s5727" xml:space="preserve">& </s>
            <s xml:id="echoid-s5728" xml:space="preserve">quotiens dat 7203. </s>
            <s xml:id="echoid-s5729" xml:space="preserve">hæc addo ad
              <lb/>
            ſinũ primæ differẽtiæ, puta 28680. </s>
            <s xml:id="echoid-s5730" xml:space="preserve">& </s>
            <s xml:id="echoid-s5731" xml:space="preserve">ꝓueniũt 35883. </s>
            <s xml:id="echoid-s5732" xml:space="preserve">numerus hic ſi quadretur, ꝓducit
              <lb/>
            1287589689. </s>
            <s xml:id="echoid-s5733" xml:space="preserve">Mox quadrabis etiã ſinus ſecũdæ differentiæ. </s>
            <s xml:id="echoid-s5734" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5735" xml:space="preserve">84119. </s>
            <s xml:id="echoid-s5736" xml:space="preserve">facit 7076106161.
              <lb/>
            </s>
            <s xml:id="echoid-s5737" xml:space="preserve">utrun hoc quadratũ cõiungo in unã ſummã, quæ erit 8363605850. </s>
            <s xml:id="echoid-s5738" xml:space="preserve">radix illius quadra
              <lb/>
            ta eſt 91453. </s>
            <s xml:id="echoid-s5739" xml:space="preserve">lã ſi arcũ radicis. </s>
            <s xml:id="echoid-s5740" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5741" xml:space="preserve">66. </s>
            <s xml:id="echoid-s5742" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5743" xml:space="preserve">8. </s>
            <s xml:id="echoid-s5744" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5745" xml:space="preserve">ſubtraxero à 90. </s>
            <s xml:id="echoid-s5746" xml:space="preserve">relinquunt̃ 23. </s>
            <s xml:id="echoid-s5747" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5748" xml:space="preserve">52. </s>
            <s xml:id="echoid-s5749" xml:space="preserve">mi.</s>
            <s xml:id="echoid-s5750" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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