Apian, Petrus, Instrvmentvm Sinvvm, sev primi mobilis

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        <div xml:id="echoid-div153" type="section" level="1" n="81">
          <p>
            <s xml:id="echoid-s5215" xml:space="preserve">
              <pb file="0069" n="69" rhead="TABVLARVM SINVVM."/>
            tiens eſt 47122. </s>
            <s xml:id="echoid-s5216" xml:space="preserve">arcus uero eius 28. </s>
            <s xml:id="echoid-s5217" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5218" xml:space="preserve">8. </s>
            <s xml:id="echoid-s5219" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5220" xml:space="preserve">eſt angulus iſte ſuperior. </s>
            <s xml:id="echoid-s5221" xml:space="preserve">Inferiorem porrò
              <lb/>
            ſic inquiro, ſinũ altitudinis Solis 44. </s>
            <s xml:id="echoid-s5222" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5223" xml:space="preserve">52. </s>
            <s xml:id="echoid-s5224" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5225" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5226" xml:space="preserve">70545. </s>
            <s xml:id="echoid-s5227" xml:space="preserve">tan̈ minorẽ duco in totũ, ꝓdu-
              <lb/>
            ctum diuido in ſinũ arcus inuenti 75011. </s>
            <s xml:id="echoid-s5228" xml:space="preserve">in quotiente uideo prouenire mihi 94046. </s>
            <s xml:id="echoid-s5229" xml:space="preserve">ar-
              <lb/>
            cus eius eſt 70. </s>
            <s xml:id="echoid-s5230" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5231" xml:space="preserve">8. </s>
            <s xml:id="echoid-s5232" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5233" xml:space="preserve">angulus inferior. </s>
            <s xml:id="echoid-s5234" xml:space="preserve">Et quia Sol eſt in ſigno Boreali, ſuperiorẽ an-
              <lb/>
            gulum ſubtraho ab inferiori, hoc eſt 28. </s>
            <s xml:id="echoid-s5235" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5236" xml:space="preserve">8. </s>
            <s xml:id="echoid-s5237" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5238" xml:space="preserve">à 70. </s>
            <s xml:id="echoid-s5239" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5240" xml:space="preserve">8. </s>
            <s xml:id="echoid-s5241" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5242" xml:space="preserve">ſic´ remanent 42. </s>
            <s xml:id="echoid-s5243" xml:space="preserve">gra.
              <lb/>
            </s>
            <s xml:id="echoid-s5244" xml:space="preserve">
              <note position="right" xlink:label="note-0069-01" xlink:href="note-0069-01a" xml:space="preserve">EXEM.
                <lb/>
              PLVM
                <lb/>
                <emph style="it">loain quo</emph>
                <lb/>
                <emph style="it">facta eſt in</emph>
                <lb/>
                <emph style="it">tronizatio.</emph>
                <lb/>
                <emph style="it">Longitudo</emph>
                <lb/>
                <emph style="it">Auguſtæ</emph>
                <lb/>
                <emph style="it">ab occidẽte</emph>
                <lb/>
                <emph style="it">gra. 28. mi.</emph>
                <lb/>
                <emph style="it">31.</emph>
              </note>
            cuius cõplementum eſt 48. </s>
            <s xml:id="echoid-s5245" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5246" xml:space="preserve">altitudo illa poli quæſita ad locum introniſationis.</s>
            <s xml:id="echoid-s5247" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div155" type="section" level="1" n="82">
          <head xml:id="echoid-head86" xml:space="preserve">PRONVNCIATVM LXX.</head>
          <p>
            <s xml:id="echoid-s5248" xml:space="preserve">Si quando duorum locorum longitudines ſunt æquales, & </s>
            <s xml:id="echoid-s5249" xml:space="preserve">inſuper eorum
              <lb/>
            latitudines notæ, at inæquales, diſtantiam inter ea ſecundum uiam directã
              <lb/>
            inueſtigare.</s>
            <s xml:id="echoid-s5250" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5251" xml:space="preserve">Quandocũ duo loca æquales habent gradus unà cum minutis in longitudine, argu
              <lb/>
            mentum rectum eſt ea ſub uno eſſe meridiano, & </s>
            <s xml:id="echoid-s5252" xml:space="preserve">ſinum hunc facile colliges in meridie
              <lb/>
            aſpiciendo Solem ſub horam 12. </s>
            <s xml:id="echoid-s5253" xml:space="preserve">quòd ſi locus ille altitudinem poli habuerit maiorem ̈
              <lb/>
            iſte alter à quo diſtantiam ſcire cupis, certum eſt eum directe poſitum eſſe uerſus ſepten
              <lb/>
              <note position="right" xlink:label="note-0069-02" xlink:href="note-0069-02a" xml:space="preserve">
                <emph style="it">Altitudo</emph>
                <lb/>
                <emph style="it">poli Augu-</emph>
                <lb/>
                <emph style="it">ſtana gra.</emph>
                <lb/>
                <emph style="it">4 s. mi. 20.</emph>
              </note>
            trionem, at eò monſtrat umbra Solis circa horam 12. </s>
            <s xml:id="echoid-s5254" xml:space="preserve">Sed ſi pauciores habeat gradus
              <lb/>
            in latitudine, ſitus erit uerſus meridiem directe ad Solem, quum dies medius eſt, iam ſi di
              <lb/>
            ſtantiam quæris, ſubtrahe latitudinem minorem à maiori, & </s>
            <s xml:id="echoid-s5255" xml:space="preserve">reſiduum tibi oſtendet di-
              <lb/>
              <note position="right" xlink:label="note-0069-03" xlink:href="note-0069-03a" xml:space="preserve">
                <emph style="it">Longitudo</emph>
                <lb/>
                <emph style="it">Erfordiana</emph>
                <lb/>
                <emph style="it">gra. 28</emph>
                <lb/>
                <emph style="it">mi. 30.</emph>
              </note>
            ſtantiam iſtam locorum in gradibus, at minutis, diſtantiam hanc in miliaria rediges,
              <lb/>
            ſi pro quolibet gradu 15. </s>
            <s xml:id="echoid-s5256" xml:space="preserve">miliaria cõnumeres Germanica uel 60. </s>
            <s xml:id="echoid-s5257" xml:space="preserve">Italica, & </s>
            <s xml:id="echoid-s5258" xml:space="preserve">ſemper pro 4
              <lb/>
            minutis graduũ unum minutũ miliarium. </s>
            <s xml:id="echoid-s5259" xml:space="preserve">?</s>
            <s xml:id="echoid-s5260" xml:space="preserve">? Exemplum ſit hoc tibi: </s>
            <s xml:id="echoid-s5261" xml:space="preserve">Si in ipſo loco in-
              <lb/>
            tronizationis, ubi longitudo eſt 28. </s>
            <s xml:id="echoid-s5262" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5263" xml:space="preserve">31. </s>
            <s xml:id="echoid-s5264" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5265" xml:space="preserve">latitudo autem 48. </s>
            <s xml:id="echoid-s5266" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5267" xml:space="preserve">20. </s>
            <s xml:id="echoid-s5268" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5269" xml:space="preserve">cupio ſcire
              <lb/>
              <note position="right" xlink:label="note-0069-04" xlink:href="note-0069-04a" xml:space="preserve">
                <emph style="it">Latitudo</emph>
                <lb/>
                <emph style="it">uero gra.</emph>
                <lb/>
                <emph style="it">51. mi. 10.</emph>
                <lb/>
                <emph style="it">Diſtantia</emph>
                <lb/>
                <emph style="it">inter Augu</emph>
                <lb/>
                <emph style="it">ſtam & Er</emph>
                <lb/>
                <emph style="it">fordiam.</emph>
              </note>
            ſitum ſimul & </s>
            <s xml:id="echoid-s5270" xml:space="preserve">diſtantiam Erfordiæ, propono etiam mihi gradus longitudinis Erfordiæ,
              <lb/>
            qui ſunt 28. </s>
            <s xml:id="echoid-s5271" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5272" xml:space="preserve">30. </s>
            <s xml:id="echoid-s5273" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5274" xml:space="preserve">latitudo aũt 51. </s>
            <s xml:id="echoid-s5275" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5276" xml:space="preserve">& </s>
            <s xml:id="echoid-s5277" xml:space="preserve">10. </s>
            <s xml:id="echoid-s5278" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5279" xml:space="preserve">habet, iam nunc conſidero, quòd lon
              <lb/>
            gitudo utriuſ eſt æqualis, eas etiam uni ſubeſſe meridiano, & </s>
            <s xml:id="echoid-s5280" xml:space="preserve">quia latitudo Er-
              <lb/>
            fordieñ, maior eſt Auguſta, certus ſum, quòd Erfordia reſpectu Auguſtæ ſit Borealis, ita
              <lb/>
            ut umbra Solis hora 12. </s>
            <s xml:id="echoid-s5281" xml:space="preserve">ſub meridiem mihi mõſtret Erfordiæ ſitum, ſi dehinc ſubtraho
              <lb/>
            latitudinẽ Auguſtanã à latitudine Erfordieñ. </s>
            <s xml:id="echoid-s5282" xml:space="preserve">remanent mibi 2. </s>
            <s xml:id="echoid-s5283" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5284" xml:space="preserve">40. </s>
            <s xml:id="echoid-s5285" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5286" xml:space="preserve">quibus reſo-
              <lb/>
            lutis, habeo 40. </s>
            <s xml:id="echoid-s5287" xml:space="preserve">miliaria. </s>
            <s xml:id="echoid-s5288" xml:space="preserve">diſtãtiã Erfordiæ ab Auguſta, quæ duæ ciuitates uno temporis
              <lb/>
              <note position="right" xlink:label="note-0069-05" xlink:href="note-0069-05a" xml:space="preserve">
                <emph style="it">Quare ha-</emph>
                <lb/>
                <emph style="it">ctenus alti-</emph>
                <lb/>
                <emph style="it">tudo poli</emph>
              </note>
            momẽto habẽt meridiẽ. </s>
            <s xml:id="echoid-s5289" xml:space="preserve">Nec eſt ꝙ mireris, cur hic latitudinẽ Auguſtæ poſuerim 48. </s>
            <s xml:id="echoid-s5290" xml:space="preserve">gra.
              <lb/>
            </s>
            <s xml:id="echoid-s5291" xml:space="preserve">20. </s>
            <s xml:id="echoid-s5292" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5293" xml:space="preserve">quũ tñ ſupra ſemꝑ 40. </s>
            <s xml:id="echoid-s5294" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5295" xml:space="preserve">tm̃ ſine minutis additis numerarim, ſiquidẽ ibi minuta
              <lb/>
            uolens prætermiſi, ut eò facilior tibi nota eſſet operatio, nunc ad reliqua progrediamur.</s>
            <s xml:id="echoid-s5296" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">
            <emph style="it">Auguſtana</emph>
            <lb/>
            <emph style="it">per gradus</emph>
            <lb/>
            <emph style="it">ſaltẽ & nõ</emph>
            <lb/>
            <emph style="it">ꝑ minuta e-</emph>
            <lb/>
            <emph style="it">tiam propo</emph>
            <lb/>
            <emph style="it">ſita ſit.</emph>
          </note>
        </div>
        <div xml:id="echoid-div157" type="section" level="1" n="83">
          <head xml:id="echoid-head87" xml:space="preserve">PRONVNCIATVM LXXI.</head>
          <p>
            <s xml:id="echoid-s5297" xml:space="preserve">Quum loca duo uni ſubiecta ſunt meridiano, & </s>
            <s xml:id="echoid-s5298" xml:space="preserve">alterius tantum nota ſit la
              <lb/>
            titudo & </s>
            <s xml:id="echoid-s5299" xml:space="preserve">diſtantia ignota, inde latitudinem alterius elicere.</s>
            <s xml:id="echoid-s5300" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5301" xml:space="preserve">Pronunciatum hoc à ſuperiori planè inuerſum eſt, ideo´ miſſa explanatione opera-
              <lb/>
            tionis, exemplum tantummodo quo ſupra uſi ſumus, adducendum erit. </s>
            <s xml:id="echoid-s5302" xml:space="preserve">?</s>
            <s xml:id="echoid-s5303" xml:space="preserve">? Eſto ut Au-
              <lb/>
              <note position="right" xlink:label="note-0069-07" xlink:href="note-0069-07a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
                <emph style="it">dc Auguſta</emph>
              </note>
            guſtæ ſciam Erfordiam planè eſſe oppoſitam uerſus ſeptentrionem, diſtare quo ab ea
              <lb/>
            per 40. </s>
            <s xml:id="echoid-s5304" xml:space="preserve">miliaria Germanica, iam ergo mutatis miliaribus in gradus, ſemper 15. </s>
            <s xml:id="echoid-s5305" xml:space="preserve">miliaria
              <lb/>
            ſupputãdo pro gradu uno, habebo 2. </s>
            <s xml:id="echoid-s5306" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5307" xml:space="preserve">40. </s>
            <s xml:id="echoid-s5308" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5309" xml:space="preserve">Auguſtæ autem latitudo eſt 48. </s>
            <s xml:id="echoid-s5310" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5311" xml:space="preserve">20.
              <lb/>
            </s>
            <s xml:id="echoid-s5312" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5313" xml:space="preserve">Et quia Erfordia propinquior eſt ſeptentrioni, addo 2. </s>
            <s xml:id="echoid-s5314" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5315" xml:space="preserve">40. </s>
            <s xml:id="echoid-s5316" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5317" xml:space="preserve">ad latitudinẽ Au-
              <lb/>
            guſtanam, & </s>
            <s xml:id="echoid-s5318" xml:space="preserve">proueniunt Erfordiæ 51. </s>
            <s xml:id="echoid-s5319" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5320" xml:space="preserve">10. </s>
            <s xml:id="echoid-s5321" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5322" xml:space="preserve">ſed ſi locus ignotus reſpectu loci intro
              <lb/>
            nizationis Auſtralior, eiuſmodi gradus diſtantiæ ſubtrahi deberent à latitudine Augu-
              <lb/>
            ſtana, in hoc ut proueniret latitudo loci illius quæſita.</s>
            <s xml:id="echoid-s5323" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div159" type="section" level="1" n="84">
          <head xml:id="echoid-head88" xml:space="preserve">PRONVNCIATVM LXXII.</head>
          <p>
            <s xml:id="echoid-s5324" xml:space="preserve">Locis duobus æqualem poli altitudinem habentibus, quæ utra ſit no-
              <lb/>
            ta, ſed ita, ut diuerſis ſubiaceant meridianis, cognita etiam differentia lon-
              <lb/>
            gitudinis, adhuc eorum inſuper diſtantiam cognoſcere.</s>
            <s xml:id="echoid-s5325" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5326" xml:space="preserve">Res hæc multo la bore nõ eget ne moleſta operatiõe, ſed tantũ tibi propone cõple-
              <lb/>
            mentũ latitudinũ, qm̃ æqualia ſunt, deinde etiam differentiã longitudinũ, eam mediato,
              <lb/>
            ſinum´ medietatis differentiæ longitudinũ duc in ſinum cõplemẽti latitudinum, </s>
          </p>
        </div>
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