Apian, Petrus, Instrvmentvm Sinvvm, sev primi mobilis

Table of contents

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[61.] PRONVNCIATVM XLIX.
Page: 56
[62.] PRONVNCIATVM L.
Page: 56
[63.] PRONVNCIATVM LI.
Page: 57
[64.] PRONVNCIATVM LII.
Page: 57
[65.] PRONVNCIATVM LIII.
Page: 57
[66.] PRONVNCIATVM LIIII.
Page: 58
[67.] PRONVNCIATVM LV.
Page: 58
[68.] PRONVNCIATVM LVI.
Page: 59
[69.] PRONVNCIATVM LVII.
Page: 59
[70.] PRONVNCIATVM LVIII.
Page: 61
[71.] PRONVNCIATVM LIX.
Page: 62
[72.] PRONVNCIATVM LX.
Page: 63
[73.] PRONVNCIATVM LXI.
Page: 64
[74.] PRONVNCIATVM LXII.
Page: 64
[75.] PRONVNCIATVM LXIII.
Page: 64
[76.] PRONVNCIATVM LXIIII.
Page: 65
[77.] PRONVNCIATVM LXV.
Page: 66
[78.] PRONVNCIATVM LXVI.
Page: 66
[79.] PRONVNCIATVM LXVII.
Page: 67
[80.] PRONVNCIATVM LXVIII.
Page: 68
[81.] PRONVNCIATVM LXIX.
Page: 68
[82.] PRONVNCIATVM LXX.
Page: 69
[83.] PRONVNCIATVM LXXI.
Page: 69
[84.] PRONVNCIATVM LXXII.
Page: 69
[85.] PRONVNCIATVM LXXIII.
Page: 70
[86.] PRONVNCIATVM LXXIIII.
Page: 70
[87.] PRONVNCIATVM LXXV.
Page: 71
[88.] PRONVNCIATVM LXXVI.
Page: 72
[89.] PRONVNCIATVM LXXVII.
Page: 73
[90.] PRONVNCIATVM LXXVIII.
Page: 74
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        <div xml:id="echoid-div168" type="section" level="1" n="88">
          <p>
            <s xml:id="echoid-s5750" xml:space="preserve">
              <pb file="0073" n="73" rhead="TABVLARVM SINVVM PER PET. APIANVM."/>
            argumentum illud operationis, ſinum illius duco in ſinum totum, & </s>
            <s xml:id="echoid-s5751" xml:space="preserve">productum diuido
              <lb/>
              <note position="right" xlink:label="note-0073-01" xlink:href="note-0073-01a" xml:space="preserve">
                <emph style="it">Differentia</emph>
                <lb/>
                <emph style="it">lõgitudinis</emph>
                <lb/>
                <emph style="it">inter Augu</emph>
                <lb/>
                <emph style="it">ſtã & Hie</emph>
                <lb/>
                <emph style="it">ruſalem.</emph>
                <lb/>
                <emph style="it">Angulus</emph>
                <lb/>
                <emph style="it">poſitionis</emph>
                <lb/>
                <emph style="it">inter Augu</emph>
                <lb/>
                <emph style="it">ſtã & Hie</emph>
                <lb/>
                <emph style="it">ruſalem.</emph>
              </note>
            in ſinum complemẽti maioris latitudinis. </s>
            <s xml:id="echoid-s5752" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5753" xml:space="preserve">66479. </s>
            <s xml:id="echoid-s5754" xml:space="preserve">tunc arcus quotientis 37. </s>
            <s xml:id="echoid-s5755" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5756" xml:space="preserve">29. </s>
            <s xml:id="echoid-s5757" xml:space="preserve">mi.
              <lb/>
            </s>
            <s xml:id="echoid-s5758" xml:space="preserve">erit differentia lõgitudinis inter meridianum Auguſtenſem & </s>
            <s xml:id="echoid-s5759" xml:space="preserve">Hieruſalem, id quod pri-
              <lb/>
            mo loco ſcire uolebam. </s>
            <s xml:id="echoid-s5760" xml:space="preserve">Dehinc duco etiam ſinum differentiæ longitudinis 60853. </s>
            <s xml:id="echoid-s5761" xml:space="preserve">in ſi-
              <lb/>
            num complementi latitudinis minoris 85111. </s>
            <s xml:id="echoid-s5762" xml:space="preserve">productum diuido in ſinum intercapedi-
              <lb/>
            nis, ſcilicet 53975. </s>
            <s xml:id="echoid-s5763" xml:space="preserve">& </s>
            <s xml:id="echoid-s5764" xml:space="preserve">quotiens producit 95783. </s>
            <s xml:id="echoid-s5765" xml:space="preserve">cuius arcus eſt 73. </s>
            <s xml:id="echoid-s5766" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5767" xml:space="preserve">18. </s>
            <s xml:id="echoid-s5768" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5769" xml:space="preserve">angulus
              <lb/>
            hic ille poſitionis, quem ſecundo loco per hanc operationem inquirebam.</s>
            <s xml:id="echoid-s5770" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div171" type="section" level="1" n="89">
          <head xml:id="echoid-head93" xml:space="preserve">PRONVNCIATVM LXXVII.</head>
          <p>
            <s xml:id="echoid-s5771" xml:space="preserve">Si trium locorum nota ſit intercapedo, duo etiam loca ex ijs cognitas ha-
              <lb/>
            beant ſuas tum latitudines tum longitudines, adhuc tertij longitudinem & </s>
            <s xml:id="echoid-s5772" xml:space="preserve">
              <lb/>
            latitudinem, angulum´ poſitionis, inquirere.</s>
            <s xml:id="echoid-s5773" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5774" xml:space="preserve">Propoſitis locis tribus, è ꝗbus duo habeãt lõgitudinẽ notã ſimul & </s>
            <s xml:id="echoid-s5775" xml:space="preserve">latitudinẽ, tu uero
              <lb/>
            ſcias, quantũ quilibet illorũ ſit poſitus ab alijs duobus, hinc uelis adhuc ſcire lõgitudinem
              <lb/>
            & </s>
            <s xml:id="echoid-s5776" xml:space="preserve">latitudinẽ loci incogniti, conſidera principio diſtantiã unius ab alio, ſiquidẽ intercape
              <lb/>
            dinẽ duorũ cognitorũ ꝑ artẽ inueniſti, illũ aũt tertij loci à duobus habes ꝑ exꝑientiã, ꝓpo
              <lb/>
            ne hic tibi intercapedines illas tres, mediã ſubtrahe à maiori, reſiduũ dicetur differentia
              <lb/>
            prima, minorem quo ſubtrahe à 90. </s>
            <s xml:id="echoid-s5777" xml:space="preserve">& </s>
            <s xml:id="echoid-s5778" xml:space="preserve">relinquetur differentia ſecũda. </s>
            <s xml:id="echoid-s5779" xml:space="preserve">Inſuꝑ ſubducito ſi
              <lb/>
            num differentiæ ſecundæ de ſinu cõplementi differentiæ primæ, & </s>
            <s xml:id="echoid-s5780" xml:space="preserve">reſiduũ duc in ſinum
              <lb/>
            complementi maioris intercapedinis, ꝓductũ diuide in ſinũ maioris intercapedinis, quo-
              <lb/>
              <note position="right" xlink:label="note-0073-02" xlink:href="note-0073-02a" xml:space="preserve">
                <emph style="it">Areatim il</emph>
                <lb/>
                <emph style="it">lud cx qua-</emph>
                <lb/>
                <emph style="it">drãte diſces</emph>
              </note>
            tientem uero adde ad ſinũ differentiæ primæ, & </s>
            <s xml:id="echoid-s5781" xml:space="preserve">ſummã iſtã duc in ſe quadrate, ſimiliter
              <lb/>
            & </s>
            <s xml:id="echoid-s5782" xml:space="preserve">ſinum differentiæ ſecundæ, utrũ illũ numerũ qua dratũ collige in unã ſummã, & </s>
            <s xml:id="echoid-s5783" xml:space="preserve">eius
              <lb/>
            radicẽ itidẽ quadratã inquire, arcũ radicis de 90. </s>
            <s xml:id="echoid-s5784" xml:space="preserve">ſubtracto relinquet̃ argumentũ oꝑatio-
              <lb/>
            nis, q̊dſeruabis in recenti memoria. </s>
            <s xml:id="echoid-s5785" xml:space="preserve">Quod ſi locus, ꝗ ignotã longitudinem habet & </s>
            <s xml:id="echoid-s5786" xml:space="preserve">lati
              <lb/>
            tudinẽ, Borealior fuerit ̈ ille à q̊ ſitũ certũ ſcire cupis, & </s>
            <s xml:id="echoid-s5787" xml:space="preserve">intercapedo loci notioris etiam
              <lb/>
            extiterit maior, quæres ꝑ 74. </s>
            <s xml:id="echoid-s5788" xml:space="preserve">ꝓnunc. </s>
            <s xml:id="echoid-s5789" xml:space="preserve">angulũ poſitiõis locorũ cognitorũ, eũ ſeruabis ſeor-
              <lb/>
            ſim, dehinc duces ſinũ argumenti operationis in ſinũ diſtantiæ loci primi uſ ad locum
              <lb/>
            ignotum, ꝓductũ uero diuides in totum, ſi iã arcũ q̊tientis addas ad illum antea reſerua-
              <lb/>
            tum angulũ poſitionis(quũ iſte prior ſit meridionalis) ſummã quo totã detrahas à ſemi
              <lb/>
              <note position="right" xlink:label="note-0073-03" xlink:href="note-0073-03a" xml:space="preserve">
                <emph style="it">Lateraliter</emph>
              </note>
            circulo, relinquetur angulus poſitionis à primo loco ꝓpoſito uſ ad ignotũ, numerãdo
              <lb/>
            â meridiano ſeptentrionali, ſiquidẽ primus angulus poſitionis à meridiano meridionali
              <lb/>
            cõputatur, uel econtra. </s>
            <s xml:id="echoid-s5790" xml:space="preserve">Si aũt locus ignotus (qñ cõtingit, ut à loco cognito ad aliũ ꝓfe-
              <lb/>
            cto fiat) fuerit Auſtralior, & </s>
            <s xml:id="echoid-s5791" xml:space="preserve">tñ intercapedo locorũ cognitorũ extiterit maior, tunc reſidu
              <lb/>
            um ꝓ ipſo angulo poſitionis habebitur, ꝗ à meridiano meridionali numeratur, hoc eſt q̊d
              <lb/>
            primo hic in ꝗrendũ erat. </s>
            <s xml:id="echoid-s5792" xml:space="preserve">Deinde duces ſinũ huius reſidui ſiue anguli poſitionis in ſinum
              <lb/>
            intercapedinis loci illius cogniti, à quo intercapedo & </s>
            <s xml:id="echoid-s5793" xml:space="preserve">poſitionis angulus computantur
              <lb/>
              <note position="right" xlink:label="note-0073-04" xlink:href="note-0073-04a" xml:space="preserve">
                <emph style="it">Later aliter</emph>
              </note>
            uſ ad ignotũ, ꝓductum diuides in ſinũ totũ, & </s>
            <s xml:id="echoid-s5794" xml:space="preserve">quotiens dabit inuentũ primum. </s>
            <s xml:id="echoid-s5795" xml:space="preserve">Hinc
              <lb/>
            ꝓpone tibi ſinũ cõplementi iſtius inuenti, & </s>
            <s xml:id="echoid-s5796" xml:space="preserve">ſinũ cõplementi intercapedinis illorũ loco-
              <lb/>
              <note position="right" xlink:label="note-0073-05" xlink:href="note-0073-05a" xml:space="preserve">
                <emph style="it">Areatim.</emph>
              </note>
            rum, numerum minorẽ duc in totũ, & </s>
            <s xml:id="echoid-s5797" xml:space="preserve">ꝓductum diuide in maiorẽ, arcum uero quotientis
              <lb/>
            ſubtrahe de 90. </s>
            <s xml:id="echoid-s5798" xml:space="preserve">& </s>
            <s xml:id="echoid-s5799" xml:space="preserve">remanebit inuentũ ſecundũ, iã porrò duc ſinus cõplementorũ primi & </s>
            <s xml:id="echoid-s5800" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0073-06" xlink:href="note-0073-06a" xml:space="preserve">
                <emph style="it">Later aliter</emph>
              </note>
            ſecundi in ſe, & </s>
            <s xml:id="echoid-s5801" xml:space="preserve">ꝓducto in totũ diuiſo, arcus quotientis dabit tibi latitudinẽ loci incogni-
              <lb/>
            ti, q̃ ſecunda eſt utilitas ex hoc ꝓnunciato inuento. </s>
            <s xml:id="echoid-s5802" xml:space="preserve">Propterea ſi adhuc ſcire deſideras dif
              <lb/>
            ferentiã lõgitudinis, adſume ſinũ cõplementi latitudinis & </s>
            <s xml:id="echoid-s5803" xml:space="preserve">ſinum primi inuenti, minorẽ
              <lb/>
              <note position="right" xlink:label="note-0073-07" xlink:href="note-0073-07a" xml:space="preserve">
                <emph style="it">Areatim</emph>
              </note>
            duc in totũ, & </s>
            <s xml:id="echoid-s5804" xml:space="preserve">ꝓductũ diuide in maiorẽ, arcus q̊tiẽtis mõſtrabit differẽtiã lõgitudinũ no
              <lb/>
              <note position="right" xlink:label="note-0073-08" xlink:href="note-0073-08a" xml:space="preserve">EXEM-
                <lb/>
              PLVM
                <lb/>
                <emph style="it">de Auguſta</emph>
                <lb/>
                <emph style="it">Hieruſalem</emph>
                <lb/>
                <emph style="it">& Craco-</emph>
                <lb/>
                <emph style="it">uia.</emph>
              </note>
            ti illius loci & </s>
            <s xml:id="echoid-s5805" xml:space="preserve">ignoti, ubi ſi ignotus fuerit occidentalior, tunc ſubtrahe illã differentiã à lõ.
              <lb/>
            </s>
            <s xml:id="echoid-s5806" xml:space="preserve">gitudine ciuitatis notæ, ſed ſi ſit orientalior, adde eam ad longitudinem notæ ciuitatis, & </s>
            <s xml:id="echoid-s5807" xml:space="preserve">
              <lb/>
            habebis longitudinem ignoti loci quo notã & </s>
            <s xml:id="echoid-s5808" xml:space="preserve">perſpectã, at is tertius eſt uſus huius ꝓ
              <lb/>
            nunciati. </s>
            <s xml:id="echoid-s5809" xml:space="preserve">?</s>
            <s xml:id="echoid-s5810" xml:space="preserve">?Nunc tandem ad exempla ueniamus. </s>
            <s xml:id="echoid-s5811" xml:space="preserve">Propono igitur mihi tres ciuitates
              <lb/>
            Auguſtam, Hieruſalem, & </s>
            <s xml:id="echoid-s5812" xml:space="preserve">Cracouiam Poloniæ, priores duæ mihi notæ ſunt ſecundum
              <lb/>
            longitudinem & </s>
            <s xml:id="echoid-s5813" xml:space="preserve">latitudinẽ, quoniã Auguſta habet in longit. </s>
            <s xml:id="echoid-s5814" xml:space="preserve">28. </s>
            <s xml:id="echoid-s5815" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5816" xml:space="preserve">31. </s>
            <s xml:id="echoid-s5817" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5818" xml:space="preserve">in latitudine
              <lb/>
              <note position="right" xlink:label="note-0073-09" xlink:href="note-0073-09a" xml:space="preserve">
                <emph style="it">Diſtãtia in</emph>
                <lb/>
                <emph style="it">ter Augu-</emph>
                <lb/>
                <emph style="it">ſtam &</emph>
                <lb/>
                <emph style="it">Cracoui@.</emph>
              </note>
            48. </s>
            <s xml:id="echoid-s5819" xml:space="preserve">gra, 20. </s>
            <s xml:id="echoid-s5820" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5821" xml:space="preserve">Hieruſalẽ aũt in longít. </s>
            <s xml:id="echoid-s5822" xml:space="preserve">66. </s>
            <s xml:id="echoid-s5823" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5824" xml:space="preserve">o. </s>
            <s xml:id="echoid-s5825" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5826" xml:space="preserve">in latitudine 301. </s>
            <s xml:id="echoid-s5827" xml:space="preserve">gra. </s>
            <s xml:id="echoid-s5828" xml:space="preserve">40. </s>
            <s xml:id="echoid-s5829" xml:space="preserve">mi. </s>
            <s xml:id="echoid-s5830" xml:space="preserve">ſed de
              <lb/>
            Cracouia nihil mihi conſtat, ne in lõgitudine ne in latitudine, unum hoc experientia
              <lb/>
            aut fama didici ab Auguſta uſ ad Cracouiam intereſſe 95. </s>
            <s xml:id="echoid-s5831" xml:space="preserve">miliaria & </s>
            <s xml:id="echoid-s5832" xml:space="preserve">quartã </s>
          </p>
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