Blancanus, Josephus, Sphaera mvndi, sev cosmographia demonstratiua , ac facile methodo tradita : in qua totius Mundi fabrica, vna cum nouis, Tychonis, Kepleri, Galilaei, aliorumq' ; Astronomorum adinuentis continentur ; Accessere I. Breuis introductio ad geographiam. II. Apparatus ad mathematicarum studium. III. Echometria, idest Geometrica tractatio de Echo. IV. Nouum instrumentum ad Horologia

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        <div xml:id="echoid-div183" type="section" level="1" n="118">
          <p>
            <s xml:id="echoid-s8700" xml:space="preserve">
              <pb o="91" file="0111" n="115" rhead="Liber Nonus."/>
            minor apex graduumo. </s>
            <s xml:id="echoid-s8701" xml:space="preserve">detractus à maiori″. </s>
            <s xml:id="echoid-s8702" xml:space="preserve">nihil minuit. </s>
            <s xml:id="echoid-s8703" xml:space="preserve">ſcribo itaque 4. </s>
            <s xml:id="echoid-s8704" xml:space="preserve">ſubtirulo″. </s>
            <s xml:id="echoid-s8705" xml:space="preserve">eadem ratione diui-
              <lb/>
            ſis 30′. </s>
            <s xml:id="echoid-s8706" xml:space="preserve">per {0/6}. </s>
            <s xml:id="echoid-s8707" xml:space="preserve">producitur 5. </s>
            <s xml:id="echoid-s8708" xml:space="preserve">tandem diuiſis gr. </s>
            <s xml:id="echoid-s8709" xml:space="preserve">36. </s>
            <s xml:id="echoid-s8710" xml:space="preserve">(reſoluo enim ſignum 1. </s>
            <s xml:id="echoid-s8711" xml:space="preserve">in gr. </s>
            <s xml:id="echoid-s8712" xml:space="preserve">30. </s>
            <s xml:id="echoid-s8713" xml:space="preserve">qui cũ gr. </s>
            <s xml:id="echoid-s8714" xml:space="preserve">6. </s>
            <s xml:id="echoid-s8715" xml:space="preserve">efficiunt efficiunt
              <lb/>
            36. </s>
            <s xml:id="echoid-s8716" xml:space="preserve">per {0/6}. </s>
            <s xml:id="echoid-s8717" xml:space="preserve">producitur 6. </s>
            <s xml:id="echoid-s8718" xml:space="preserve">ideſt, ſex integra; </s>
            <s xml:id="echoid-s8719" xml:space="preserve">qui in exemplo ſunt gradus.</s>
            <s xml:id="echoid-s8720" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8721" xml:space="preserve">4 In reliquis caſibus, quando ſcilicet numerus, aut apex diuiſoris eſt maior numero, aut apice diuidendi,
              <lb/>
            & </s>
            <s xml:id="echoid-s8722" xml:space="preserve">vterque aut alter conſtat gradibus, primis, ſecundis, & </s>
            <s xml:id="echoid-s8723" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8724" xml:space="preserve">tunc occurrunt variæ, ac magnę difficultates; </s>
            <s xml:id="echoid-s8725" xml:space="preserve">quas
              <lb/>
            hac vnica regula ſuperabis. </s>
            <s xml:id="echoid-s8726" xml:space="preserve">Quando numerus diuidendus minor eſt, quam diuiſor, cum toties multiplica per
              <lb/>
            60. </s>
            <s xml:id="echoid-s8727" xml:space="preserve">donec ſit ei æqualis, aut mai
              <unsure/>
            or. </s>
            <s xml:id="echoid-s8728" xml:space="preserve">ſimiliter ſi apex numeri diuidendi ſit minor apice diuiſoris, multiplica nu-
              <lb/>
            merum diuidendum toties per 60. </s>
            <s xml:id="echoid-s8729" xml:space="preserve">quouſque apex eius ſit æqualis, aut maior apice diuiſoris: </s>
            <s xml:id="echoid-s8730" xml:space="preserve">ex hac enim mul-
              <lb/>
            tiplicatione per 60. </s>
            <s xml:id="echoid-s8731" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s8732" xml:space="preserve">fiunt prima, prima vero fiunt ſecunda, ſecunda euadunt tertia, &</s>
            <s xml:id="echoid-s8733" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8734" xml:space="preserve">vt conſideranti ea,
              <lb/>
            quæ initio huius tractatus diximus, patere poteſt. </s>
            <s xml:id="echoid-s8735" xml:space="preserve">Exemplum. </s>
            <s xml:id="echoid-s8736" xml:space="preserve">ſint diuidenda 3′ per 6′. </s>
            <s xml:id="echoid-s8737" xml:space="preserve">quia numerus diuiden-
              <lb/>
            dus minor eſt, diu dente eum due in 60. </s>
            <s xml:id="echoid-s8738" xml:space="preserve">fientque 180″. </s>
            <s xml:id="echoid-s8739" xml:space="preserve">qui erit nouus diuidendus priori æqualis, aptus tamen
              <lb/>
            diuiſioni, diuiſis ig@tur 180″. </s>
            <s xml:id="echoid-s8740" xml:space="preserve">per 6′. </s>
            <s xml:id="echoid-s8741" xml:space="preserve">erit quotiens 30′. </s>
            <s xml:id="echoid-s8742" xml:space="preserve">cuius apexerit′. </s>
            <s xml:id="echoid-s8743" xml:space="preserve">iuxta ſecundam regulam. </s>
            <s xml:id="echoid-s8744" xml:space="preserve">rurſus diui-
              <lb/>
            denda ſint 4′. </s>
            <s xml:id="echoid-s8745" xml:space="preserve">per 2″. </s>
            <s xml:id="echoid-s8746" xml:space="preserve">quia apex diuidendi eſt minor altero, due 4′. </s>
            <s xml:id="echoid-s8747" xml:space="preserve">in 60′. </s>
            <s xml:id="echoid-s8748" xml:space="preserve">fientq; </s>
            <s xml:id="echoid-s8749" xml:space="preserve">240″. </s>
            <s xml:id="echoid-s8750" xml:space="preserve">ea iam diuide per 2″.
              <lb/>
            </s>
            <s xml:id="echoid-s8751" xml:space="preserve">productus erit 120. </s>
            <s xml:id="echoid-s8752" xml:space="preserve">ideſt, gr. </s>
            <s xml:id="echoid-s8753" xml:space="preserve">120. </s>
            <s xml:id="echoid-s8754" xml:space="preserve">aut aliud genus integrorum; </s>
            <s xml:id="echoid-s8755" xml:space="preserve">quia detracto apice diuiſoris, qui eſt″. </s>
            <s xml:id="echoid-s8756" xml:space="preserve">ab apice
              <lb/>
            diuidẽdi″. </s>
            <s xml:id="echoid-s8757" xml:space="preserve">ei æquali relinquitur o. </s>
            <s xml:id="echoid-s8758" xml:space="preserve">apex quotientis. </s>
            <s xml:id="echoid-s8759" xml:space="preserve">Pręterea diuide gr. </s>
            <s xml:id="echoid-s8760" xml:space="preserve">30. </s>
            <s xml:id="echoid-s8761" xml:space="preserve">per 5′. </s>
            <s xml:id="echoid-s8762" xml:space="preserve">ductis 30. </s>
            <s xml:id="echoid-s8763" xml:space="preserve">in 60′. </s>
            <s xml:id="echoid-s8764" xml:space="preserve">fiunt 1800′. </s>
            <s xml:id="echoid-s8765" xml:space="preserve">
              <lb/>
            cùm iam ſintæquales apic s, diuide 1800′. </s>
            <s xml:id="echoid-s8766" xml:space="preserve">per 5′. </s>
            <s xml:id="echoid-s8767" xml:space="preserve">erit quotiens 360. </s>
            <s xml:id="echoid-s8768" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s8769" xml:space="preserve">integra, ex præſcriptis regulis. </s>
            <s xml:id="echoid-s8770" xml:space="preserve">ſi tam
              <lb/>
            apex, quam numerus ſint minores, vtrumq; </s>
            <s xml:id="echoid-s8771" xml:space="preserve">augebis per eodem ductu in 60′. </s>
            <s xml:id="echoid-s8772" xml:space="preserve">vt ſi 3′. </s>
            <s xml:id="echoid-s8773" xml:space="preserve">diuidenda ſint in 12″. </s>
            <s xml:id="echoid-s8774" xml:space="preserve">du-
              <lb/>
            ctis 3′. </s>
            <s xml:id="echoid-s8775" xml:space="preserve">in 60′. </s>
            <s xml:id="echoid-s8776" xml:space="preserve">producuntur 180″. </s>
            <s xml:id="echoid-s8777" xml:space="preserve">quæ iam per 12″. </s>
            <s xml:id="echoid-s8778" xml:space="preserve">diuiſibilia ſunt, prouenitque ex diuiſione quotiens {0/15}. </s>
            <s xml:id="echoid-s8779" xml:space="preserve">in-
              <lb/>
            tegra. </s>
            <s xml:id="echoid-s8780" xml:space="preserve">Atque ſic agendum eſt cùm vterque numerus ſimplex eſt, vt in allatis exemplis.</s>
            <s xml:id="echoid-s8781" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8782" xml:space="preserve">5 Quod ſi plura habeant membra, ideſt, ſigna, gradus, prima, ſecunda, &</s>
            <s xml:id="echoid-s8783" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8784" xml:space="preserve">tuncomnia illa membra reſol-
              <lb/>
            nenda ſunt per multiplicationem per 60′. </s>
            <s xml:id="echoid-s8785" xml:space="preserve">ad vltimam denominationem ſeu ad maiorem apicem, v.</s>
            <s xml:id="echoid-s8786" xml:space="preserve">g. </s>
            <s xml:id="echoid-s8787" xml:space="preserve">ſit diui-
              <lb/>
            dendus, aut diuiſor, numerus hic Sig. </s>
            <s xml:id="echoid-s8788" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8789" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s8790" xml:space="preserve">6. </s>
            <s xml:id="echoid-s8791" xml:space="preserve">4′. </s>
            <s xml:id="echoid-s8792" xml:space="preserve">5″. </s>
            <s xml:id="echoid-s8793" xml:space="preserve">ſed quia figna non conſid rantur niſi vt gradus, ideo erũt
              <lb/>
            gr. </s>
            <s xml:id="echoid-s8794" xml:space="preserve">36. </s>
            <s xml:id="echoid-s8795" xml:space="preserve">4′. </s>
            <s xml:id="echoid-s8796" xml:space="preserve">5″. </s>
            <s xml:id="echoid-s8797" xml:space="preserve">tria hæc membra reducenda ſunt ad vltimam denomioationem quæ eſt ſecundorum, ideſt, om-
              <lb/>
            nia ſunt conuertenda|in″. </s>
            <s xml:id="echoid-s8798" xml:space="preserve">per multipl. </s>
            <s xml:id="echoid-s8799" xml:space="preserve">in 60′. </s>
            <s xml:id="echoid-s8800" xml:space="preserve">ſic, duco gr. </s>
            <s xml:id="echoid-s8801" xml:space="preserve">36. </s>
            <s xml:id="echoid-s8802" xml:space="preserve">in 60′. </s>
            <s xml:id="echoid-s8803" xml:space="preserve">fiunt 2160′. </s>
            <s xml:id="echoid-s8804" xml:space="preserve">quibus addo 4′. </s>
            <s xml:id="echoid-s8805" xml:space="preserve">quę prius erãt
              <lb/>
            in ipſo numero fiuntque 2164′. </s>
            <s xml:id="echoid-s8806" xml:space="preserve">hæc rurſus duco in 60′. </s>
            <s xml:id="echoid-s8807" xml:space="preserve">fiuutque 129840″. </s>
            <s xml:id="echoid-s8808" xml:space="preserve">ſecunda. </s>
            <s xml:id="echoid-s8809" xml:space="preserve">quæ cum 5″. </s>
            <s xml:id="echoid-s8810" xml:space="preserve">prioribus ef-
              <lb/>
            ficiunt 129845″. </s>
            <s xml:id="echoid-s8811" xml:space="preserve">idem ſaciendum eſt cum diuidente ſi plures habeat partes. </s>
            <s xml:id="echoid-s8812" xml:space="preserve">facta hac reductionẽ ad vltimam
              <lb/>
            denominationem, ſi contingat diuidendum adhuc eſſe minorem, aut habere minorem denominationẽ quam
              <lb/>
            diuiſor, adhuc ducendus eſt in 60′. </s>
            <s xml:id="echoid-s8813" xml:space="preserve">vt diuiſore non ſit minor, nec minorem habeat apicem. </s>
            <s xml:id="echoid-s8814" xml:space="preserve">Exemplum. </s>
            <s xml:id="echoid-s8815" xml:space="preserve">ſint
              <lb/>
            gr. </s>
            <s xml:id="echoid-s8816" xml:space="preserve">1 {0/0}. </s>
            <s xml:id="echoid-s8817" xml:space="preserve">15′. </s>
            <s xml:id="echoid-s8818" xml:space="preserve">30″. </s>
            <s xml:id="echoid-s8819" xml:space="preserve">diuidenda per 15′. </s>
            <s xml:id="echoid-s8820" xml:space="preserve">quia diuidendus habet plures partes, quarum vltima eſt ſecundorum, ideo
              <lb/>
            reliquas omnes ad ſeci
              <unsure/>
            nda reduco, eas per 60′. </s>
            <s xml:id="echoid-s8821" xml:space="preserve">multiplicando, ſic; </s>
            <s xml:id="echoid-s8822" xml:space="preserve">ductis {0/10}. </s>
            <s xml:id="echoid-s8823" xml:space="preserve">in 60′. </s>
            <s xml:id="echoid-s8824" xml:space="preserve">fiunt 600′. </s>
            <s xml:id="echoid-s8825" xml:space="preserve">quæ cum prio-
              <lb/>
            ribus 15′. </s>
            <s xml:id="echoid-s8826" xml:space="preserve">erunt 615′. </s>
            <s xml:id="echoid-s8827" xml:space="preserve">quibus rurſum ductis in 60′. </s>
            <s xml:id="echoid-s8828" xml:space="preserve">proueniunt 36900″. </s>
            <s xml:id="echoid-s8829" xml:space="preserve">quę cũ prioribus 30″. </s>
            <s xml:id="echoid-s8830" xml:space="preserve">efficiunt 36930″.
              <lb/>
            </s>
            <s xml:id="echoid-s8831" xml:space="preserve">quia vero diuiſor 15′. </s>
            <s xml:id="echoid-s8832" xml:space="preserve">eſt ſimplex, non eſt opus reductionem ad vltimam denominationem. </s>
            <s xml:id="echoid-s8833" xml:space="preserve">ſimiliter quia di-
              <lb/>
            uidendus reductus ad vltimam denominationem eſt maior diuiſore, habentque maiorem denominationem
              <lb/>
            non eſt opus vlteriori reductione. </s>
            <s xml:id="echoid-s8834" xml:space="preserve">iam igitur diuido 36930″. </s>
            <s xml:id="echoid-s8835" xml:space="preserve">per 15. </s>
            <s xml:id="echoid-s8836" xml:space="preserve">oriturque Quotiens 2464′. </s>
            <s xml:id="echoid-s8837" xml:space="preserve">quę ſunt pri-
              <lb/>
            ma, quia detracto apice diuiſoris, qui eſt′. </s>
            <s xml:id="echoid-s8838" xml:space="preserve">ab apice diuidendi qui eſt″. </s>
            <s xml:id="echoid-s8839" xml:space="preserve">relinquitur′. </s>
            <s xml:id="echoid-s8840" xml:space="preserve">apex quotientis, ex præ-
              <lb/>
            in@ffis regulis. </s>
            <s xml:id="echoid-s8841" xml:space="preserve">Quod ſi diuiſor 15″. </s>
            <s xml:id="echoid-s8842" xml:space="preserve">fuiſſet ſecundorum, quo iens fuiſſet graduum, ſeu integrorum {0/2462}. </s>
            <s xml:id="echoid-s8843" xml:space="preserve">quia
              <lb/>
            detractis ſecundis a ſecundis, relinquitur o. </s>
            <s xml:id="echoid-s8844" xml:space="preserve">quæ eſt graduum ſeu alterius integri appellatio.</s>
            <s xml:id="echoid-s8845" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8846" xml:space="preserve">Quando autem quotiens eſt minor quam 60. </s>
            <s xml:id="echoid-s8847" xml:space="preserve">vt in noſtro exemplo, tunc diuidendus eſt per 60. </s>
            <s xml:id="echoid-s8848" xml:space="preserve">vt appareat
              <lb/>
            quotſcrupula contineat minoris proximè appellationis. </s>
            <s xml:id="echoid-s8849" xml:space="preserve">in caſu noſtro 2464′. </s>
            <s xml:id="echoid-s8850" xml:space="preserve">diuiſa per 60′. </s>
            <s xml:id="echoid-s8851" xml:space="preserve">producunt {0/411}.
              <lb/>
            </s>
            <s xml:id="echoid-s8852" xml:space="preserve">gradus, nam@o. </s>
            <s xml:id="echoid-s8853" xml:space="preserve">prima efficiunt gr. </s>
            <s xml:id="echoid-s8854" xml:space="preserve">vnum. </s>
            <s xml:id="echoid-s8855" xml:space="preserve">pariter ſi eadem {0/462}. </s>
            <s xml:id="echoid-s8856" xml:space="preserve">ſint gradus, diuidenda ſunt per 30. </s>
            <s xml:id="echoid-s8857" xml:space="preserve">vt exhibeãt
              <lb/>
            ſigna omnia, quæ in ipſis continentur, eruntque ſigna 82. </s>
            <s xml:id="echoid-s8858" xml:space="preserve">& </s>
            <s xml:id="echoid-s8859" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s8860" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8861" xml:space="preserve">relinquentur.</s>
            <s xml:id="echoid-s8862" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8863" xml:space="preserve">6 Accidit aliquando diuiſorem eſſe maiorem diuidẽdo, ynde oritur quotiens qui eſt fractio vnius integri.
              <lb/>
            </s>
            <s xml:id="echoid-s8864" xml:space="preserve">quæ fractio ſi bene perſpecta ſit, indicat an quotiens ſit primorum, an ſecundorum, & </s>
            <s xml:id="echoid-s8865" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8866" xml:space="preserve">v.</s>
            <s xml:id="echoid-s8867" xml:space="preserve">g. </s>
            <s xml:id="echoid-s8868" xml:space="preserve">ſi diuidantur 6′. </s>
            <s xml:id="echoid-s8869" xml:space="preserve">
              <lb/>
            per 12′. </s>
            <s xml:id="echoid-s8870" xml:space="preserve">producentur {6/12}. </s>
            <s xml:id="echoid-s8871" xml:space="preserve">hoc eſt, per minutiarum depreſſionem {2/1}. </s>
            <s xml:id="echoid-s8872" xml:space="preserve">ideſt dimidius gradus, ſiue 30′. </s>
            <s xml:id="echoid-s8873" xml:space="preserve">ſimiliter ſi
              <lb/>
            2′. </s>
            <s xml:id="echoid-s8874" xml:space="preserve">diuidantur per {0/4}. </s>
            <s xml:id="echoid-s8875" xml:space="preserve">4′. </s>
            <s xml:id="echoid-s8876" xml:space="preserve">reſoluo diuiſorem in 244′. </s>
            <s xml:id="echoid-s8877" xml:space="preserve">diu@ſis iam 2. </s>
            <s xml:id="echoid-s8878" xml:space="preserve">per 244′. </s>
            <s xml:id="echoid-s8879" xml:space="preserve">ſic ſtabit quotiens 2@4. </s>
            <s xml:id="echoid-s8880" xml:space="preserve">vnius integri,
              <lb/>
            ſiue per minutiarum depreſſionem, 1 {1/22}. </s>
            <s xml:id="echoid-s8881" xml:space="preserve">vnius integri. </s>
            <s xml:id="echoid-s8882" xml:space="preserve">quæ fractio valet quaſi dimidium vnius primi, nã gra-
              <lb/>
            dus vnus continet 60. </s>
            <s xml:id="echoid-s8883" xml:space="preserve">quare dimidium vnius primi erit 1 {1/20}. </s>
            <s xml:id="echoid-s8884" xml:space="preserve">pars gradus. </s>
            <s xml:id="echoid-s8885" xml:space="preserve">ſimili ſpeculatione opus eſt in ſimili-
              <lb/>
            ac proinde prima eſſe ſexageeſimas gradus, ſecunda eſſe termilleſimas eiuſdem gradus, tertia eſſe ducenteſimas
              <lb/>
            ſex decemilleſimas grad. </s>
            <s xml:id="echoid-s8886" xml:space="preserve">&</s>
            <s xml:id="echoid-s8887" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8888" xml:space="preserve">Ratio huius diuiſionis pendet ex diuiſione minutiarum communium, quemad-
              <lb/>
            modum etiam multiplicationis, atque hæc breuitati noſtræ ſufficiant.</s>
            <s xml:id="echoid-s8889" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div184" type="section" level="1" n="119">
          <head xml:id="echoid-head131" style="it" xml:space="preserve">Vſus pramiſſarum Tabularum, ex quo calculus Lunæ fit. Cap. XIIII.</head>
          <p>
            <s xml:id="echoid-s8890" xml:space="preserve">EXemplis melius, quam præceptis multis, rem hanc percipiemus. </s>
            <s xml:id="echoid-s8891" xml:space="preserve">ſit igitur hæc propoſitio.</s>
            <s xml:id="echoid-s8892" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div185" type="section" level="1" n="120">
          <head xml:id="echoid-head132" style="it" xml:space="preserve">Ad datum tempus, medium motum longitudinis Lunæreperire. Propoſ. 1.</head>
          <p>
            <s xml:id="echoid-s8893" xml:space="preserve">SItergo exempli cauſa, datum tempus, quo hæc ſcribimus, annus Chriſti 1616. </s>
            <s xml:id="echoid-s8894" xml:space="preserve">dies 16. </s>
            <s xml:id="echoid-s8895" xml:space="preserve">Iulij, hora vna poſt
              <lb/>
            meridiem cum minutis 15′. </s>
            <s xml:id="echoid-s8896" xml:space="preserve">ideſt ad inſtans vltimum huius temporis reperire diſtantiam centriepicycli ab
              <lb/>
            æquinoctio. </s>
            <s xml:id="echoid-s8897" xml:space="preserve">porrò in primis conſiderandũ eſt quid ſibi velit vulgare illud tempus, ſeu qua ratione illud Aſtro-
              <lb/>
            nomi accipiant. </s>
            <s xml:id="echoid-s8898" xml:space="preserve">Cum ergo vulgo dicitur anno Domini 1616. </s>
            <s xml:id="echoid-s8899" xml:space="preserve">die 16. </s>
            <s xml:id="echoid-s8900" xml:space="preserve">lulij, h. </s>
            <s xml:id="echoid-s8901" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8902" xml:space="preserve">p.</s>
            <s xml:id="echoid-s8903" xml:space="preserve">m. </s>
            <s xml:id="echoid-s8904" xml:space="preserve">aduertendum eſt annum
              <lb/>
            1616. </s>
            <s xml:id="echoid-s8905" xml:space="preserve">nondum eſſe completum, ſed labentem. </s>
            <s xml:id="echoid-s8906" xml:space="preserve">ſimiliter lulius nondum eſt abſolutus, ſed dies eius 16. </s>
            <s xml:id="echoid-s8907" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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