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

Table of Notes

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          <p>
            <s xml:id="echoid-s21140" xml:space="preserve">
              <pb o="15" file="0269" n="274" rhead="DE HOROLOGIIS."/>
            lib. </s>
            <s xml:id="echoid-s21141" xml:space="preserve">8. </s>
            <s xml:id="echoid-s21142" xml:space="preserve">Pappi. </s>
            <s xml:id="echoid-s21143" xml:space="preserve">& </s>
            <s xml:id="echoid-s21144" xml:space="preserve">per prop. </s>
            <s xml:id="echoid-s21145" xml:space="preserve">1. </s>
            <s xml:id="echoid-s21146" xml:space="preserve">de Cochlea mechanicorum Guidubaldi, qui docent ex hypotemuſa trian-
              <lb/>
            guli plani eirca cylindum circumuoluti fieri Helicem. </s>
            <s xml:id="echoid-s21147" xml:space="preserve">vide etiam prop. </s>
            <s xml:id="echoid-s21148" xml:space="preserve">4. </s>
            <s xml:id="echoid-s21149" xml:space="preserve">& </s>
            <s xml:id="echoid-s21150" xml:space="preserve">8. </s>
            <s xml:id="echoid-s21151" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s21152" xml:space="preserve">2. </s>
            <s xml:id="echoid-s21153" xml:space="preserve">de Cochlea
              <lb/>
            aquatica eiuſdem Guidubaldi vbi oſtendit Helicem, ſeu ſpiralem habere puncta primæ medietatis
              <lb/>
            altiora iuſto puncta vero ſecundæ medietatis depreſſiora iuſto;</s>
            <s xml:id="echoid-s21154" xml:space="preserve">|illa enim ſunt ſupra ellipſim deſcri-
              <lb/>
            ptam per extrema puncta, ac medium Helicis, iſta vero infra. </s>
            <s xml:id="echoid-s21155" xml:space="preserve">Ea propter ſi in lamina horarij huius
              <lb/>
            plana duceretur linea recta per tria puncta G B K. </s>
            <s xml:id="echoid-s21156" xml:space="preserve">ea poſtea cylindricata haberet puncta omnia me-
              <lb/>
            dietatis primæ B K. </s>
            <s xml:id="echoid-s21157" xml:space="preserve">altiora iuſto; </s>
            <s xml:id="echoid-s21158" xml:space="preserve">alerius vero medietatis B G. </s>
            <s xml:id="echoid-s21159" xml:space="preserve">depreſſiora.</s>
            <s xml:id="echoid-s21160" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s21161" xml:space="preserve">8 Vnde apertè apparet errare, qui Zonas illas explanatas linets rectis horarijs ad horas Italicas
              <lb/>
              <note position="right" xlink:label="note-0269-01" xlink:href="note-0269-01a" xml:space="preserve">Errata
                <lb/>
              Zonæ fe-
                <lb/>
              neſtratæ,
                <lb/>
              necnon
                <lb/>
              Horarij
                <lb/>
              cylindri-
                <lb/>
              ci antea
                <lb/>
              viſitati.</note>
            deſcribendas prius excidunt; </s>
            <s xml:id="echoid-s21162" xml:space="preserve">nam Zonis illis cylindricè poſtea curuatis, neceſſe eſt lineas rectas eua-
              <lb/>
            dere ſpirales ſeu Helices, quorum omnia puncta non ſunt in eodem plano: </s>
            <s xml:id="echoid-s21163" xml:space="preserve">deberent autem omnia
              <lb/>
            eſſe in communi ſectione plani circuli horarij Italici ſecantis cylindricum, & </s>
            <s xml:id="echoid-s21164" xml:space="preserve">conſequemer eſſe in li-
              <lb/>
            nea elliptica ſeu ouali; </s>
            <s xml:id="echoid-s21165" xml:space="preserve">ſectio enim cylindri à plano facta ellipſis eſt, ex Sereno de ſectione cylindri:
              <lb/>
            </s>
            <s xml:id="echoid-s21166" xml:space="preserve">neceſſe pariter eſt mendoſum eſſe horarium illud, quod iſtius Zonæ portio eſt, vti ſupra innuebamus.</s>
            <s xml:id="echoid-s21167" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s21168" xml:space="preserve">9 Sequitur tandem ex pręmiſſis noſtras lineas Italicas, & </s>
            <s xml:id="echoid-s21169" xml:space="preserve">Babylonicas punctuales in plano factas,
              <lb/>
            curuata cylindricè lamina euadere ellipticas ſeu ouales; </s>
            <s xml:id="echoid-s21170" xml:space="preserve">cum enim oſtenſum ſit omnia earum puncta
              <lb/>
            eſſe in lineis horarijs Ital. </s>
            <s xml:id="echoid-s21171" xml:space="preserve">& </s>
            <s xml:id="echoid-s21172" xml:space="preserve">Babylon. </s>
            <s xml:id="echoid-s21173" xml:space="preserve">erunt conſequenter in planis circulorum horariorum earum,
              <lb/>
            cruntq; </s>
            <s xml:id="echoid-s21174" xml:space="preserve">in ſectione facta ab ijs planis in ſuperficie cylindri, quæ ſectio ellipſis eſt, ex Sereno de ſect.
              <lb/>
            </s>
            <s xml:id="echoid-s21175" xml:space="preserve">cylindri. </s>
            <s xml:id="echoid-s21176" xml:space="preserve">Praxis porrò noſtra, eſt fere eandem cum ea quam docet Guidubaldus prop. </s>
            <s xml:id="echoid-s21177" xml:space="preserve">28. </s>
            <s xml:id="echoid-s21178" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s21179" xml:space="preserve">2. </s>
            <s xml:id="echoid-s21180" xml:space="preserve">de Co-
              <lb/>
            chela; </s>
            <s xml:id="echoid-s21181" xml:space="preserve">eſt tamen breuior, quia omifi deſcriptionem cuiuſdam paralellogrammi.</s>
            <s xml:id="echoid-s21182" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s21183" xml:space="preserve">10 Notandum angulos G B i. </s>
            <s xml:id="echoid-s21184" xml:space="preserve">H B i. </s>
            <s xml:id="echoid-s21185" xml:space="preserve">quos faciunt Italica, & </s>
            <s xml:id="echoid-s21186" xml:space="preserve">Babylonica cum Aſtronomica in ſu-
              <lb/>
            perficie explanata, minime debere eſſe æquales altitudini polari ſicuti in hor. </s>
            <s xml:id="echoid-s21187" xml:space="preserve">plano, ſed eſſe paulo
              <lb/>
            maiores: </s>
            <s xml:id="echoid-s21188" xml:space="preserve">cylindricata enim lamina deberent eſſe æquales altitudini poli, ſed eam curuando fiunt mi-
              <lb/>
            nores ergo prius debant eſſe maiores. </s>
            <s xml:id="echoid-s21189" xml:space="preserve">Idem patebit per circinum experienti: </s>
            <s xml:id="echoid-s21190" xml:space="preserve">deſcripto enim ex cẽtro
              <lb/>
            B. </s>
            <s xml:id="echoid-s21191" xml:space="preserve">arcu G Z. </s>
            <s xml:id="echoid-s21192" xml:space="preserve">reperies eum eſſe maiorem altitudine poli, ideſt, plures gradus continere. </s>
            <s xml:id="echoid-s21193" xml:space="preserve">quapropter
              <lb/>
            ij erroris conuincuntur, qui præcipiunt, & </s>
            <s xml:id="echoid-s21194" xml:space="preserve">Zonas prædictas, & </s>
            <s xml:id="echoid-s21195" xml:space="preserve">horaria pariter earum portiones con-
              <lb/>
            ſtruenda eſſe ſecundum angulos æquales altitudini poli. </s>
            <s xml:id="echoid-s21196" xml:space="preserve">Vnde tandem ſequitur Ital. </s>
            <s xml:id="echoid-s21197" xml:space="preserve">& </s>
            <s xml:id="echoid-s21198" xml:space="preserve">Babylon. </s>
            <s xml:id="echoid-s21199" xml:space="preserve">per
              <lb/>
            altitudinem hanc haberi non poſſe.</s>
            <s xml:id="echoid-s21200" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s21201" xml:space="preserve">11 Exiſtimo tamen errorem nullum ſenſibilem committi, ſi in loeo minoris altitudinis quam gr.
              <lb/>
            </s>
            <s xml:id="echoid-s21202" xml:space="preserve">43. </s>
            <s xml:id="echoid-s21203" xml:space="preserve">vel 44. </s>
            <s xml:id="echoid-s21204" xml:space="preserve">prædicti anguli ſiant æquales altitudini poli; </s>
            <s xml:id="echoid-s21205" xml:space="preserve">nam in altitudine 43. </s>
            <s xml:id="echoid-s21206" xml:space="preserve">& </s>
            <s xml:id="echoid-s21207" xml:space="preserve">44. </s>
            <s xml:id="echoid-s21208" xml:space="preserve">incipit appare-
              <lb/>
            reſenſibilis curuitas helicis, & </s>
            <s xml:id="echoid-s21209" xml:space="preserve">diſcrepantia ab ellipſi; </s>
            <s xml:id="echoid-s21210" xml:space="preserve">quæ quidem ſemper maior| euadit, quanto
              <lb/>
            maiores fiunt dicti anguli, quia quanto creſcit altitudo poli, tanto creſcunt hi anguli, & </s>
            <s xml:id="echoid-s21211" xml:space="preserve">conſequen-
              <lb/>
            @ar Italica, & </s>
            <s xml:id="echoid-s21212" xml:space="preserve">Babybilonica longiores euadunt, & </s>
            <s xml:id="echoid-s21213" xml:space="preserve">ideo Helices etiam longiores, atque adeo magis
              <lb/>
            ſenſibiliter ab ellipſi diſcrepantes.</s>
            <s xml:id="echoid-s21214" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s21215" xml:space="preserve">12 De vſu eius nihil noui occurit, præter ea quæ deplano dicta ſunt: </s>
            <s xml:id="echoid-s21216" xml:space="preserve">Sicut enim omnia huic
              <lb/>
              <note position="right" xlink:label="note-0269-02" xlink:href="note-0269-02a" xml:space="preserve">Vſus
                <lb/>
              eius.</note>
            communia, & </s>
            <s xml:id="echoid-s21217" xml:space="preserve">applicabilia. </s>
            <s xml:id="echoid-s21218" xml:space="preserve">Si quis tamen velit eo vti ad horas tantum Italicas ſolo triangulo G I K.
              <lb/>
            </s>
            <s xml:id="echoid-s21219" xml:space="preserve">opus habet, quo præterea potuit horas Aſtronom icas deſcribere, ſi vtatur latere G I. </s>
            <s xml:id="echoid-s21220" xml:space="preserve">& </s>
            <s xml:id="echoid-s21221" xml:space="preserve">latere regu-
              <lb/>
            læ A I. </s>
            <s xml:id="echoid-s21222" xml:space="preserve">quæ illi reſpondent, vtatur pro linea fiduciæ, illam applicando horis tympani deſcribendis,
              <lb/>
            ſicuti vtitur. </s>
            <s xml:id="echoid-s21223" xml:space="preserve">linea B A C. </s>
            <s xml:id="echoid-s21224" xml:space="preserve">pro Italicis. </s>
            <s xml:id="echoid-s21225" xml:space="preserve">Hic pariter idem examen per tabellas interſectionum adhiben-
              <lb/>
            dum eſt; </s>
            <s xml:id="echoid-s21226" xml:space="preserve">& </s>
            <s xml:id="echoid-s21227" xml:space="preserve">ſtylus eodem modo fingendum, & </s>
            <s xml:id="echoid-s21228" xml:space="preserve">Horologium euadet idem cum ſuperiori, quare, & </s>
            <s xml:id="echoid-s21229" xml:space="preserve">
              <lb/>
            idem vſus, &</s>
            <s xml:id="echoid-s21230" xml:space="preserve">c.</s>
            <s xml:id="echoid-s21231" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div578" type="section" level="1" n="423">
          <head xml:id="echoid-head445" xml:space="preserve">Laus Deo O. M.</head>
        </div>
      </text>
    </echo>
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