Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres

Table of figures

< >
[Figure 281]
Page: 428
[Figure 282]
Page: 430
[Figure 283]
Page: 430
[Figure 284]
Page: 431
[Figure 285]
Page: 431
[Figure 286]
Page: 432
[Figure 287]
Page: 433
[Figure 288]
Page: 434
[Figure 289]
Page: 435
[Figure 290]
Page: 436
[Figure 291]
Page: 437
[Figure 292]
Page: 438
[Figure 293]
Page: 440
[Figure 294]
Page: 440
[Figure 295]
Page: 441
[Figure 296]
Page: 441
[Figure 297]
Page: 442
[Figure 298]
Page: 442
[Figure 299]
Page: 443
[Figure 300]
Page: 444
[Figure 301]
Page: 444
[Figure 302]
Page: 445
[Figure 303]
Page: 445
[Figure 304]
Page: 446
[Figure 305]
Page: 446
[Figure 306]
Page: 447
[Figure 307]
Page: 448
[Figure 308]
Page: 448
[Figure 309]
Page: 449
[Figure 310]
Page: 450
< >
page |< < (425) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1183" type="section" level="1" n="565">
          <p style="it">
            <s xml:id="echoid-s14877" xml:space="preserve">
              <pb o="425" file="437" n="437" rhead=""/>
            problema propoſ. </s>
            <s xml:id="echoid-s14878" xml:space="preserve">43. </s>
            <s xml:id="echoid-s14879" xml:space="preserve">ex datis duobus arcubus. </s>
            <s xml:id="echoid-s14880" xml:space="preserve">Deinde per problema 1. </s>
            <s xml:id="echoid-s14881" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s14882" xml:space="preserve">41.
              <lb/>
            </s>
            <s xml:id="echoid-s14883" xml:space="preserve">ex hoc arcu inuento, & </s>
            <s xml:id="echoid-s14884" xml:space="preserve">alterutro circa angulum rectum dato, inueniendus angulus
              <lb/>
            huic dato arcui oppoſitus. </s>
            <s xml:id="echoid-s14885" xml:space="preserve">Vides igitur, id, quod primo loco in vtroque problemate
              <lb/>
            quæritur, duplici opere inueſtigari per ſinus, quod ſimplici per tangentes inuenimus. </s>
            <s xml:id="echoid-s14886" xml:space="preserve">
              <lb/>
            Eadem ratio eſt in ſequentibus problematibus, quod ſemel hic monuiſſe ſatis ſit.</s>
            <s xml:id="echoid-s14887" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1187" type="section" level="1" n="566">
          <head xml:id="echoid-head601" xml:space="preserve">THEOR. 43. PROPOS. 45.</head>
          <p>
            <s xml:id="echoid-s14888" xml:space="preserve">IN omni triangulo ſphærico rectangulo, cu-
              <lb/>
            ius omnes arcus quadrante ſint minores: </s>
            <s xml:id="echoid-s14889" xml:space="preserve">ſinus to-
              <lb/>
            tus ad ſinum complementi vtriuſuis angulorum
              <lb/>
            acutorum eandem proportionem habet, quam tan
              <lb/>
            gens arcus recto angulo oppoſiti ad tangentem ar-
              <lb/>
            cus dicto acuto angulo adiacentis.</s>
            <s xml:id="echoid-s14890" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14891" xml:space="preserve">IN triangulo ſphærico ABC, cuius omnes arcus quadrante minores, ſit
              <lb/>
            angulus B, rectus. </s>
            <s xml:id="echoid-s14892" xml:space="preserve">Dico ita eſſe ſinum totum ad ſinum complementi anguli A,
              <lb/>
            vt eſt tangens arcus AC, ad tangentem arcus AB. </s>
            <s xml:id="echoid-s14893" xml:space="preserve">Productis enim arcubus
              <lb/>
            AB, AC, dictum angulum comprehendenti-
              <lb/>
            bus, donec quadrantes ſiant AD, AE; </s>
            <s xml:id="echoid-s14894" xml:space="preserve">de-
              <lb/>
              <figure xlink:label="fig-437-01" xlink:href="fig-437-01a" number="291">
                <image file="437-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/437-01"/>
              </figure>
            ſcriptoq́; </s>
            <s xml:id="echoid-s14895" xml:space="preserve">per D, E, arcu circuli maximi DE,
              <lb/>
            productoq́ue, donec cum arcu BC, produ-
              <lb/>
            cto coëat in F: </s>
            <s xml:id="echoid-s14896" xml:space="preserve">erit vterque angulus D, E,
              <lb/>
              <note position="right" xlink:label="note-437-01" xlink:href="note-437-01a" xml:space="preserve">25. huius.</note>
            rectus, ob quadrantes AD, AE; </s>
            <s xml:id="echoid-s14897" xml:space="preserve">& </s>
            <s xml:id="echoid-s14898" xml:space="preserve">DE, ar-
              <lb/>
            cus erit anguli A, cum A, ſit polus arcus DE.
              <lb/>
            </s>
            <s xml:id="echoid-s14899" xml:space="preserve">
              <note position="right" xlink:label="note-437-02" xlink:href="note-437-02a" xml:space="preserve">26. huius.</note>
            Item arcus DF, BF, quadrantes erunt, ob re-
              <lb/>
            ctos angulos B, D; </s>
            <s xml:id="echoid-s14900" xml:space="preserve">ac proinde arcus EF, com
              <lb/>
            plementum anguli A. </s>
            <s xml:id="echoid-s14901" xml:space="preserve">Quoniam igitur duo
              <lb/>
            circuli maximi in ſphæra BF, DF, ſe in terſe-
              <lb/>
            cant in F; </s>
            <s xml:id="echoid-s14902" xml:space="preserve">ductiq́; </s>
            <s xml:id="echoid-s14903" xml:space="preserve">ſunt ex punctis B, C, arcus
              <lb/>
            BF, ad arcum DF, arcus perpẽdiculares BD,
              <lb/>
            CE; </s>
            <s xml:id="echoid-s14904" xml:space="preserve">erit vt ſinus totus quadrantis DF, ad tangentem arcus BD, ita ſinus ar-
              <lb/>
              <note position="right" xlink:label="note-437-03" xlink:href="note-437-03a" xml:space="preserve">Theor. 6.
                <lb/>
              ſcholij 40.
                <lb/>
              huius.</note>
            cus EF, hoc eſt, ſinus complementi anguli A, ad tangentem arcus CE: </s>
            <s xml:id="echoid-s14905" xml:space="preserve">Et
              <lb/>
            permutando, vt ſinus totus ad ſinum complementi anguli A, ita tangens ar-
              <lb/>
            cus BD, ad tangentem arcus CE. </s>
            <s xml:id="echoid-s14906" xml:space="preserve">Eſt autem (cum AC, AB, ſint complemen
              <lb/>
            ta arcuum CE, BD.) </s>
            <s xml:id="echoid-s14907" xml:space="preserve">vt tangens arcus BD, ad tangentem arcus CE, ita tan
              <lb/>
              <note position="right" xlink:label="note-437-04" xlink:href="note-437-04a" xml:space="preserve">21. Sinuũ.</note>
            gens arcus AC, ad tangentem arcus AB. </s>
            <s xml:id="echoid-s14908" xml:space="preserve">Igitur erit quoque, vt ſinus totus
              <lb/>
            ad ſinum complementi anguli A, ita tangens arcus AC, recto angulo oppoſi-
              <lb/>
            ti ad tangentem arcus AB, acuto angulo A, adiacentis. </s>
            <s xml:id="echoid-s14909" xml:space="preserve">Eodem modo oſten-
              <lb/>
            demus, ita eſſe ſinum totum ad ſinum complementi anguli C, vt eſt tangens
              <lb/>
            arcus AC, recto angulo oppoſiti ad tangentem arcus BC, angulo acuto C,
              <lb/>
            adiacentis, ſi nimirum arcus CA, CB, angulum C, continentes producantur,
              <lb/>
            &</s>
            <s xml:id="echoid-s14910" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14911" xml:space="preserve">In omni ergo triangulo ſphærico rectangulo, &</s>
            <s xml:id="echoid-s14912" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14913" xml:space="preserve">Quod oſtendendũ erat.</s>
            <s xml:id="echoid-s14914" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum