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

Table of contents

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[521.] THEOR. 25. PROPOS. 27.
Page: 394 (382)
[522.] SCHOLIVM.
Page: 396 (384)
[523.] THEOR. 26. PROPOS. 28.
Page: 397 (385)
[524.] SCHOLIVM.
Page: 398 (386)
[525.] THEOR. 27. PROPOS. 29.
Page: 398 (386)
[526.] SCHOLIVM.
Page: 400 (388)
[527.] THEOR. 28. PROPOS. 30.
Page: 400 (388)
[528.] THEOR. 29. PROPOS. 31.
Page: 401 (389)
[529.] THEOR. 30. PROPOS. 32.
Page: 402 (390)
[530.] THEOR. 31. PROPOS. 33.
Page: 403 (391)
[531.] THEOR. 32. PROPOS. 34.
Page: 403 (391)
[532.] THEOR. 33. PROPOS. 35.
Page: 404 (392)
[533.] THEOR. 34. PROPOS. 36.
Page: 406 (394)
[534.] THEOR. 35. PROPOS. 37.
Page: 407 (395)
[535.] THEOR. 36. PROPOS. 38.
Page: 408 (396)
[536.] COROLLARIVM.
Page: 408 (396)
[537.] THEOR. 37. PROPOS. 39.
Page: 409 (397)
[538.] COROLLARIVM.
Page: 409 (397)
[539.] THEOR. 38. PROPOS. 40.
Page: 410 (398)
[540.] SCHOLIVM.
Page: 413 (401)
[541.] I.
Page: 414 (402)
[542.] II.
Page: 415 (403)
[543.] III.
Page: 415 (403)
[544.] IIII.
Page: 416 (404)
[545.] V.
Page: 417 (405)
[546.] VI.
Page: 417 (405)
[547.] VII.
Page: 418 (406)
[548.] VIII.
Page: 419 (407)
[549.] THEOR. 39. PROPOS. 41.
Page: 420 (408)
[550.] COROLLARIVM.
Page: 423 (411)
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            nor. </s>
            <s xml:id="echoid-s13644" xml:space="preserve">Igitur cum arcus BC, quadrante quidem maior ſit, & </s>
            <s xml:id="echoid-s13645" xml:space="preserve">AB, minor, erit
              <lb/>
            arcus AC, quadrante maior. </s>
            <s xml:id="echoid-s13646" xml:space="preserve">Quamobrem in omni triangulo ſphærico re-
              <lb/>
              <note position="left" xlink:label="note-408-01" xlink:href="note-408-01a" xml:space="preserve">35. huiu@.</note>
            ctangulo, &</s>
            <s xml:id="echoid-s13647" xml:space="preserve">c. </s>
            <s xml:id="echoid-s13648" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s13649" xml:space="preserve"/>
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        <div xml:id="echoid-div1084" type="section" level="1" n="535">
          <head xml:id="echoid-head570" xml:space="preserve">THEOR. 36. PROPOS. 38.</head>
          <p>
            <s xml:id="echoid-s13650" xml:space="preserve">IN omni triangulo ſphærico rectangulo, ſi ar-
              <lb/>
            cus rectum angulum ſubtendens fuerit quadrans,
              <lb/>
            erit ſaltem alter reliquorum angulorũ rectus quo-
              <lb/>
            que: </s>
            <s xml:id="echoid-s13651" xml:space="preserve">ſi verò minor quadrante, erit vterq; </s>
            <s xml:id="echoid-s13652" xml:space="preserve">reliquo-
              <lb/>
            rum angulorum vel maior recto, vel minor: </s>
            <s xml:id="echoid-s13653" xml:space="preserve">ſi de-
              <lb/>
            nique quadrante maior, erit alter reliquorum an-
              <lb/>
            gulorum maior recto, & </s>
            <s xml:id="echoid-s13654" xml:space="preserve">alter minor.</s>
            <s xml:id="echoid-s13655" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13656" xml:space="preserve">IN triangulo ſphærico ABC, cuius angulus B, rectus, ſit primum arcus
              <lb/>
            AC, ſubtendens angulum rectum B, quadrans. </s>
            <s xml:id="echoid-s13657" xml:space="preserve">Dico ſaltem alterum angu-
              <lb/>
            lorum A, C, rectum quoque eſſe. </s>
            <s xml:id="echoid-s13658" xml:space="preserve">Cum enim angulus B, ſit rectus, & </s>
            <s xml:id="echoid-s13659" xml:space="preserve">arcus
              <lb/>
            AC, quadrans, erit ſaltem alter arcuum AB, BC, quadrans; </s>
            <s xml:id="echoid-s13660" xml:space="preserve">atque adeò & </s>
            <s xml:id="echoid-s13661" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-408-02" xlink:href="note-408-02a" xml:space="preserve">36. huius.</note>
            angulus A, vel C, quem ille arcus ſubtendit, rectus erit.</s>
            <s xml:id="echoid-s13662" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">34. huius.</note>
          <figure number="257">
            <image file="408-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/408-01"/>
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          <p>
            <s xml:id="echoid-s13663" xml:space="preserve">SIT deinde areus AC, quadrante minor. </s>
            <s xml:id="echoid-s13664" xml:space="preserve">Dico
              <lb/>
            vtrumque angulorum A, C, eſſe maiorem, vel mino-
              <lb/>
            rem recto. </s>
            <s xml:id="echoid-s13665" xml:space="preserve">Erit enim vterque arcus AB, BC, vel ma-
              <lb/>
              <note position="left" xlink:label="note-408-04" xlink:href="note-408-04a" xml:space="preserve">36. huius.</note>
            ior quadrante, vel minor. </s>
            <s xml:id="echoid-s13666" xml:space="preserve">Quare vterque angulus
              <lb/>
            A, C, maior erit recto, vel minor.</s>
            <s xml:id="echoid-s13667" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">34. huius.</note>
          <p>
            <s xml:id="echoid-s13668" xml:space="preserve">POSTREMO ſit arcus AC, maior quadran-
              <lb/>
            te. </s>
            <s xml:id="echoid-s13669" xml:space="preserve">Dico alterum angulorum A, C, eſſe recto maio-
              <lb/>
            rem, & </s>
            <s xml:id="echoid-s13670" xml:space="preserve">alterum minorem. </s>
            <s xml:id="echoid-s13671" xml:space="preserve">Erit enim alter arcuum
              <lb/>
            AB, BC, quadrante maior, & </s>
            <s xml:id="echoid-s13672" xml:space="preserve">alter minor. </s>
            <s xml:id="echoid-s13673" xml:space="preserve">Igitur
              <lb/>
              <note position="left" xlink:label="note-408-06" xlink:href="note-408-06a" xml:space="preserve">36. huius.</note>
            alter angulorum A, C, recto erit maior, & </s>
            <s xml:id="echoid-s13674" xml:space="preserve">alter mi-
              <lb/>
              <note position="left" xlink:label="note-408-07" xlink:href="note-408-07a" xml:space="preserve">34. huius.</note>
            nor. </s>
            <s xml:id="echoid-s13675" xml:space="preserve">Quapropter In omni triangulo ſphærico rectangulo, &</s>
            <s xml:id="echoid-s13676" xml:space="preserve">c. </s>
            <s xml:id="echoid-s13677" xml:space="preserve">Quod oſten-
              <lb/>
            dendum erat.</s>
            <s xml:id="echoid-s13678" xml:space="preserve"/>
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        <div xml:id="echoid-div1088" type="section" level="1" n="536">
          <head xml:id="echoid-head571" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s13679" xml:space="preserve">EX his omnibus colligitur, In omni triangulo ſphærico, cuius vnus arcuum eſt qua-
              <lb/>
            drans, vnusq́ue angulorum rectus, reliquorum quoque arcuum vnum ſal@em eſſe quadran
              <lb/>
            tem, & </s>
            <s xml:id="echoid-s13680" xml:space="preserve">reliquotum angulorum vnum ſaltem rectum. </s>
            <s xml:id="echoid-s13681" xml:space="preserve">Nam ſi vnus angulorum rectus eſt,
              <lb/>
            & </s>
            <s xml:id="echoid-s13682" xml:space="preserve">alter arcuum ipſum com prehendentium quadrans, erit & </s>
            <s xml:id="echoid-s13683" xml:space="preserve">arcus rectum angulum ſubten
              <lb/>
              <note position="left" xlink:label="note-408-08" xlink:href="note-408-08a" xml:space="preserve">35. huius.</note>
            dens quadrans; </s>
            <s xml:id="echoid-s13684" xml:space="preserve">& </s>
            <s xml:id="echoid-s13685" xml:space="preserve">angulus quem prior quadrans ſubtendit rectus: </s>
            <s xml:id="echoid-s13686" xml:space="preserve">Si verò arcus angulum
              <lb/>
              <note position="left" xlink:label="note-408-09" xlink:href="note-408-09a" xml:space="preserve">34. huius.</note>
            rectum ſubtendens quadrans eſt, erit & </s>
            <s xml:id="echoid-s13687" xml:space="preserve">vel vterque arcuum rectum angulum comprehen-
              <lb/>
              <note position="left" xlink:label="note-408-10" xlink:href="note-408-10a" xml:space="preserve">36. huius.</note>
            dentium, vel alter ſaltem quadrans; </s>
            <s xml:id="echoid-s13688" xml:space="preserve">& </s>
            <s xml:id="echoid-s13689" xml:space="preserve">vel vterque reliquorum angulorum, vel alter ſaltem
              <lb/>
              <note position="left" xlink:label="note-408-11" xlink:href="note-408-11a" xml:space="preserve">38. huius.</note>
            rectus. </s>
            <s xml:id="echoid-s13690" xml:space="preserve">Itaque fieri non poteſt, vt detur triangulum ſphæricum rectangulum, cuius vnus
              <lb/>
              <note position="left" xlink:label="note-408-12" xlink:href="note-408-12a" xml:space="preserve">Nota.</note>
            duntaxat arcus ſit quadrans, ſed vel nullus erit quadrans, vel omnes tres, vel duo quadran-
              <lb/>
            ces erunt.</s>
            <s xml:id="echoid-s13691" xml:space="preserve"/>
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