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

Table of contents

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[401.] arcuum eiuſdem Quadrantis
Page: 281 (269)
[402.] complementorum arcuum eiuſdem Quadrantis
Page: 281 (269)
[403.] Gradus Quadrantis pro ſecantibus
Page: 282 (270)
[404.] Gradus Quadrantis pro ſecantibus
Page: 282 (270)
[405.] arcuum eiuſdem Quadrantis
Page: 283 (271)
[406.] complementorum arcuum eiuſdem Quadrantis
Page: 283 (271)
[407.] Gradus Quadrantis pro ſecantibus
Page: 284 (272)
[408.] Gradus Quadrantis pro ſecantibus
Page: 284 (272)
[409.] arcuum eiuſdem Quadrantis
Page: 285 (273)
[410.] complementorum arcuum eiuſdem Quadrantis.
Page: 285 (273)
[411.] Gradus Quadrantis pro ſecantibus
Page: 286 (274)
[412.] Gradus Quadrantis pro ſecantibus
Page: 286 (274)
[413.] arcuum eiuſdem Quadrantis
Page: 287 (275)
[414.] complementorum arcuum eiuſdem Quadrantis.
Page: 287 (275)
[415.] Gradus Quadrantis pro ſecantibus
Page: 288 (276)
[416.] Gradus Quadrantis pro ſecantibus
Page: 288 (276)
[417.] arcuum eiuſdem Quadrantis
Page: 289 (277)
[418.] complementorum arcuum eiuſdem Quadrantis.
Page: 289 (277)
[419.] Gradus Quadrantis pro ſecantibus
Page: 290 (278)
[420.] Gradus Quadrantis pro ſecantibus
Page: 290 (278)
[421.] arcuum eiuſdem Quadrantis
Page: 291 (279)
[422.] complementorum arcuum eiuſdem Quadrantis.
Page: 291 (279)
[423.] Gradus Quadrantis pro ſecantibus
Page: 292 (280)
[424.] Gradus Quadrantis pro ſecantibus
Page: 292 (280)
[425.] arcuum eiuſdem Quadrantis.
Page: 293 (281)
[426.] complementorum arcuum eiuſdem Quadrantis.
Page: 293 (281)
[427.] Gradus Quadrantis pro ſecantibus
Page: 294 (282)
[428.] Gradus Quadrantis pro ſecantibus
Page: 294 (282)
[429.] arcuum eiuſdem Quadrantis.
Page: 295 (283)
[430.] complementorum arcuum eiuſdem Quadrantis.
Page: 295 (283)
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            ximus, atque adeò idem non ſit, qui EF; </s>
            <s xml:id="echoid-s12217" xml:space="preserve">ſed vel cadat infra arcum EF, ſiue
              <lb/>
            ſupra, (nihil enim intereſt, quocunque cadat.) </s>
            <s xml:id="echoid-s12218" xml:space="preserve">fiat nihilominus angulus
              <lb/>
              <note position="left" xlink:label="note-378-01" xlink:href="note-378-01a" xml:space="preserve">10. huius.</note>
            FDH, angulo A, æqualis: </s>
            <s xml:id="echoid-s12219" xml:space="preserve">eritq̀ue rurſus arcus DH, arcui DE, hoc eſt, ar-
              <lb/>
              <note position="left" xlink:label="note-378-02" xlink:href="note-378-02a" xml:space="preserve">28. tertij.</note>
            cui AB, æqualis; </s>
            <s xml:id="echoid-s12220" xml:space="preserve">eo quòd rectæ ſubtendentes DE, DH, æquales ſint, ex de-
              <lb/>
            fin. </s>
            <s xml:id="echoid-s12221" xml:space="preserve">poli. </s>
            <s xml:id="echoid-s12222" xml:space="preserve">Ducto igitur per puncta F, H, arcu circuli maximi FH; </s>
            <s xml:id="echoid-s12223" xml:space="preserve">cum latera
              <lb/>
              <note position="left" xlink:label="note-378-03" xlink:href="note-378-03a" xml:space="preserve">10. 1. Theo.</note>
            AB, AC, lateribus DH, DF, æqualia ſint, angulosq̀ue contineant æquales;
              <lb/>
            </s>
            <s xml:id="echoid-s12224" xml:space="preserve">erunt & </s>
            <s xml:id="echoid-s12225" xml:space="preserve">baſes BC, HF, æquales. </s>
            <s xml:id="echoid-s12226" xml:space="preserve">Quoniam verò circulus maximus DF, per
              <lb/>
              <note position="left" xlink:label="note-378-04" xlink:href="note-378-04a" xml:space="preserve">7. huius.</note>
            D, polum circuli EHF, tranſiens eum bifariam ſecat; </s>
            <s xml:id="echoid-s12227" xml:space="preserve">erit arcus EHF, ſemi-
              <lb/>
              <note position="left" xlink:label="note-378-05" xlink:href="note-378-05a" xml:space="preserve">15. 1. Theo.</note>
            circulo minor; </s>
            <s xml:id="echoid-s12228" xml:space="preserve">(quia arcus à puncto F, per E, vſque ad illud punctum, in quo,
              <lb/>
            ſi protractus eſſet vltra E, ſecaretur ab arcu FD, ad partes D, producto, eſt
              <lb/>
            ſemicirculus: </s>
            <s xml:id="echoid-s12229" xml:space="preserve">quandoquidem circulus arcus EHF, bifariam ſecatur a circulo
              <lb/>
            arcus FD, vt dictum eſt.) </s>
            <s xml:id="echoid-s12230" xml:space="preserve">atque adeo recta FE, maior, quàm recta FH, in eo-
              <lb/>
              <note position="left" xlink:label="note-378-06" xlink:href="note-378-06a" xml:space="preserve">25. tertij.</note>
            dem circulo: </s>
            <s xml:id="echoid-s12231" xml:space="preserve">quia illa propin quior eſt centro circuli EHF, hoc eſt, diame-
              <lb/>
            tro, quàm hæc. </s>
            <s xml:id="echoid-s12232" xml:space="preserve">Cum ergo circuli arcuum EF, HF, maximi ſint, ideoq̀ æqua-
              <lb/>
            les; </s>
            <s xml:id="echoid-s12233" xml:space="preserve">ſit autem vterque arcus EF, HF, ſemicirculo minor; </s>
            <s xml:id="echoid-s12234" xml:space="preserve">erit arcus EF, ma-
              <lb/>
              <note position="left" xlink:label="note-378-07" xlink:href="note-378-07a" xml:space="preserve">2. huius.</note>
            ior arcu HF: </s>
            <s xml:id="echoid-s12235" xml:space="preserve">Oſtenſus autem eſt arcus HF, æqualis arcui BC. </s>
            <s xml:id="echoid-s12236" xml:space="preserve">Maior igitur
              <lb/>
              <note position="left" xlink:label="note-378-08" xlink:href="note-378-08a" xml:space="preserve">ſchol. 28.</note>
            erit quoque arcus EF, arcu BC. </s>
            <s xml:id="echoid-s12237" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s12238" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">tertij.</note>
          <p>
            <s xml:id="echoid-s12239" xml:space="preserve">SINT deinde triangula propoſita non Iſoſcelia, ſed latus AB, maius
              <lb/>
            ſit latere AC, ac proinde & </s>
            <s xml:id="echoid-s12240" xml:space="preserve">latus DE, maius latere DF. </s>
            <s xml:id="echoid-s12241" xml:space="preserve">Producto ergo arcu
              <lb/>
            DF, ad partes F, abſciſſoq́ue arcu DG, æquali ipſi DE, qui minor eſt ſe-
              <lb/>
              <note position="left" xlink:label="note-378-10" xlink:href="note-378-10a" xml:space="preserve">1. huius.</note>
              <figure xlink:label="fig-378-01" xlink:href="fig-378-01a" number="210">
                <image file="378-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/378-01"/>
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            micirculo, deſcribatur ex polo D, per pun
              <lb/>
              <note position="left" xlink:label="note-378-11" xlink:href="note-378-11a" xml:space="preserve">2. huius.</note>
            cta E, G, arcus circuli EHG, ſiue maxi-
              <lb/>
            ximus is ſit, ſiue non maximus. </s>
            <s xml:id="echoid-s12242" xml:space="preserve">Fiat rur-
              <lb/>
            ſus angulus FDH, angulo A, æqualis;
              <lb/>
            </s>
            <s xml:id="echoid-s12243" xml:space="preserve">
              <note position="left" xlink:label="note-378-12" xlink:href="note-378-12a" xml:space="preserve">20. huius.</note>
            eritq́ue arcus DH, arcui DE, hoc eſt, ar-
              <lb/>
              <note position="left" xlink:label="note-378-13" xlink:href="note-378-13a" xml:space="preserve">28. tertij.</note>
            cui AB, æqualis; </s>
            <s xml:id="echoid-s12244" xml:space="preserve">eò quòd rectæ ſubtenſæ
              <lb/>
            DH, DE, æquales ſint, ex defin. </s>
            <s xml:id="echoid-s12245" xml:space="preserve">poli. </s>
            <s xml:id="echoid-s12246" xml:space="preserve">Du-
              <lb/>
            cto igitur per puncta H, F, arcu circuli
              <lb/>
            maximi HF, erit, vt prius, arcus BC, ar-
              <lb/>
            cui HF, æqualis. </s>
            <s xml:id="echoid-s12247" xml:space="preserve">Quoniam verò circulus
              <lb/>
            maximus DG, per D, polum circuli EG,
              <lb/>
              <note position="left" xlink:label="note-378-14" xlink:href="note-378-14a" xml:space="preserve">7. huius.</note>
            ducitur, eſtq́ue punctum F, intra periphe-
              <lb/>
            riam circuli EG, (nempe inter circulum, & </s>
            <s xml:id="echoid-s12248" xml:space="preserve">polum D.) </s>
            <s xml:id="echoid-s12249" xml:space="preserve">& </s>
            <s xml:id="echoid-s12250" xml:space="preserve">præter eius polum;
              <lb/>
            </s>
            <s xml:id="echoid-s12251" xml:space="preserve">erit arcus FE, maior arcu FH, cum ille propin quior ſit arcui FD, per po-
              <lb/>
              <note position="left" xlink:label="note-378-15" xlink:href="note-378-15a" xml:space="preserve">Schol. 21.</note>
            lum D, tranſeunti, & </s>
            <s xml:id="echoid-s12252" xml:space="preserve">vterque arcus FE, FH, ſemicirculo ſit minor: </s>
            <s xml:id="echoid-s12253" xml:space="preserve">propte-
              <lb/>
              <note position="left" xlink:label="note-378-16" xlink:href="note-378-16a" xml:space="preserve">2. Theod.</note>
            rea quòd non ſe interſecant, niſi in puncto F: </s>
            <s xml:id="echoid-s12254" xml:space="preserve">Oſten ſus eſt autem arcus HF,
              <lb/>
            arcui BC, æqualis. </s>
            <s xml:id="echoid-s12255" xml:space="preserve">Maior ergo erit quoque arcus EF, arcu BC. </s>
            <s xml:id="echoid-s12256" xml:space="preserve">Quod eſt
              <lb/>
            propoſitum.</s>
            <s xml:id="echoid-s12257" xml:space="preserve"/>
          </p>
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            <image file="378-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/378-02"/>
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          <p>
            <s xml:id="echoid-s12258" xml:space="preserve">SED iam baſis EF, maior ſit baſi BC.
              <lb/>
            </s>
            <s xml:id="echoid-s12259" xml:space="preserve">Dico & </s>
            <s xml:id="echoid-s12260" xml:space="preserve">angulum D, maiorem eſſe angulo
              <lb/>
            A. </s>
            <s xml:id="echoid-s12261" xml:space="preserve">Si enim angulus D, maior non eſt angu-
              <lb/>
            lo A, erit vel æqualis, vel minor. </s>
            <s xml:id="echoid-s12262" xml:space="preserve">Si æqualis
              <lb/>
            dicatur eſſe, erit arcus EF, æqualis arcui
              <lb/>
              <note position="left" xlink:label="note-378-17" xlink:href="note-378-17a" xml:space="preserve">9. huius.</note>
            B C. </s>
            <s xml:id="echoid-s12263" xml:space="preserve">quod eſt abſurdum. </s>
            <s xml:id="echoid-s12264" xml:space="preserve">Ponitur enim arcus
              <lb/>
            EF, maior arcu BC. </s>
            <s xml:id="echoid-s12265" xml:space="preserve">Si verò minor dicatur
              <lb/>
            eſſe angulus D, angulo A, erit, vt iam oſten
              <lb/>
            ſum eſt, arcus BC, maior arcu EF. </s>
            <s xml:id="echoid-s12266" xml:space="preserve">quod
              <lb/>
            etiam abſurdum eſt, cum EF, maior </s>
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