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

Table of figures

< >
[Figure 121]
Page: 124
[Figure 122]
Page: 125
[Figure 123]
Page: 126
[Figure 124]
Page: 127
[Figure 125]
Page: 128
[Figure 126]
Page: 129
[Figure 127]
Page: 130
[Figure 128]
Page: 131
[Figure 129]
Page: 132
[Figure 130]
Page: 133
[Figure 131]
Page: 135
[Figure 132]
Page: 137
[Figure 133]
Page: 140
[Figure 134]
Page: 143
[Figure 135]
Page: 185
[Figure 136]
Page: 186
[Figure 137]
Page: 187
[Figure 138]
Page: 188
[Figure 139]
Page: 189
[Figure 140]
Page: 190
[Figure 141]
Page: 191
[Figure 142]
Page: 191
[Figure 143]
Page: 192
[Figure 144]
Page: 193
[Figure 145]
Page: 193
[Figure 146]
Page: 195
[Figure 147]
Page: 198
[Figure 148]
Page: 199
[Figure 149]
Page: 202
[Figure 150]
Page: 203
< >
page |< < (114) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div363" type="section" level="1" n="159">
          <pb o="114" file="126" n="126" rhead=""/>
          <p>
            <s xml:id="echoid-s4283" xml:space="preserve">IN quadrante ABC, ſit BD, arcus grad. </s>
            <s xml:id="echoid-s4284" xml:space="preserve">54. </s>
            <s xml:id="echoid-s4285" xml:space="preserve">ac proinde eius cõplementum
              <lb/>
            CD, grad. </s>
            <s xml:id="echoid-s4286" xml:space="preserve">36. </s>
            <s xml:id="echoid-s4287" xml:space="preserve">quod diuidatur bifariam in H, vt vterq; </s>
            <s xml:id="echoid-s4288" xml:space="preserve">arcuũ CH, HD, habeat
              <lb/>
            grad. </s>
            <s xml:id="echoid-s4289" xml:space="preserve">18. </s>
            <s xml:id="echoid-s4290" xml:space="preserve">Ducatur DM, ad AB, perpendicularis pro ſinu arcus grad. </s>
            <s xml:id="echoid-s4291" xml:space="preserve">54. </s>
            <s xml:id="echoid-s4292" xml:space="preserve">& </s>
            <s xml:id="echoid-s4293" xml:space="preserve">DE,
              <lb/>
              <figure xlink:label="fig-126-01" xlink:href="fig-126-01a" number="123">
                <image file="126-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/126-01"/>
              </figure>
            ad AC, perpédicularis pro ſinu arcus grad. </s>
            <s xml:id="echoid-s4294" xml:space="preserve">36. </s>
            <s xml:id="echoid-s4295" xml:space="preserve">Iunga
              <lb/>
            tur quoq; </s>
            <s xml:id="echoid-s4296" xml:space="preserve">recta AH, quæ per lẽma in definitionibus
              <lb/>
            demonſtratũ ſecabit rectã CD, in I, bifariam, ac pro
              <lb/>
            inde & </s>
            <s xml:id="echoid-s4297" xml:space="preserve">ad angulos rectos: </s>
            <s xml:id="echoid-s4298" xml:space="preserve">eritq́ propterea CI, ſinus
              <lb/>
              <note position="left" xlink:label="note-126-01" xlink:href="note-126-01a" xml:space="preserve">3. tertij.</note>
            rectus arcus CH, grad. </s>
            <s xml:id="echoid-s4299" xml:space="preserve">18. </s>
            <s xml:id="echoid-s4300" xml:space="preserve">Sũpta tandẽ recta EF, ipſi
              <lb/>
            EC, æquali, diuidantur AC, AF, bifariã in G, K, & </s>
            <s xml:id="echoid-s4301" xml:space="preserve">
              <lb/>
            ex K, ad AC, perpendicularis ducatur KL. </s>
            <s xml:id="echoid-s4302" xml:space="preserve">Dico ſi-
              <lb/>
            num rectũ DM, arcus grad. </s>
            <s xml:id="echoid-s4303" xml:space="preserve">54. </s>
            <s xml:id="echoid-s4304" xml:space="preserve">hoc eſt, rectam AE,
              <lb/>
              <note position="left" xlink:label="note-126-02" xlink:href="note-126-02a" xml:space="preserve">34. primi.</note>
            illi ęqualẽ, componi ex AG, dimidio ſinus totius, & </s>
            <s xml:id="echoid-s4305" xml:space="preserve">
              <lb/>
            ex CI, ſinu recto arcus grad. </s>
            <s xml:id="echoid-s4306" xml:space="preserve">18. </s>
            <s xml:id="echoid-s4307" xml:space="preserve">hoc eſt, rectam GE,
              <lb/>
            (quæ cũ AG, conſtituit totam rectã AE,) ęqualẽ eſ
              <lb/>
            ſe ſinui recto CI. </s>
            <s xml:id="echoid-s4308" xml:space="preserve">Item ſinũ verſum arcus grad. </s>
            <s xml:id="echoid-s4309" xml:space="preserve">72. </s>
            <s xml:id="echoid-s4310" xml:space="preserve">componi ex dimidio ſinus to
              <lb/>
            tius, & </s>
            <s xml:id="echoid-s4311" xml:space="preserve">ex CE, ſinu verſo arcus CD, grad. </s>
            <s xml:id="echoid-s4312" xml:space="preserve">36. </s>
            <s xml:id="echoid-s4313" xml:space="preserve">hoc eſt, rectam EK, (quæ cum
              <lb/>
            ſinu verſo CE, rectam CK, componit) æqualem eſſe dimidio ſinus totius, ip-
              <lb/>
            ſam vero CK, eſſe ſinum verſum arcus grad. </s>
            <s xml:id="echoid-s4314" xml:space="preserve">72. </s>
            <s xml:id="echoid-s4315" xml:space="preserve">hoc eſt, arcum CL, (cuius ſi-
              <lb/>
            nus verſus eſt CK,) eſſe grad. </s>
            <s xml:id="echoid-s4316" xml:space="preserve">72. </s>
            <s xml:id="echoid-s4317" xml:space="preserve">Ducta enim recta LN, ad AB, perpendicu-
              <lb/>
            lari, pro ſinu arcus BL, iungantur rectæ AD, DF. </s>
            <s xml:id="echoid-s4318" xml:space="preserve">Quoniam igitur arcus
              <lb/>
            CH, grad. </s>
            <s xml:id="echoid-s4319" xml:space="preserve">18. </s>
            <s xml:id="echoid-s4320" xml:space="preserve">continet {1/5}. </s>
            <s xml:id="echoid-s4321" xml:space="preserve">quadrantis BC, (quòd quinquies 18. </s>
            <s xml:id="echoid-s4322" xml:space="preserve">faciant 90.)
              <lb/>
            </s>
            <s xml:id="echoid-s4323" xml:space="preserve">continebit arcus CD, {2/5}. </s>
            <s xml:id="echoid-s4324" xml:space="preserve">eiuſdem quadrantis, ac proinde proportio arcus
              <lb/>
            CD, ad arcum BC, erit vt 2. </s>
            <s xml:id="echoid-s4325" xml:space="preserve">ad 5. </s>
            <s xml:id="echoid-s4326" xml:space="preserve">Eſt autem, vt arcus CD, ad arcum BC, ita
              <lb/>
              <note position="left" xlink:label="note-126-03" xlink:href="note-126-03a" xml:space="preserve">33. fexti.</note>
            angulus CAD, ad rectum angulum BAC. </s>
            <s xml:id="echoid-s4327" xml:space="preserve">Igitur proportio anguli CAD,
              <lb/>
            ad angulum rectum BAC, erit quoque, vt 2. </s>
            <s xml:id="echoid-s4328" xml:space="preserve">ad 5. </s>
            <s xml:id="echoid-s4329" xml:space="preserve">ac proinde angulus CAD,
              <lb/>
            continebit {2/5}. </s>
            <s xml:id="echoid-s4330" xml:space="preserve">vnius anguli recti. </s>
            <s xml:id="echoid-s4331" xml:space="preserve">Cum ergo tres anguli trianguli CAD, con-
              <lb/>
            tineant {10/5}. </s>
            <s xml:id="echoid-s4332" xml:space="preserve">vnius recti, hoc eſt, æquales ſint duobus rectis, ſintq́ue inter ſe
              <lb/>
              <note position="left" xlink:label="note-126-04" xlink:href="note-126-04a" xml:space="preserve">32. primi.</note>
            æquales duo anguli ACD, ADC; </s>
            <s xml:id="echoid-s4333" xml:space="preserve">continebit vterque eorum {4/5}. </s>
            <s xml:id="echoid-s4334" xml:space="preserve">vnius recti.
              <lb/>
            </s>
            <s xml:id="echoid-s4335" xml:space="preserve">
              <note position="left" xlink:label="note-126-05" xlink:href="note-126-05a" xml:space="preserve">5.primi.</note>
            Et quoniam angulus DFC, angulo DCF, eſt æqualis, quòd & </s>
            <s xml:id="echoid-s4336" xml:space="preserve">rectę DF, DC,
              <lb/>
              <note position="left" xlink:label="note-126-06" xlink:href="note-126-06a" xml:space="preserve">5.primi.</note>
            æquales ſint; </s>
            <s xml:id="echoid-s4337" xml:space="preserve">(cum enim DE, EF, latera trianguli DEF, æqualia ſint lateri-
              <lb/>
            bus DE, EC, trianguli DEC, angulosq́ue ad E, contineant æquales, vtpo-
              <lb/>
            te rectos; </s>
            <s xml:id="echoid-s4338" xml:space="preserve">æquales erunt baſes DF, DC,) continebit quoque angulus DFC,
              <lb/>
              <note position="left" xlink:label="note-126-07" xlink:href="note-126-07a" xml:space="preserve">4. primi.</note>
            {4/5}. </s>
            <s xml:id="echoid-s4339" xml:space="preserve">vnius recti; </s>
            <s xml:id="echoid-s4340" xml:space="preserve">ac proinde reliquus angulus DFA, ex duobus rectis, hoc eſt, ex
              <lb/>
            {10/5}. </s>
            <s xml:id="echoid-s4341" xml:space="preserve">vnius recti, continebit {6/5}. </s>
            <s xml:id="echoid-s4342" xml:space="preserve">vnius recti. </s>
            <s xml:id="echoid-s4343" xml:space="preserve">Cum ergo angulus DAF, oſtenſus
              <lb/>
            ſit continere {2/5}. </s>
            <s xml:id="echoid-s4344" xml:space="preserve">vnius recti, & </s>
            <s xml:id="echoid-s4345" xml:space="preserve">omnes tres anguli in triangulo AFD, conti-
              <lb/>
              <note position="left" xlink:label="note-126-08" xlink:href="note-126-08a" xml:space="preserve">32. primi.</note>
            neant {10/5}. </s>
            <s xml:id="echoid-s4346" xml:space="preserve">vnius recti, continebit angulus ADF, {2/5}. </s>
            <s xml:id="echoid-s4347" xml:space="preserve">vnius recti, propte-
              <lb/>
            reaq́ue angulo DAF, æqualis erit. </s>
            <s xml:id="echoid-s4348" xml:space="preserve">Quare æqualia erunt latera DF, AF.
              <lb/>
            </s>
            <s xml:id="echoid-s4349" xml:space="preserve">
              <note position="left" xlink:label="note-126-09" xlink:href="note-126-09a" xml:space="preserve">6. primi.</note>
            Cum ergo recta DF, rectæ DC, oſtenſa ſit æqualis, erit & </s>
            <s xml:id="echoid-s4350" xml:space="preserve">recta AF, rectæ DC,
              <lb/>
            æqualis: </s>
            <s xml:id="echoid-s4351" xml:space="preserve">ideoque & </s>
            <s xml:id="echoid-s4352" xml:space="preserve">k F, medietas ipſius AF, ipſi CI, medietati ipſius DC,
              <lb/>
            æqualis erit.</s>
            <s xml:id="echoid-s4353" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4354" xml:space="preserve">RVRSVS quoniam AK, KF, æquales ſunt; </s>
            <s xml:id="echoid-s4355" xml:space="preserve">additis æqualibus EC, FE,
              <lb/>
            erit recta compoſita ex Ak, EC, æqualis rectæ KE: </s>
            <s xml:id="echoid-s4356" xml:space="preserve">ac proinde KE, medie-
              <lb/>
            tas erit ſemidiametri AC; </s>
            <s xml:id="echoid-s4357" xml:space="preserve">quandoquidem AC, diuiſa eſt in duas partes æqua
              <lb/>
            les, quarum vna eſt KE, altera vero, recta ex AK, EC, compoſita. </s>
            <s xml:id="echoid-s4358" xml:space="preserve">Eſt igi-
              <lb/>
            tur KE, æqualis ipſi CG. </s>
            <s xml:id="echoid-s4359" xml:space="preserve">Ablata ergo communi recta GE, remanebunt
              <lb/>
            æquales GK, EC. </s>
            <s xml:id="echoid-s4360" xml:space="preserve">Eſt autem EC, ſumpta ipſi EF, æqualis. </s>
            <s xml:id="echoid-s4361" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s4362" xml:space="preserve">
              <lb/>
            GK, ipſi EF, æqualis erit; </s>
            <s xml:id="echoid-s4363" xml:space="preserve">additaque communi recta FG, erit EG, ipſi FK,
              <lb/>
            æqualis, hoc eſt, ipſi CI, cui oſtendimus ſupra rectam k F, eſſe æqualem. </s>
            <s xml:id="echoid-s4364" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum