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

Page concordance

< >
Scan Original
111 99
112 100
113 101
114 102
115 103
116 104
117 105
118 106
119 107
120 108
121 109
122 110
123 111
124 112
125 113
126 114
127 115
128 116
129 117
130 118
131 119
132 120
133 121
134 122
135 123
136 124
137 125
138 126
139 127
140 128
< >
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