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

Page concordance

< >
Scan Original
161 149
162 150
163 151
164 152
165 153
166 154
167 155
168 156
169 157
170 158
171 159
172 160
173 161
174 162
175 163
176 164
177 165
178 166
179 167
180 168
181 169
182 170
183 171
184 172
185 173
186 174
187 175
188 176
189 177
190 178
< >
page |< < (191) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div547" type="section" level="1" n="257">
          <pb o="191" file="203" n="203" rhead=""/>
        </div>
        <div xml:id="echoid-div548" type="section" level="1" n="258">
          <head xml:id="echoid-head285" xml:space="preserve">THEOR. 10. PROPOS. 18.</head>
          <p>
            <s xml:id="echoid-s7749" xml:space="preserve">QVAM proportionem habet ſinus comple
              <lb/>
              <note position="right" xlink:label="note-203-01" xlink:href="note-203-01a" xml:space="preserve">Quam pro
                <lb/>
              portionem
                <lb/>
              habeat ſinꝰ
                <lb/>
              totus ad :5
                <lb/>
              genté, & ſe
                <lb/>
              cantem cu-
                <lb/>
              iuſuis arcꝰ.</note>
            menti arcus cuiuſuis ad ſinum rectum eiuſdem ar
              <lb/>
            cus, eam habet ſinus totus ad tangentem eiuſdem
              <lb/>
            arcus: </s>
            <s xml:id="echoid-s7750" xml:space="preserve">Item quam proportionem habet ſinus re-
              <lb/>
            ctus cuiuſlibet arcus ad ſinum complementi eiuſ-
              <lb/>
            dem arcus, eam habet ſinus totus ad tangentem
              <lb/>
            eiuſdem complementi. </s>
            <s xml:id="echoid-s7751" xml:space="preserve">Sinus autem totus medio
              <lb/>
            loco proportionalis eſt inter ſinum complementi
              <lb/>
            cuiuſuis arcus, & </s>
            <s xml:id="echoid-s7752" xml:space="preserve">ſecantem eiuſdem aicus: </s>
            <s xml:id="echoid-s7753" xml:space="preserve">Item
              <lb/>
            inter ſinum rectum cuiuſlibet arcus, & </s>
            <s xml:id="echoid-s7754" xml:space="preserve">ſecantem
              <lb/>
            complementi eiuſdem arcus. </s>
            <s xml:id="echoid-s7755" xml:space="preserve">Sinus denique idem
              <lb/>
            totus medius proportionalis eſt inter tangentem
              <lb/>
            arcus cuiuſuis, & </s>
            <s xml:id="echoid-s7756" xml:space="preserve">tangentem complementi eiuſ-
              <lb/>
            dem arcus.</s>
            <s xml:id="echoid-s7757" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7758" xml:space="preserve">IN quadrante ABC, ſit DF, ſinus arcus CD; </s>
            <s xml:id="echoid-s7759" xml:space="preserve">& </s>
            <s xml:id="echoid-s7760" xml:space="preserve">CE, eiuſdem tangens
              <lb/>
            inter ſemidiametrum AC, & </s>
            <s xml:id="echoid-s7761" xml:space="preserve">ſecantem AE: </s>
            <s xml:id="echoid-s7762" xml:space="preserve">Item BG, tangens arcus BD, qui
              <lb/>
            complementum eſt arcus CD. </s>
            <s xml:id="echoid-s7763" xml:space="preserve">Dico ita eſſe ſinum complementi arcus CD, ad
              <lb/>
            ſinum rectum eiuſdé arcus, vt eſt ſinus totus AC,
              <lb/>
              <figure xlink:label="fig-203-01" xlink:href="fig-203-01a" number="150">
                <image file="203-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/203-01"/>
              </figure>
            ad tangentem CE, &</s>
            <s xml:id="echoid-s7764" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7765" xml:space="preserve">Quoniam enim, vt in ex-
              <lb/>
            poſitione definitionum dictum eſt, AF, æqualis
              <lb/>
            eſt ſinui complementi arcus CD, cum ſit æqualis
              <lb/>
            ſinui recto arcus BD, qui complementum eſt arcus
              <lb/>
            CD; </s>
            <s xml:id="echoid-s7766" xml:space="preserve">ſuntq́; </s>
            <s xml:id="echoid-s7767" xml:space="preserve">triangula AFD, ACE, æquiangula,
              <lb/>
            ob rectos angulos F, C, & </s>
            <s xml:id="echoid-s7768" xml:space="preserve">communem angulum
              <lb/>
            A: </s>
            <s xml:id="echoid-s7769" xml:space="preserve">erit vt AF, ſinus complementi arcus CD, ad
              <lb/>
              <note position="right" xlink:label="note-203-02" xlink:href="note-203-02a" xml:space="preserve">4. ſexti.</note>
            FD, ſinum rectum eiuſdem arcus CD, ita AC, ſi-
              <lb/>
            nus totus ad CE, tangentem eiuſdem arcus. </s>
            <s xml:id="echoid-s7770" xml:space="preserve">quod
              <lb/>
            eſt primum.</s>
            <s xml:id="echoid-s7771" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7772" xml:space="preserve">DEINDE eadem ratione erit, vt AF, ſinus
              <lb/>
            rectus arcus BD, ad FD, ſinũ complementi eiuſdem arcus BD, ita AC, ſinus
              <lb/>
            totus ad CE, tangentem eiuſdem complementi arcus BD. </s>
            <s xml:id="echoid-s7773" xml:space="preserve">quod eſt ſecundum.</s>
            <s xml:id="echoid-s7774" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7775" xml:space="preserve">TERTIO in eiſdem triangulis erit, vt AF, ſinus complementi arcus
              <lb/>
            CD, ad AD, ſinum totum, ita AC, ſinus totus ad AE, ſecantem </s>
          </p>
        </div>
      </text>
    </echo>
Impressum