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

Page concordance

< >
Scan Original
131 119
132 120
133 121
134 122
135 123
136 124
137 125
138 126
139 127
140 128
141 129
142 130
143 131
144 132
145 133
146 134
147 135
148 136
149 137
150 138
151 139
152 140
153 141
154 142
155 143
156 144
157 145
158 146
159 147
160 148
< >
page |< < (123) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div379" type="section" level="1" n="166">
          <p>
            <s xml:id="echoid-s4895" xml:space="preserve">
              <pb o="123" file="135" n="135" rhead=""/>
              <note position="right" xlink:label="note-135-01" xlink:href="note-135-01a" xml:space="preserve">
                <lb/>
              24 # 45 # 4186597 # 56 # 15 # 8314696 # 87 # 45 # 9992290 # 75 # 0 # 965925
                <lb/>
              27 # 0 # 4539905 # 58 # 30 # 8526402 # 3 # 45 # 654031 # 82 # 30 # 9914449
                <lb/>
              9 # 15 # 4886212 # 60 # 45 # 8724960 # 7 # 30 # 1305262 # 86 # 15 # 9978589
                <lb/>
              31 # 30 # 5224986 # 63 # 0 # 8910065 # 15 # 0 # 2588190 # 90 # 0 # 10000000
                <lb/>
              </note>
            ſtum eſt, ſinum grad. </s>
            <s xml:id="echoid-s4896" xml:space="preserve">54. </s>
            <s xml:id="echoid-s4897" xml:space="preserve">hoc eſt. </s>
            <s xml:id="echoid-s4898" xml:space="preserve">8090170. </s>
            <s xml:id="echoid-s4899" xml:space="preserve">componi præciſe ex ſinubus grad. </s>
            <s xml:id="echoid-s4900" xml:space="preserve">18.
              <lb/>
            </s>
            <s xml:id="echoid-s4901" xml:space="preserve">& </s>
            <s xml:id="echoid-s4902" xml:space="preserve">30. </s>
            <s xml:id="echoid-s4903" xml:space="preserve">hoc eſt, ex 3090170. </s>
            <s xml:id="echoid-s4904" xml:space="preserve">& </s>
            <s xml:id="echoid-s4905" xml:space="preserve">5000000. </s>
            <s xml:id="echoid-s4906" xml:space="preserve">Et quia ſinus grad. </s>
            <s xml:id="echoid-s4907" xml:space="preserve">30. </s>
            <s xml:id="echoid-s4908" xml:space="preserve">æqualis eſt ſemiſ-
              <lb/>
            ſi ſinus totius, vt ſupra oſtenſum eſt, liquet ſinum grad. </s>
            <s xml:id="echoid-s4909" xml:space="preserve">54. </s>
            <s xml:id="echoid-s4910" xml:space="preserve">componi ad vngué
              <lb/>
            ex ſemiſſe ſinus totius, & </s>
            <s xml:id="echoid-s4911" xml:space="preserve">ſinu recto grad. </s>
            <s xml:id="echoid-s4912" xml:space="preserve">18. </s>
            <s xml:id="echoid-s4913" xml:space="preserve">Id quod propoſ. </s>
            <s xml:id="echoid-s4914" xml:space="preserve">6. </s>
            <s xml:id="echoid-s4915" xml:space="preserve">à nobis eſt de-
              <lb/>
            monſtratum.</s>
            <s xml:id="echoid-s4916" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4917" xml:space="preserve">IAM vero ſinum arcus grad. </s>
            <s xml:id="echoid-s4918" xml:space="preserve">12. </s>
            <s xml:id="echoid-s4919" xml:space="preserve">beneſicio ſinuum grad. </s>
            <s xml:id="echoid-s4920" xml:space="preserve">30. </s>
            <s xml:id="echoid-s4921" xml:space="preserve">& </s>
            <s xml:id="echoid-s4922" xml:space="preserve">54. </s>
            <s xml:id="echoid-s4923" xml:space="preserve">qui iam
              <lb/>
              <note position="right" xlink:label="note-135-02" xlink:href="note-135-02a" xml:space="preserve">Supputatio
                <lb/>
              ſinus arcus
                <lb/>
              grad. 12.</note>
            noti facti ſunt, ita inueſtigabimus. </s>
            <s xml:id="echoid-s4924" xml:space="preserve">Sit in quadrā
              <lb/>
              <figure xlink:label="fig-135-01" xlink:href="fig-135-01a" number="131">
                <image file="135-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/135-01"/>
              </figure>
            te ABC, arcus BD, grad. </s>
            <s xml:id="echoid-s4925" xml:space="preserve">30. </s>
            <s xml:id="echoid-s4926" xml:space="preserve">& </s>
            <s xml:id="echoid-s4927" xml:space="preserve">BE, grad. </s>
            <s xml:id="echoid-s4928" xml:space="preserve">54. </s>
            <s xml:id="echoid-s4929" xml:space="preserve">at-
              <lb/>
            que adeò arcus DE, eorum differentia, grad. </s>
            <s xml:id="echoid-s4930" xml:space="preserve">24.
              <lb/>
            </s>
            <s xml:id="echoid-s4931" xml:space="preserve">ducanturque rectæ DF, EG, ad AB, perpendi-
              <lb/>
            culares, quæ ſinus recti erunt arcuum BD, BE; </s>
            <s xml:id="echoid-s4932" xml:space="preserve">
              <lb/>
            Item rectæ DH, EI, ad AC, perpendiculares,
              <lb/>
            quæ finus recti erunt arcuum CD, CE, grad. </s>
            <s xml:id="echoid-s4933" xml:space="preserve">
              <lb/>
            60. </s>
            <s xml:id="echoid-s4934" xml:space="preserve">& </s>
            <s xml:id="echoid-s4935" xml:space="preserve">36. </s>
            <s xml:id="echoid-s4936" xml:space="preserve">qui complementa ſunt arcuum BD,
              <lb/>
            BE. </s>
            <s xml:id="echoid-s4937" xml:space="preserve">Secet autem recta DH, rectam EG, in K. </s>
            <s xml:id="echoid-s4938" xml:space="preserve">
              <lb/>
            Et quoniam ſinus DF, hoc eſt, KG, illi æqua-
              <lb/>
              <note position="right" xlink:label="note-135-03" xlink:href="note-135-03a" xml:space="preserve">34. primi.</note>
            lis, & </s>
            <s xml:id="echoid-s4939" xml:space="preserve">EG, noti ſunt; </s>
            <s xml:id="echoid-s4940" xml:space="preserve">erit quoque eorum diffe-
              <lb/>
            rentia EK, nota. </s>
            <s xml:id="echoid-s4941" xml:space="preserve">Similiter quia ſinus EI, hoc
              <lb/>
            eſt, KH, illi æqualis, & </s>
            <s xml:id="echoid-s4942" xml:space="preserve">DH, noti quoque ſunt, per propof. </s>
            <s xml:id="echoid-s4943" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4944" xml:space="preserve">cum ſint ſinus
              <lb/>
              <note position="right" xlink:label="note-135-04" xlink:href="note-135-04a" xml:space="preserve">34. primi.</note>
            complementorum arcuum BE, BD; </s>
            <s xml:id="echoid-s4945" xml:space="preserve">erit etiam eorum differentia DK, nota;
              <lb/>
            </s>
            <s xml:id="echoid-s4946" xml:space="preserve">ac proinde duo quadrata rectarum notarum Ek, DK, nota erunt: </s>
            <s xml:id="echoid-s4947" xml:space="preserve">quæ cum
              <lb/>
            æqualia ſint quadrato rectæ DE, notum quoque erit quadratum rectæ DE,
              <lb/>
              <note position="right" xlink:label="note-135-05" xlink:href="note-135-05a" xml:space="preserve">47. primi</note>
            proptereaque & </s>
            <s xml:id="echoid-s4948" xml:space="preserve">ipſarecta DE, nota erit, nem pe chorda arcus grad. </s>
            <s xml:id="echoid-s4949" xml:space="preserve">24. </s>
            <s xml:id="echoid-s4950" xml:space="preserve">Hinc
              <lb/>
            & </s>
            <s xml:id="echoid-s4951" xml:space="preserve">eius medietas nota erit, nimirum ſinus rectus arcus grad. </s>
            <s xml:id="echoid-s4952" xml:space="preserve">12. </s>
            <s xml:id="echoid-s4953" xml:space="preserve">continebitque
              <lb/>
              <note position="right" xlink:label="note-135-06" xlink:href="note-135-06a" xml:space="preserve">Ex duorũ
                <lb/>
              arcuũ ſinu
                <lb/>
              bus notis
                <lb/>
              notus quo-
                <lb/>
              que ſit ſinꝰ
                <lb/>
              medietatis
                <lb/>
              differentiæ
                <lb/>
              arcuum.</note>
            particulas 2079117. </s>
            <s xml:id="echoid-s4954" xml:space="preserve">Hac eadem arte; </s>
            <s xml:id="echoid-s4955" xml:space="preserve">ſi duorum arcuum quorumcumque ſinus
              <lb/>
            cogniti ſint, cognoſcetur etiam ſinus medietatis differentiæ illorum arcuum.
              <lb/>
            </s>
            <s xml:id="echoid-s4956" xml:space="preserve">Vt ſi ſinus arcuum BD, BE, quorumcumque etiam ſi non contineant grad. </s>
            <s xml:id="echoid-s4957" xml:space="preserve">30. </s>
            <s xml:id="echoid-s4958" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s4959" xml:space="preserve">54. </s>
            <s xml:id="echoid-s4960" xml:space="preserve">noti ſint, erunt & </s>
            <s xml:id="echoid-s4961" xml:space="preserve">ſinus complementorum CD, CE, per propof. </s>
            <s xml:id="echoid-s4962" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4963" xml:space="preserve">noti. </s>
            <s xml:id="echoid-s4964" xml:space="preserve">
              <lb/>
            Quare, vt modo demon ſtrauimus, nota ſiet chorda DE; </s>
            <s xml:id="echoid-s4965" xml:space="preserve">ac proinde eius me-
              <lb/>
            dietas nota quoque erit, nempe ſinus medietatis arcus DE.</s>
            <s xml:id="echoid-s4966" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4967" xml:space="preserve">
              <emph style="sc">Cae</emph>
              <emph style="sc">Tervm</emph>
            ex ſinu arcus grad. </s>
            <s xml:id="echoid-s4968" xml:space="preserve">12. </s>
            <s xml:id="echoid-s4969" xml:space="preserve">(ſi hunc arcum bifariam ſecemus
              <lb/>
              <note position="right" xlink:label="note-135-07" xlink:href="note-135-07a" xml:space="preserve">Supputatio
                <lb/>
              ſinuu ar-
                <lb/>
              cuum Mi-
                <lb/>
              nutis 45. ſe
                <lb/>
              ſe ſupeian-
                <lb/>
              tium.</note>
            continue, quoad poſſumus, medietatumq́; </s>
            <s xml:id="echoid-s4970" xml:space="preserve">complementa accipiamus, vnà cum
              <lb/>
            ſinu complementi arcus grad. </s>
            <s xml:id="echoid-s4971" xml:space="preserve">12. </s>
            <s xml:id="echoid-s4972" xml:space="preserve">quæ rurſus ſecemus bifariam continue, &</s>
            <s xml:id="echoid-s4973" xml:space="preserve">c.)
              <lb/>
            </s>
            <s xml:id="echoid-s4974" xml:space="preserve">reperiemus per coroll. </s>
            <s xml:id="echoid-s4975" xml:space="preserve">propof. </s>
            <s xml:id="echoid-s4976" xml:space="preserve">4. </s>
            <s xml:id="echoid-s4977" xml:space="preserve">& </s>
            <s xml:id="echoid-s4978" xml:space="preserve">per propoſ. </s>
            <s xml:id="echoid-s4979" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4980" xml:space="preserve">ſinus omnium hor um arcuũ,
              <lb/>
            qui in hac tabella continentur. </s>
            <s xml:id="echoid-s4981" xml:space="preserve">Quos ſinus ſi cum ſinubus proxime antece-
              <lb/>
            dentis tabellæ in ordinem redigamus, habebimus ſinus arcuum numero 120. </s>
            <s xml:id="echoid-s4982" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-135-08" xlink:href="note-135-08a" xml:space="preserve">
                <lb/>
              ## Arcus # Sinus # ## Arcus # Sinus # ## Arcus # Sinus # ## Arcus # Sinus
                <lb/>
              G # M # # G # M # # G # M # # G # M
                <lb/>
              12 # 0 # 2079117 # 42 # 0 # 6691306 # 12 # 45 # 2206974 # 33 # 0 # 5446390
                <lb/>
              78 # 0 # 9781476 # 48 # 0 # 7431448 # 77 # 15 # 9753423 # 57 # 0 # 8386706
                <lb/>
              </note>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum