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

List of thumbnails

< >
121
121 (109) 		122
122 (110)
123
123 (111) 		124
124 (112)
125
125 (113) 		126
126 (114)
127
127 (115) 		128
128 (116)
129
129 (117) 		130
130 (118)
< >
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