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

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            <s xml:id="echoid-s4849" xml:space="preserve">
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            adeo & </s>
            <s xml:id="echoid-s4850" xml:space="preserve">quadratum rectæ BF, quod illis duobus æquale eſt, cognitum erit; </s>
            <s xml:id="echoid-s4851" xml:space="preserve">cu-
              <lb/>
              <note position="left" xlink:label="note-134-01" xlink:href="note-134-01a" xml:space="preserve">47. primi.</note>
            ius radix quadrata notam reddet rectam BF: </s>
            <s xml:id="echoid-s4852" xml:space="preserve">quæ cũ fubtendat grad. </s>
            <s xml:id="echoid-s4853" xml:space="preserve">72. </s>
            <s xml:id="echoid-s4854" xml:space="preserve">in cir
              <lb/>
            culo ABC, vtpote quintam partem circunferentiæ, quòd ſit latus pentago-
              <lb/>
            ni, nota erit chorda arcus grad. </s>
            <s xml:id="echoid-s4855" xml:space="preserve">72. </s>
            <s xml:id="echoid-s4856" xml:space="preserve">cuius medietas partium 5877852. </s>
            <s xml:id="echoid-s4857" xml:space="preserve">dabit ſi-
              <lb/>
            num rectum arcus grad. </s>
            <s xml:id="echoid-s4858" xml:space="preserve">36. </s>
            <s xml:id="echoid-s4859" xml:space="preserve">qui illius dimidium eſt.</s>
            <s xml:id="echoid-s4860" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4861" xml:space="preserve">PORRO ex hoc ſinu arcus grad. </s>
            <s xml:id="echoid-s4862" xml:space="preserve">36. </s>
            <s xml:id="echoid-s4863" xml:space="preserve">inueniemus, per propof. </s>
            <s xml:id="echoid-s4864" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4865" xml:space="preserve">ſinum eius
              <lb/>
              <note position="left" xlink:label="note-134-02" xlink:href="note-134-02a" xml:space="preserve">Supputatio
                <lb/>
              ſinuum at-
                <lb/>
              cuum gra-
                <lb/>
              dibus 2.
                <lb/>
              Min. 15. ſe-
                <lb/>
              ſe ſuperan
                <lb/>
              tiũ, & alio-
                <lb/>
              rum quorũ
                <lb/>
              dam.</note>
            complementi, hoc eſt, ſinum arcus grad. </s>
            <s xml:id="echoid-s4866" xml:space="preserve">54. </s>
            <s xml:id="echoid-s4867" xml:space="preserve">Quos duos arcus ſi biſariam fece-
              <lb/>
            mus, eorumq́ue medietates rurſus bifariam, & </s>
            <s xml:id="echoid-s4868" xml:space="preserve">ita deinceps, donec ad minuta
              <lb/>
            numero imparia veniamus, quæ amplius diuidi nequeunt, reperiemus quoque
              <lb/>
            per coroll. </s>
            <s xml:id="echoid-s4869" xml:space="preserve">propof. </s>
            <s xml:id="echoid-s4870" xml:space="preserve">4. </s>
            <s xml:id="echoid-s4871" xml:space="preserve">harum medietatum ſinus, nec non, per propoſ. </s>
            <s xml:id="echoid-s4872" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4873" xml:space="preserve">ſinus ea-
              <lb/>
            rum complementorum: </s>
            <s xml:id="echoid-s4874" xml:space="preserve">quæ complementa ſi rurſus bifariam ſecemus, quoad
              <lb/>
            poſſumus, & </s>
            <s xml:id="echoid-s4875" xml:space="preserve">harum medietatum complementa accipiamus, quæ rurſus ſece-
              <lb/>
            mus bifariam, &</s>
            <s xml:id="echoid-s4876" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4877" xml:space="preserve">inueniemus eodem modo ſinus omnium ar cuum in hac ta-
              <lb/>
            bella contentorum. </s>
            <s xml:id="echoid-s4878" xml:space="preserve">Quos ſinus ſi cum præcedentibus hactenus inuentis in or-
              <lb/>
              <note position="right" xlink:label="note-134-03" xlink:href="note-134-03a" xml:space="preserve">
                <lb/>
              ## Arcus # Sinus # ## Arcus # Sinus # ## Arcus # Sinus # ## Arcus # Sinus
                <lb/>
              G # M # # G # M # # G # M # # G # M
                <lb/>
              36 # 0 # 5877852 # 12 # 15 # 392598 # 40 # 30 # 6494480 # 15 # 45 # 2714405
                <lb/>
              54 # 0 # 8090170 # 87 # 45 # 9992290 # 49 # 30 # 7604060 # 74 # 15 # 9624552
                <lb/>
              18 # 0 # 3090170 # 27 # 0 # 4539905 # 20 # 15 # 3461171 # 38 # 15 # 6190940
                <lb/>
              72 # 0 # 9510565 # 63 # 0 # 8910065 # 69 # 45 # 9381913 # 51 # 45 # 7853169
                <lb/>
              9 # 0 # 1564345 # 13 # 30 # 2334454 # 42 # 45 # 6788007 # 24 # 45 # 4186597
                <lb/>
              81 # 0 # 9876883 # 76 # 30 # 9723699 # 47 # 15 # 7343225 # 65 # 15 # 9081432
                <lb/>
              4 # 30 # 784591 # 6 # 45 # 1175374 # 31 # 30 # 5224986 # 29 # 15 # 4886212
                <lb/>
              85 # 30 # 9969173 # 83 # 15 # 9930665 # 58 # 30 # 8526402 # 60 # 45 # 8724960
                <lb/>
              </note>
            dinem redigamus, habebimus ſinus rectos omnium arcuum ſeſe ordine ſupe-
              <lb/>
            rantium gradibus 2. </s>
            <s xml:id="echoid-s4879" xml:space="preserve">& </s>
            <s xml:id="echoid-s4880" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s4881" xml:space="preserve">15. </s>
            <s xml:id="echoid-s4882" xml:space="preserve">initio facto ab arcu grad. </s>
            <s xml:id="echoid-s4883" xml:space="preserve">2. </s>
            <s xml:id="echoid-s4884" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s4885" xml:space="preserve">15. </s>
            <s xml:id="echoid-s4886" xml:space="preserve">vſque ad
              <lb/>
            arcum grad. </s>
            <s xml:id="echoid-s4887" xml:space="preserve">87. </s>
            <s xml:id="echoid-s4888" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s4889" xml:space="preserve">45. </s>
            <s xml:id="echoid-s4890" xml:space="preserve">incluſiue; </s>
            <s xml:id="echoid-s4891" xml:space="preserve">& </s>
            <s xml:id="echoid-s4892" xml:space="preserve">inſuper ſinus aliorum 17. </s>
            <s xml:id="echoid-s4893" xml:space="preserve">arcuum, qui
              <lb/>
            non ſeruant huiuſmodi incrementum. </s>
            <s xml:id="echoid-s4894" xml:space="preserve">Vt in hac tabella appparet. </s>
            <s xml:id="echoid-s4895" xml:space="preserve">Vbi manife
              <lb/>
              <note position="right" xlink:label="note-134-04" xlink:href="note-134-04a" xml:space="preserve">
                <lb/>
              ## Arcus # Sinus # ## Arcus # Sinus # ## Arcus # Sinus # ## Arcus # Sinus
                <lb/>
              G # M # # G # M # # G # M # # G # M
                <lb/>
              2 # 15 # 392598 # 33 # 45 # 5555702 # 65 # 15 # 9081432 # 18 # 45 # 3214395
                <lb/>
              4 # 30 # 784591 # 36 # 0 # 5877852 # 67 # 30 # 9238795 # 26 # 15 # 4422887
                <lb/>
              6 # 45 # 1175374 # 38 # 15 # 6190940 # 69 # 45 # 9381913 # 30 # 0 # 5000000
                <lb/>
              9 # 0 # 1564345 # 40 # 30 # 6494480 # 72 # 0 # 9510565 # 37 # 30 # 6087614
                <lb/>
              11 # 15 # 1950903 # 42 # 45 # 6788007 # 74 # 15 # 9624552 # 41 # 15 # 6593458
                <lb/>
              13 # 30 # 2334454 # 45 # 0 # 7071068 # 76 # 30 # 9723699 # 48 # 45 # 7518398
                <lb/>
              15 # 45 # 2714405 # 47 # 15 # 7343225 # 78 # 45 # 9807853 # 52 # 30 # 7933533
                <lb/>
              18 # 0 # 3090170 # 49 # 30 # 7604060 # 81 # 0 # 9876883 # 60 # 0 # 8660254
                <lb/>
              20 # 15 # 3461171 # 51 # 45 # 7853169 # 83 # 15 # 9930685 # 63 # 45 # 8968727
                <lb/>
              22 # 30 # 3826834 # 54 # 0 # 8090170 # 85 # 30 # 9969173 # 71 # 15 # 9469301
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              </note>
            </s>
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