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

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        <div xml:id="echoid-div566" type="section" level="1" n="263">
          <p style="it">
            <s xml:id="echoid-s8079" xml:space="preserve">
              <pb o="196" file="208" n="208" rhead=""/>
            16. </s>
            <s xml:id="echoid-s8080" xml:space="preserve">Huius enim tangens, & </s>
            <s xml:id="echoid-s8081" xml:space="preserve">ſecant component illius tangentem, vt demonſtratum eſt.</s>
            <s xml:id="echoid-s8082" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">19. huius.</note>
          <p style="it">
            <s xml:id="echoid-s8083" xml:space="preserve">INVENTIS autem hoc modo tangentibus arcuum ſemiſſe quadrantis maiorũ
              <lb/>
            vſque ad arcum grad. </s>
            <s xml:id="echoid-s8084" xml:space="preserve">67. </s>
            <s xml:id="echoid-s8085" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8086" xml:space="preserve">30. </s>
            <s xml:id="echoid-s8087" xml:space="preserve">incluſiue; </s>
            <s xml:id="echoid-s8088" xml:space="preserve">ſi rurſus tangentem, ac ſecantem cuiuſq;
              <lb/>
            </s>
            <s xml:id="echoid-s8089" xml:space="preserve">horum arcuum, qui minuta numero paria complectatur, (quales ſunt arcus grad. </s>
            <s xml:id="echoid-s8090" xml:space="preserve">45. </s>
            <s xml:id="echoid-s8091" xml:space="preserve">
              <lb/>
            Min. </s>
            <s xml:id="echoid-s8092" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8093" xml:space="preserve">& </s>
            <s xml:id="echoid-s8094" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s8095" xml:space="preserve">45. </s>
            <s xml:id="echoid-s8096" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8097" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8098" xml:space="preserve">&</s>
            <s xml:id="echoid-s8099" xml:space="preserve">c.) </s>
            <s xml:id="echoid-s8100" xml:space="preserve">in vnam ſummam colligamus, reperiemus tangentes
              <lb/>
            maiorum adhuc arcuum, nempe grad. </s>
            <s xml:id="echoid-s8101" xml:space="preserve">67. </s>
            <s xml:id="echoid-s8102" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8103" xml:space="preserve">31. </s>
            <s xml:id="echoid-s8104" xml:space="preserve">& </s>
            <s xml:id="echoid-s8105" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s8106" xml:space="preserve">67. </s>
            <s xml:id="echoid-s8107" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8108" xml:space="preserve">32. </s>
            <s xml:id="echoid-s8109" xml:space="preserve">&</s>
            <s xml:id="echoid-s8110" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8111" xml:space="preserve">vſque ad
              <lb/>
            arcũ gra. </s>
            <s xml:id="echoid-s8112" xml:space="preserve">78. </s>
            <s xml:id="echoid-s8113" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8114" xml:space="preserve">45. </s>
            <s xml:id="echoid-s8115" xml:space="preserve">incluſiue. </s>
            <s xml:id="echoid-s8116" xml:space="preserve">Nam huius arcus grad. </s>
            <s xml:id="echoid-s8117" xml:space="preserve">33. </s>
            <s xml:id="echoid-s8118" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8119" xml:space="preserve">45. </s>
            <s xml:id="echoid-s8120" xml:space="preserve">quo arcus grad. </s>
            <s xml:id="echoid-s8121" xml:space="preserve">
              <lb/>
            78 Min 45 ſemiſſem quadrantis excedit, duplus eſt arcus grad. </s>
            <s xml:id="echoid-s8122" xml:space="preserve">67. </s>
            <s xml:id="echoid-s8123" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8124" xml:space="preserve">30. </s>
            <s xml:id="echoid-s8125" xml:space="preserve">cu-
              <lb/>
            ius tangens vltimo loco inuenta ſuit. </s>
            <s xml:id="echoid-s8126" xml:space="preserve">Item ex his tangentibus arcuum maiorum,
              <lb/>
            quàm grad. </s>
            <s xml:id="echoid-s8127" xml:space="preserve">67. </s>
            <s xml:id="echoid-s8128" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8129" xml:space="preserve">30. </s>
            <s xml:id="echoid-s8130" xml:space="preserve">@ſque ad arcum grad. </s>
            <s xml:id="echoid-s8131" xml:space="preserve">78. </s>
            <s xml:id="echoid-s8132" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8133" xml:space="preserve">45. </s>
            <s xml:id="echoid-s8134" xml:space="preserve">incluſiue inuentis; </s>
            <s xml:id="echoid-s8135" xml:space="preserve">ſi
              <lb/>
            rurſus tangentem, & </s>
            <s xml:id="echoid-s8136" xml:space="preserve">ſecantem cuiuſq; </s>
            <s xml:id="echoid-s8137" xml:space="preserve">illorum, qui minuta numero paria compre-
              <lb/>
            hendat, in vnam colligamus ſummá, inueniemus tágentes maiorum adhuc arcuum,
              <lb/>
            cuiuſmodi ſunt arcus grad. </s>
            <s xml:id="echoid-s8138" xml:space="preserve">78. </s>
            <s xml:id="echoid-s8139" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8140" xml:space="preserve">46. </s>
            <s xml:id="echoid-s8141" xml:space="preserve">& </s>
            <s xml:id="echoid-s8142" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s8143" xml:space="preserve">78. </s>
            <s xml:id="echoid-s8144" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8145" xml:space="preserve">47. </s>
            <s xml:id="echoid-s8146" xml:space="preserve">&</s>
            <s xml:id="echoid-s8147" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8148" xml:space="preserve">vſque ad arcum
              <lb/>
            grad. </s>
            <s xml:id="echoid-s8149" xml:space="preserve">84. </s>
            <s xml:id="echoid-s8150" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8151" xml:space="preserve">22. </s>
            <s xml:id="echoid-s8152" xml:space="preserve">incluſiue. </s>
            <s xml:id="echoid-s8153" xml:space="preserve">Nam huius arcus grad. </s>
            <s xml:id="echoid-s8154" xml:space="preserve">39. </s>
            <s xml:id="echoid-s8155" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8156" xml:space="preserve">22. </s>
            <s xml:id="echoid-s8157" xml:space="preserve">quo arcus grad. </s>
            <s xml:id="echoid-s8158" xml:space="preserve">
              <lb/>
            84. </s>
            <s xml:id="echoid-s8159" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8160" xml:space="preserve">22. </s>
            <s xml:id="echoid-s8161" xml:space="preserve">ſemißem quadrantis ſuperat, duplus eſt arcus grad. </s>
            <s xml:id="echoid-s8162" xml:space="preserve">78. </s>
            <s xml:id="echoid-s8163" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8164" xml:space="preserve">44. </s>
            <s xml:id="echoid-s8165" xml:space="preserve">qui maxi-
              <lb/>
            mus eſt eorum, qui minuta numero paria habent, & </s>
            <s xml:id="echoid-s8166" xml:space="preserve">quorum tangentes iam inuentæ
              <lb/>
            ſunt. </s>
            <s xml:id="echoid-s8167" xml:space="preserve">Sic etiam ex his inuentis reperiemus tangentes maiorum adhuc arcuum, quàm
              <lb/>
            grad. </s>
            <s xml:id="echoid-s8168" xml:space="preserve">84. </s>
            <s xml:id="echoid-s8169" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8170" xml:space="preserve">22. </s>
            <s xml:id="echoid-s8171" xml:space="preserve">vſque ad arcum grad. </s>
            <s xml:id="echoid-s8172" xml:space="preserve">87. </s>
            <s xml:id="echoid-s8173" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8174" xml:space="preserve">11. </s>
            <s xml:id="echoid-s8175" xml:space="preserve">Quia huius arcus grad 42. </s>
            <s xml:id="echoid-s8176" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8177" xml:space="preserve">
              <lb/>
            11 quo arcus grad 87 Min 11. </s>
            <s xml:id="echoid-s8178" xml:space="preserve">dimidium quadrantis excedit, duplus eſt arcus grad. </s>
            <s xml:id="echoid-s8179" xml:space="preserve">
              <lb/>
            84. </s>
            <s xml:id="echoid-s8180" xml:space="preserve">Min 22. </s>
            <s xml:id="echoid-s8181" xml:space="preserve">cuius tangens vltimo loco fuit inuenta. </s>
            <s xml:id="echoid-s8182" xml:space="preserve">Ex his vero repertis conficiemus
              <lb/>
            tangentes ſequentium arcuum, vſque ad arcum grad. </s>
            <s xml:id="echoid-s8183" xml:space="preserve">88. </s>
            <s xml:id="echoid-s8184" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8185" xml:space="preserve">35. </s>
            <s xml:id="echoid-s8186" xml:space="preserve">propterea quòd hu-
              <lb/>
            ius arcus grad. </s>
            <s xml:id="echoid-s8187" xml:space="preserve">43 Min. </s>
            <s xml:id="echoid-s8188" xml:space="preserve">35. </s>
            <s xml:id="echoid-s8189" xml:space="preserve">quo arcus grad. </s>
            <s xml:id="echoid-s8190" xml:space="preserve">88. </s>
            <s xml:id="echoid-s8191" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8192" xml:space="preserve">35. </s>
            <s xml:id="echoid-s8193" xml:space="preserve">quadrátis dimidiũ excedit, d@
              <lb/>
            plus eſt arcus gra. </s>
            <s xml:id="echoid-s8194" xml:space="preserve">87. </s>
            <s xml:id="echoid-s8195" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8196" xml:space="preserve">10. </s>
            <s xml:id="echoid-s8197" xml:space="preserve">qui maximus eſt eorũ, qui minuta habent numero paria,
              <lb/>
            & </s>
            <s xml:id="echoid-s8198" xml:space="preserve">quorum tangentes proxime inuent æ ſunt. </s>
            <s xml:id="echoid-s8199" xml:space="preserve">Per has quoque reperiemus aliorum ar-
              <lb/>
            cuum tangentes, vſque ad arcum grad. </s>
            <s xml:id="echoid-s8200" xml:space="preserve">89. </s>
            <s xml:id="echoid-s8201" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8202" xml:space="preserve">17. </s>
            <s xml:id="echoid-s8203" xml:space="preserve">incluſiue; </s>
            <s xml:id="echoid-s8204" xml:space="preserve">cum huius arcus grad. </s>
            <s xml:id="echoid-s8205" xml:space="preserve">
              <lb/>
            44. </s>
            <s xml:id="echoid-s8206" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8207" xml:space="preserve">17. </s>
            <s xml:id="echoid-s8208" xml:space="preserve">quo arcus grad. </s>
            <s xml:id="echoid-s8209" xml:space="preserve">89 Min. </s>
            <s xml:id="echoid-s8210" xml:space="preserve">17. </s>
            <s xml:id="echoid-s8211" xml:space="preserve">dimidiatum quadrantem excedit, duplus ſit
              <lb/>
            arcus grad. </s>
            <s xml:id="echoid-s8212" xml:space="preserve">88. </s>
            <s xml:id="echoid-s8213" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8214" xml:space="preserve">34. </s>
            <s xml:id="echoid-s8215" xml:space="preserve">vtpote maximus eorum, qui minuta numero paria continent,
              <lb/>
            & </s>
            <s xml:id="echoid-s8216" xml:space="preserve">quorum iam tangentes ſunt cognitæ. </s>
            <s xml:id="echoid-s8217" xml:space="preserve">Beneficio deinde harum tangentium inuen-
              <lb/>
            tarum eliciemus tangentes aliorum arcuum, vſque ad arcum grad. </s>
            <s xml:id="echoid-s8218" xml:space="preserve">89. </s>
            <s xml:id="echoid-s8219" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8220" xml:space="preserve">38. </s>
            <s xml:id="echoid-s8221" xml:space="preserve">in-
              <lb/>
            cluſiue; </s>
            <s xml:id="echoid-s8222" xml:space="preserve">eo quod huius arcus grad. </s>
            <s xml:id="echoid-s8223" xml:space="preserve">44. </s>
            <s xml:id="echoid-s8224" xml:space="preserve">Min 38. </s>
            <s xml:id="echoid-s8225" xml:space="preserve">quo arcus grad. </s>
            <s xml:id="echoid-s8226" xml:space="preserve">89. </s>
            <s xml:id="echoid-s8227" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8228" xml:space="preserve">38. </s>
            <s xml:id="echoid-s8229" xml:space="preserve">ſemiſſem
              <lb/>
            quadrantis ſuperat, duplus eſt arcus grad. </s>
            <s xml:id="echoid-s8230" xml:space="preserve">89. </s>
            <s xml:id="echoid-s8231" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8232" xml:space="preserve">16. </s>
            <s xml:id="echoid-s8233" xml:space="preserve">qui maximus eſt eorum, qui
              <lb/>
            minuta numero habent paria, & </s>
            <s xml:id="echoid-s8234" xml:space="preserve">quorũ tangentes iam factæ ſunt notæ; </s>
            <s xml:id="echoid-s8235" xml:space="preserve">Hinc aliorum
              <lb/>
            arcuũ tãgentes inquiremus, vſq; </s>
            <s xml:id="echoid-s8236" xml:space="preserve">ad arcũ gra. </s>
            <s xml:id="echoid-s8237" xml:space="preserve">89. </s>
            <s xml:id="echoid-s8238" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8239" xml:space="preserve">49. </s>
            <s xml:id="echoid-s8240" xml:space="preserve">quippe qui ſuperet quadrã
              <lb/>
            tis dimidiũ drcugrad. </s>
            <s xml:id="echoid-s8241" xml:space="preserve">44. </s>
            <s xml:id="echoid-s8242" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8243" xml:space="preserve">49 cuius duplus eſt arcus grad. </s>
            <s xml:id="echoid-s8244" xml:space="preserve">89. </s>
            <s xml:id="echoid-s8245" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8246" xml:space="preserve">38. </s>
            <s xml:id="echoid-s8247" xml:space="preserve">ad quẽ pro-
              <lb/>
            xime peruenimus. </s>
            <s xml:id="echoid-s8248" xml:space="preserve">At ex his inueſtigabimus tangentes ſequentium arcuum vſq; </s>
            <s xml:id="echoid-s8249" xml:space="preserve">ad ar-
              <lb/>
            cum grad. </s>
            <s xml:id="echoid-s8250" xml:space="preserve">89. </s>
            <s xml:id="echoid-s8251" xml:space="preserve">Min 54 quippe qui quadran
              <unsure/>
            tis medietatẽ ſuperet arcu grad. </s>
            <s xml:id="echoid-s8252" xml:space="preserve">44. </s>
            <s xml:id="echoid-s8253" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8254" xml:space="preserve">
              <lb/>
            54. </s>
            <s xml:id="echoid-s8255" xml:space="preserve">cuius duplus ſt arcus grad. </s>
            <s xml:id="echoid-s8256" xml:space="preserve">89. </s>
            <s xml:id="echoid-s8257" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8258" xml:space="preserve">48. </s>
            <s xml:id="echoid-s8259" xml:space="preserve">qui maximus eſt eorum, qui minuta ha-
              <lb/>
            bent numero paria, & </s>
            <s xml:id="echoid-s8260" xml:space="preserve">quorum tangentes iam ſunt inuentæ. </s>
            <s xml:id="echoid-s8261" xml:space="preserve">Eadẽ ratione ex his in-
              <lb/>
            ueniemus tangentes ſequentium arcuum vſq@ ad arcum grad. </s>
            <s xml:id="echoid-s8262" xml:space="preserve">89. </s>
            <s xml:id="echoid-s8263" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8264" xml:space="preserve">57 Quia hu-
              <lb/>
            ius arcus grad. </s>
            <s xml:id="echoid-s8265" xml:space="preserve">44. </s>
            <s xml:id="echoid-s8266" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8267" xml:space="preserve">57. </s>
            <s xml:id="echoid-s8268" xml:space="preserve">quo arcus grad. </s>
            <s xml:id="echoid-s8269" xml:space="preserve">89. </s>
            <s xml:id="echoid-s8270" xml:space="preserve">Min 57 quadrantis dimidium ſupe-
              <lb/>
            rat, duplus eſt arcus grad. </s>
            <s xml:id="echoid-s8271" xml:space="preserve">89. </s>
            <s xml:id="echoid-s8272" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8273" xml:space="preserve">54. </s>
            <s xml:id="echoid-s8274" xml:space="preserve">ad quem proxime peruentum fuit. </s>
            <s xml:id="echoid-s8275" xml:space="preserve">Denique ex
              <lb/>
            tangente, & </s>
            <s xml:id="echoid-s8276" xml:space="preserve">ſecante arcus grad. </s>
            <s xml:id="echoid-s8277" xml:space="preserve">89. </s>
            <s xml:id="echoid-s8278" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8279" xml:space="preserve">56. </s>
            <s xml:id="echoid-s8280" xml:space="preserve">conficiemus tangentem arcus grad. </s>
            <s xml:id="echoid-s8281" xml:space="preserve">89. </s>
            <s xml:id="echoid-s8282" xml:space="preserve">
              <lb/>
            Min. </s>
            <s xml:id="echoid-s8283" xml:space="preserve">58. </s>
            <s xml:id="echoid-s8284" xml:space="preserve">Et hinc tangentem explor abimus arcus grad. </s>
            <s xml:id="echoid-s8285" xml:space="preserve">89. </s>
            <s xml:id="echoid-s8286" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8287" xml:space="preserve">59. </s>
            <s xml:id="echoid-s8288" xml:space="preserve">Atq; </s>
            <s xml:id="echoid-s8289" xml:space="preserve">ita, vt vides,
              <lb/>
            ex tangentibus arcuum vſque ad grad. </s>
            <s xml:id="echoid-s8290" xml:space="preserve">45. </s>
            <s xml:id="echoid-s8291" xml:space="preserve">& </s>
            <s xml:id="echoid-s8292" xml:space="preserve">ex ſecantibus omnium arcuum qua-
              <lb/>
            drantis perficitur integra tabula tangentium.</s>
            <s xml:id="echoid-s8293" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8294" xml:space="preserve">QVOD ſi ſecantem cuiuſcunq; </s>
            <s xml:id="echoid-s8295" xml:space="preserve">arcus ſubducas ex tangente alterius arcus, qui
              <lb/>
            ex priore illo, ac ſemiſſe complementi eiuſdem componitur, reliquam facies tangen-
              <lb/>
              <lb/>
            </s>
          </p>
        </div>
      </text>
    </echo>
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