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

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      <text xml:lang="la" type="free">
        <div xml:id="echoid-div476" type="section" level="1" n="240">
          <p style="it">
            <s xml:id="echoid-s5825" xml:space="preserve">
              <pb o="169" file="181" n="181" rhead=""/>
            areus proxime minoris, vt fiat ſinus propositi arcus? </s>
            <s xml:id="echoid-s5826" xml:space="preserve">_N_am differentia inuenta erit
              <lb/>
              <note position="right" xlink:label="note-181-01" xlink:href="note-181-01a" xml:space="preserve">partem pre
                <lb/>
              pottionalẽ</note>
            pars proportionalis, quæ ſi addatur ſinui arcus proxime minoris, efficietur ſinus re-
              <lb/>
            ctus arcus propoſiti. </s>
            <s xml:id="echoid-s5827" xml:space="preserve">_V_t ſi propoſitus ſit arcus grad. </s>
            <s xml:id="echoid-s5828" xml:space="preserve">_20_. </s>
            <s xml:id="echoid-s5829" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s5830" xml:space="preserve">_43_. </s>
            <s xml:id="echoid-s5831" xml:space="preserve">_S_ec. </s>
            <s xml:id="echoid-s5832" xml:space="preserve">_20._ </s>
            <s xml:id="echoid-s5833" xml:space="preserve">_A_ccipe dif-
              <lb/>
            ferentiam _2721_. </s>
            <s xml:id="echoid-s5834" xml:space="preserve">inter ſinum _3537469_. </s>
            <s xml:id="echoid-s5835" xml:space="preserve">arcus grad. </s>
            <s xml:id="echoid-s5836" xml:space="preserve">_20_. </s>
            <s xml:id="echoid-s5837" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s5838" xml:space="preserve">_43_. </s>
            <s xml:id="echoid-s5839" xml:space="preserve">proxime minoris,
              <lb/>
            & </s>
            <s xml:id="echoid-s5840" xml:space="preserve">ſinum _3540190_. </s>
            <s xml:id="echoid-s5841" xml:space="preserve">arcus grad. </s>
            <s xml:id="echoid-s5842" xml:space="preserve">_20_. </s>
            <s xml:id="echoid-s5843" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s5844" xml:space="preserve">_44_. </s>
            <s xml:id="echoid-s5845" xml:space="preserve">proxime maioris, & </s>
            <s xml:id="echoid-s5846" xml:space="preserve">dic. </s>
            <s xml:id="echoid-s5847" xml:space="preserve">_S_i _60._ </s>
            <s xml:id="echoid-s5848" xml:space="preserve">ſecunda
              <lb/>
            vequirunt differentiam _2721_. </s>
            <s xml:id="echoid-s5849" xml:space="preserve">addendam ſinui _3537469_. </s>
            <s xml:id="echoid-s5850" xml:space="preserve">arcus grad. </s>
            <s xml:id="echoid-s5851" xml:space="preserve">_20_. </s>
            <s xml:id="echoid-s5852" xml:space="preserve">min _43_.
              <lb/>
            </s>
            <s xml:id="echoid-s5853" xml:space="preserve">vt efficiatur ſinus _3540190_. </s>
            <s xml:id="echoid-s5854" xml:space="preserve">arcus grad. </s>
            <s xml:id="echoid-s5855" xml:space="preserve">_20_. </s>
            <s xml:id="echoid-s5856" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s5857" xml:space="preserve">_44_. </s>
            <s xml:id="echoid-s5858" xml:space="preserve">quantam differentiam poſtu-
              <lb/>
            lant _20_. </s>
            <s xml:id="echoid-s5859" xml:space="preserve">ſecunda addendam eidem ſinui _3537469_. </s>
            <s xml:id="echoid-s5860" xml:space="preserve">arcus grad. </s>
            <s xml:id="echoid-s5861" xml:space="preserve">_20_. </s>
            <s xml:id="echoid-s5862" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s5863" xml:space="preserve">_43_. </s>
            <s xml:id="echoid-s5864" xml:space="preserve">vt fiat
              <lb/>
            ſinus arcus grad. </s>
            <s xml:id="echoid-s5865" xml:space="preserve">_20_. </s>
            <s xml:id="echoid-s5866" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s5867" xml:space="preserve">_43_. </s>
            <s xml:id="echoid-s5868" xml:space="preserve">ſec. </s>
            <s xml:id="echoid-s5869" xml:space="preserve">_20_? </s>
            <s xml:id="echoid-s5870" xml:space="preserve">_I_nuenies enim differentiam, ſiue partem pro-
              <lb/>
            portionalem _907_. </s>
            <s xml:id="echoid-s5871" xml:space="preserve">quæ addita ſinui _3537469_. </s>
            <s xml:id="echoid-s5872" xml:space="preserve">efficiet _3538376_. </s>
            <s xml:id="echoid-s5873" xml:space="preserve">ſinum arcus grad. </s>
            <s xml:id="echoid-s5874" xml:space="preserve">_20_. </s>
            <s xml:id="echoid-s5875" xml:space="preserve">
              <lb/>
            _M_in. </s>
            <s xml:id="echoid-s5876" xml:space="preserve">_43_ ſec. </s>
            <s xml:id="echoid-s5877" xml:space="preserve">_20_. </s>
            <s xml:id="echoid-s5878" xml:space="preserve">_C_ommuniter tamen ab _A_ſtronomis negliguntur in hoc negotio _S_e-
              <lb/>
              <note position="right" xlink:label="note-181-02" xlink:href="note-181-02a" xml:space="preserve">Secũda cõl
                <lb/>
              ter ĩttacta
                <lb/>
              tione ſinuũ
                <lb/>
              negligũ tut
                <lb/>
              ab Aſtrone
                <lb/>
              mis.</note>
            cunda, ſi pauciora ſunt, quàm _30._ </s>
            <s xml:id="echoid-s5879" xml:space="preserve">_S_i vero pl@ra, addunt proillis vnum minutum
              <lb/>
            alijs _M_inutis. </s>
            <s xml:id="echoid-s5880" xml:space="preserve">_N_ullus enim error, qui alicuius momenti ſit, inde oritur. </s>
            <s xml:id="echoid-s5881" xml:space="preserve">_I_taq; </s>
            <s xml:id="echoid-s5882" xml:space="preserve">pro
              <lb/>
            dato arcugrad. </s>
            <s xml:id="echoid-s5883" xml:space="preserve">_20._ </s>
            <s xml:id="echoid-s5884" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s5885" xml:space="preserve">_43._ </s>
            <s xml:id="echoid-s5886" xml:space="preserve">_S_ec. </s>
            <s xml:id="echoid-s5887" xml:space="preserve">_20._ </s>
            <s xml:id="echoid-s5888" xml:space="preserve">accipiunt ſinum arcus grad. </s>
            <s xml:id="echoid-s5889" xml:space="preserve">_20._ </s>
            <s xml:id="echoid-s5890" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s5891" xml:space="preserve">_43._ </s>
            <s xml:id="echoid-s5892" xml:space="preserve">ne-
              <lb/>
            glectis illis _20_ ſec. </s>
            <s xml:id="echoid-s5893" xml:space="preserve">_P_ro arcu vero grad. </s>
            <s xml:id="echoid-s5894" xml:space="preserve">_20._ </s>
            <s xml:id="echoid-s5895" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s5896" xml:space="preserve">_43_ ſec. </s>
            <s xml:id="echoid-s5897" xml:space="preserve">_48._ </s>
            <s xml:id="echoid-s5898" xml:space="preserve">ſumunt ſinum arcus grad.
              <lb/>
            </s>
            <s xml:id="echoid-s5899" xml:space="preserve">_20._ </s>
            <s xml:id="echoid-s5900" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s5901" xml:space="preserve">_44._ </s>
            <s xml:id="echoid-s5902" xml:space="preserve">computatis illis _48._ </s>
            <s xml:id="echoid-s5903" xml:space="preserve">ſec. </s>
            <s xml:id="echoid-s5904" xml:space="preserve">pro vno _M_inuto.</s>
            <s xml:id="echoid-s5905" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5906" xml:space="preserve">_SEMICIRCVLI_porro, atq; </s>
            <s xml:id="echoid-s5907" xml:space="preserve">arcus ſemicirculo maioris, non eſt quòd ſinus rectus
              <lb/>
              <note position="right" xlink:label="note-181-03" xlink:href="note-181-03a" xml:space="preserve">Semicircu-
                <lb/>
              li, & arcꝰ ſe
                <lb/>
              micirculo
                <lb/>
              maioris, nõ
                <lb/>
              eſt ſinus re
                <lb/>
              ctus inqui-
                <lb/>
              rendus; im-
                <lb/>
              mo nullus
                <lb/>
              eft eorũ ſi-
                <lb/>
              nus rectus.</note>
            inueſtigetur, cùm nunquam in ſupputationibus _A_ſtronomicis buiuſmodi arcuum ſi-
              <lb/>
            nus adbibeantur, quod ijs perſptcuum eſt, qui in triangulis rectilineis, ac ſphæri-
              <lb/>
            cis, in quibus tota _S_inuum ſcientia verſatur, ſunt exercitati. </s>
            <s xml:id="echoid-s5908" xml:space="preserve">_I_mmo ſemicirculus
              <lb/>
            nullum habet ſinum, vt ex vtraq; </s>
            <s xml:id="echoid-s5909" xml:space="preserve">defin. </s>
            <s xml:id="echoid-s5910" xml:space="preserve">ſinus recti patet. </s>
            <s xml:id="echoid-s5911" xml:space="preserve">quod etiam de arcu ma-
              <lb/>
            iore dici poteſt, niſi quis in prima figura definitionum rectam _FK,_ ſinum rectum velit
              <lb/>
            appellare arcus _DBF_, ſecundum poſteriorem defin. </s>
            <s xml:id="echoid-s5912" xml:space="preserve">ſinus recti; </s>
            <s xml:id="echoid-s5913" xml:space="preserve">& </s>
            <s xml:id="echoid-s5914" xml:space="preserve">rectam _FH_, ſinum
              <lb/>
            rectum arcus _
              <emph style="sc">ACf</emph>
            _. </s>
            <s xml:id="echoid-s5915" xml:space="preserve">quod non videturproprie dici, cum huiuſmodi lineis prior defi-
              <lb/>
            nitio ſinus recti nullo modo conuenire poſsit, vt ex eadem figura perſpicuum eſt.
              <lb/>
            </s>
            <s xml:id="echoid-s5916" xml:space="preserve">
              <note position="right" xlink:label="note-181-04" xlink:href="note-181-04a" xml:space="preserve">Sinus com
                <lb/>
              plemẽti ar-
                <lb/>
              cus quadrã
                <lb/>
              te minoris
                <lb/>
              quomodo
                <lb/>
              i tabula re
                <lb/>
              periatur.</note>
            </s>
          </p>
          <p style="it">
            <s xml:id="echoid-s5917" xml:space="preserve">_QVANDO_ autemdati arcus _Q_uadrante minoris ſinum complementi quæris, cape
              <lb/>
            gradus illius in in feriori parte tabulæ, _M_inuta vero ad dexteram. </s>
            <s xml:id="echoid-s5918" xml:space="preserve">_I_n communi enim
              <lb/>
            angulo continuò ſinum complementireperies, hoc eſt, ſinum rectum illius arcus, qui
              <lb/>
            dati arcus complementum eſt. </s>
            <s xml:id="echoid-s5919" xml:space="preserve">_N_am ſinus ille rectus debetur arcui, cuius gradus in
              <lb/>
            vertice tabulæ, & </s>
            <s xml:id="echoid-s5920" xml:space="preserve">minuta in ſiniſtro latere collocantur, qui quidem dati arcus com-
              <lb/>
            plementum eſt, vt ſupra diximus. </s>
            <s xml:id="echoid-s5921" xml:space="preserve">_I_ta ſinum complementi arcus grad. </s>
            <s xml:id="echoid-s5922" xml:space="preserve">_30_. </s>
            <s xml:id="echoid-s5923" xml:space="preserve">ſupra
              <lb/>
            grad. </s>
            <s xml:id="echoid-s5924" xml:space="preserve">_30._ </s>
            <s xml:id="echoid-s5925" xml:space="preserve">infimi lateris tabulæ è regione _M_inuti _0._ </s>
            <s xml:id="echoid-s5926" xml:space="preserve">ad dextram collocati inuenies
              <lb/>
            _8660254_. </s>
            <s xml:id="echoid-s5927" xml:space="preserve">qui quidem ſinus rectus eſt arcus grad. </s>
            <s xml:id="echoid-s5928" xml:space="preserve">_59_. </s>
            <s xml:id="echoid-s5929" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s5930" xml:space="preserve">_60_. </s>
            <s xml:id="echoid-s5931" xml:space="preserve">hoc eſt, arcus grad.
              <lb/>
            </s>
            <s xml:id="echoid-s5932" xml:space="preserve">_60_. </s>
            <s xml:id="echoid-s5933" xml:space="preserve">qui complementum eſt arcus grad. </s>
            <s xml:id="echoid-s5934" xml:space="preserve">_30_. </s>
            <s xml:id="echoid-s5935" xml:space="preserve">_I_tem ſinum complementi arcus grad. </s>
            <s xml:id="echoid-s5936" xml:space="preserve">_30_. </s>
            <s xml:id="echoid-s5937" xml:space="preserve">
              <lb/>
            _M_in. </s>
            <s xml:id="echoid-s5938" xml:space="preserve">_49_. </s>
            <s xml:id="echoid-s5939" xml:space="preserve">reperies _8588110_. </s>
            <s xml:id="echoid-s5940" xml:space="preserve">qui quidem sinus rectus eſt arcus grad. </s>
            <s xml:id="echoid-s5941" xml:space="preserve">_59._ </s>
            <s xml:id="echoid-s5942" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s5943" xml:space="preserve">_11._ </s>
            <s xml:id="echoid-s5944" xml:space="preserve">qui
              <lb/>
            complementum eſt arcus grad. </s>
            <s xml:id="echoid-s5945" xml:space="preserve">_30_. </s>
            <s xml:id="echoid-s5946" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s5947" xml:space="preserve">_49_. </s>
            <s xml:id="echoid-s5948" xml:space="preserve">_S_i vero offeratur arcus _Q_uadrante
              <lb/>
              <note position="right" xlink:label="note-181-05" xlink:href="note-181-05a" xml:space="preserve">Sinus cõple
                <lb/>
              mẽti cuiuſ
                <lb/>
              uis arcꝰ qua
                <lb/>
              drãte maio
                <lb/>
              ris, qua arte
                <lb/>
              deprehen -
                <lb/>
              datur.</note>
            maior, ſed ſemicirculo minor, ita ſinum complementi ipſius reperies. </s>
            <s xml:id="echoid-s5949" xml:space="preserve">_D_etrabe ex eo
              <lb/>
            quadrantem, & </s>
            <s xml:id="echoid-s5950" xml:space="preserve">reſidui arcus ſinum rectum cape. </s>
            <s xml:id="echoid-s5951" xml:space="preserve">_C_um enim reliquus hic arcus ſit
              <lb/>
            complementum dati arcus, vt in definitionibus dictum eſt, erit eius ſinus rectus, ſinus
              <lb/>
            complementi dati arcus. </s>
            <s xml:id="echoid-s5952" xml:space="preserve">_V_t ſi oblatus ſit arcus grad. </s>
            <s xml:id="echoid-s5953" xml:space="preserve">_127_. </s>
            <s xml:id="echoid-s5954" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s5955" xml:space="preserve">_30._ </s>
            <s xml:id="echoid-s5956" xml:space="preserve">_D_etrabe ex eo
              <lb/>
            quadrantem, hoc eſt, _90._ </s>
            <s xml:id="echoid-s5957" xml:space="preserve">gradus. </s>
            <s xml:id="echoid-s5958" xml:space="preserve">_S_inus namque rectus _6087614._ </s>
            <s xml:id="echoid-s5959" xml:space="preserve">reliqui arcus grad.
              <lb/>
            </s>
            <s xml:id="echoid-s5960" xml:space="preserve">_37._ </s>
            <s xml:id="echoid-s5961" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s5962" xml:space="preserve">_30._ </s>
            <s xml:id="echoid-s5963" xml:space="preserve">eſt ſinus complementi dati arcus grad. </s>
            <s xml:id="echoid-s5964" xml:space="preserve">_127._ </s>
            <s xml:id="echoid-s5965" xml:space="preserve">_M_in. </s>
            <s xml:id="echoid-s5966" xml:space="preserve">_30._ </s>
            <s xml:id="echoid-s5967" xml:space="preserve">cumille arcus ſit
              <lb/>
            buius complementum. </s>
            <s xml:id="echoid-s5968" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-181-06" xlink:href="note-181-06a" xml:space="preserve">Sinꝰ cõple-
                <lb/>
              mẽti cuiuſ
                <lb/>
              uis arcꝰ ha
                <lb/>
              bẽtis Secũ-
                <lb/>
              da, p̃ter Mi
                <lb/>
              nuta, quo</note>
            </s>
          </p>
          <p style="it">
            <s xml:id="echoid-s5969" xml:space="preserve">_QVOD_ ſi datus arcus præter gradus, ac _M_inuta habeat etiã _S_ecunda; </s>
            <s xml:id="echoid-s5970" xml:space="preserve">ſi quidem
              <lb/>
            _Q_uadrante minor ſit, inueſtigabis eius ſinum complementi per regulam proportio-
              <lb/>
            num, quemadmodum ſupra de ſinu recto diximus, niſi quòd hic differentia inuenta,
              <lb/>
            ſiue pars proportionalis ſubtrahenda eſt à ſinu arcus proxime minoris, _S_i vero </s>
          </p>
        </div>
      </text>
    </echo>
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