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

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          <p style="it">
            <s xml:id="echoid-s6426" xml:space="preserve">
              <pb o="173" file="185" n="185" rhead=""/>
            operationis ratio perſpicua eſt ex prima figura in expoſitione definitionũ poſita. </s>
            <s xml:id="echoid-s6427" xml:space="preserve">_I_n ea
              <lb/>
            enim ſinus verſus _AH,_ ex ſinu toto _
              <emph style="sc">Ae</emph>
            _, ſublatus relinquit _HE_, vel _
              <emph style="sc">F</emph>
            K_, ſinum comple
              <lb/>
            menti arcus _AF_, qui dicto ſinui verſo _AH_, debetur. </s>
            <s xml:id="echoid-s6428" xml:space="preserve">_I_tem ex ſinu verſo _HC_, ſubdu-
              <lb/>
            ctus ſinus totus _
              <emph style="sc">E</emph>
            C_, relinquit _
              <emph style="sc">E</emph>
            H_, vel _
              <emph style="sc">Kf</emph>
            _, ſinum rectum arcus _
              <emph style="sc">F</emph>
            B_, qui quadranti
              <lb/>
            _BC_, adiectus componit arcum _
              <emph style="sc">F</emph>
            C_, dicto ſinui verſo _HC_, reſpondentem.</s>
            <s xml:id="echoid-s6429" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6430" xml:space="preserve">_EX_ eadem tabula ſinuum rectorum indagabimus quoq; </s>
            <s xml:id="echoid-s6431" xml:space="preserve">cuiusq; </s>
            <s xml:id="echoid-s6432" xml:space="preserve">arcus chordam;
              <lb/>
            </s>
            <s xml:id="echoid-s6433" xml:space="preserve">
              <note position="right" xlink:label="note-185-01" xlink:href="note-185-01a" xml:space="preserve">Chorda cu-
                <lb/>
              iuſq; arcꝰ;
                <lb/>
              & cõtra, ar-
                <lb/>
              cus chordæ
                <lb/>
              cuiuſq; qua
                <lb/>
              rõne ex ta-
                <lb/>
              bula ſinuũ
                <lb/>
              eliciatur.</note>
            & </s>
            <s xml:id="echoid-s6434" xml:space="preserve">contra datæ cuiusq; </s>
            <s xml:id="echoid-s6435" xml:space="preserve">chordæ arcum reperiemus. </s>
            <s xml:id="echoid-s6436" xml:space="preserve">_N_am ſi dimidij arcus propoſiti ſi-
              <lb/>
            num rectũ accipiamus, eumq; </s>
            <s xml:id="echoid-s6437" xml:space="preserve">duplicemus, conflabimus dicti arcus chordam. </s>
            <s xml:id="echoid-s6438" xml:space="preserve">_I_tem ſi
              <lb/>
            datæ chordæ dimidium, tanquàm sinum rectum ſumamus, eiuſq́; </s>
            <s xml:id="echoid-s6439" xml:space="preserve">arcum eliciamus, da
              <lb/>
            bit hic arcus duplicatus arcum datæ chordæ reſpondentem. </s>
            <s xml:id="echoid-s6440" xml:space="preserve">_I_d quod ex eadem figura
              <lb/>
            prima, quã in definitionum explicatione deſcripsimus, manifeſtum eſt. </s>
            <s xml:id="echoid-s6441" xml:space="preserve">_N_ã in ea _
              <emph style="sc">F</emph>
            H_,
              <lb/>
            ſinus rectus arcus _
              <emph style="sc">AF</emph>
            ,_ vel _
              <emph style="sc">F</emph>
            C_, eſt ſemißis chordæ _
              <emph style="sc">F</emph>
            G_, arcus _
              <emph style="sc">F</emph>
            AG_, vel _
              <emph style="sc">F</emph>
            CG_, &</s>
            <s xml:id="echoid-s6442" xml:space="preserve">c.</s>
            <s xml:id="echoid-s6443" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6444" xml:space="preserve">_
              <emph style="sc">Ve</emph>
            RVM_ quia tabulam ſinuum non ſemper in promptu habemus, non iniucun-
              <lb/>
            dum ſtudioſis fore ſum arbitratus, ſi breuiter hoc loco doceam, antequam ad alia
              <lb/>
            progrediar, qua ratione ſinubus _G_eometrice, ſine auxilio numerorum, vti poßimus in
              <lb/>
            theorematibus, atq; </s>
            <s xml:id="echoid-s6445" xml:space="preserve">problematibus _A_ſtronomorum ac _G_eometrarũ explicandis: </s>
            <s xml:id="echoid-s6446" xml:space="preserve">ita vt
              <lb/>
            ſolo circini beneficio omnia illa conſequamur, quæ longis multiplicationibus, diuiſioni
              <lb/>
            busq́; </s>
            <s xml:id="echoid-s6447" xml:space="preserve">numerorum in ſinuum tabula contentorũ inquiri ſolẽt. </s>
            <s xml:id="echoid-s6448" xml:space="preserve">_H_ac enim reijs præſer
              <lb/>
            tim conſultum erit, qui vel magnã moleſtiam in numerorũ ſupputationibus ſentiũt,
              <lb/>
            vel non admodum in ijs ſeſe exercuerunt. </s>
            <s xml:id="echoid-s6449" xml:space="preserve">_Q_uod vt commodius exequamur, rem totam
              <lb/>
            vno aut altero exemplo exponemus. </s>
            <s xml:id="echoid-s6450" xml:space="preserve">_S_it ergo, exempli cauſa, inueſtiganda deslinatio
              <lb/>
            cuiuſuis puncti _E_clipticæ, vt grad. </s>
            <s xml:id="echoid-s6451" xml:space="preserve">_20_. </s>
            <s xml:id="echoid-s6452" xml:space="preserve">
              <de:unknown code="022"/>
            . </s>
            <s xml:id="echoid-s6453" xml:space="preserve">_D_eſcribatur circulus _
              <emph style="sc">Ab</emph>
            CD_, vnà cum
              <lb/>
              <note position="right" xlink:label="note-185-02" xlink:href="note-185-02a" xml:space="preserve">Quo pacto
                <lb/>
              ſinubus vtẽ
                <lb/>
              dũ ſit Geo-
                <lb/>
              metricè ſi-
                <lb/>
              ne tabu la
                <lb/>
              finuum.</note>
            duabus diame-
              <lb/>
              <figure xlink:label="fig-185-01" xlink:href="fig-185-01a" number="135">
                <image file="185-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/185-01"/>
              </figure>
            tris _AC, BD_,
              <lb/>
            ſeſe in centro
              <lb/>
            _
              <emph style="sc">E</emph>
            _, ad angulos
              <lb/>
            rectos ſecanti-
              <lb/>
            bus. </s>
            <s xml:id="echoid-s6454" xml:space="preserve">_
              <emph style="sc">E</emph>
            _tquoniã,
              <lb/>
            vt in coroll.
              <lb/>
            </s>
            <s xml:id="echoid-s6455" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s6456" xml:space="preserve">_1._ </s>
            <s xml:id="echoid-s6457" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6458" xml:space="preserve">
              <lb/>
            _1._ </s>
            <s xml:id="echoid-s6459" xml:space="preserve">noſtræ _G_no-
              <lb/>
            monices oſten-
              <lb/>
            dimus, ea eſt
              <lb/>
            proportio ſi-
              <lb/>
            nus totius ad
              <lb/>
            ſinum maximæ declinationis, quæ ſinus illius arcus, quo datum punctum à viciniori
              <lb/>
            puncto æquinoctij diſtat, ad ſinum declinationis eiuſdem puncti; </s>
            <s xml:id="echoid-s6460" xml:space="preserve">ſumatur arcus maxi-
              <lb/>
            mæ declinationis _
              <emph style="sc">Df</emph>
            _, (quod quidem facile fiet, ſi adſit quadrãs æneus, aut ligneus ac-
              <lb/>
            curate in _90_. </s>
            <s xml:id="echoid-s6461" xml:space="preserve">gradus diuiſus, de quo in initio noſtræ _G_nomonices ſcripſimus. </s>
            <s xml:id="echoid-s6462" xml:space="preserve">_S_ine hoc
              <lb/>
            enim quadrãte non eſſet operæ pretium velle ſinubus vti ſine numeris.) </s>
            <s xml:id="echoid-s6463" xml:space="preserve">& </s>
            <s xml:id="echoid-s6464" xml:space="preserve">arcus grad. </s>
            <s xml:id="echoid-s6465" xml:space="preserve">
              <lb/>
            _50._ </s>
            <s xml:id="echoid-s6466" xml:space="preserve">_DG_, quo nimirum datus gradus _20._ </s>
            <s xml:id="echoid-s6467" xml:space="preserve">
              <de:unknown code="022"/>
            . </s>
            <s xml:id="echoid-s6468" xml:space="preserve">à principio γ. </s>
            <s xml:id="echoid-s6469" xml:space="preserve">abeſt: </s>
            <s xml:id="echoid-s6470" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s6471" xml:space="preserve">ex _
              <emph style="sc">F</emph>
            , G_, ad _
              <emph style="sc">De</emph>
            _,
              <lb/>
            perpendiculares demittantur _
              <emph style="sc">F</emph>
            I, GH_; </s>
            <s xml:id="echoid-s6472" xml:space="preserve">quod facile fiet, ſi arcubus _DF,
              <emph style="sc">Dg</emph>
            ,_ ſuman-
              <lb/>
            tur arcus _DK, DL_, æquales: </s>
            <s xml:id="echoid-s6473" xml:space="preserve">_R_ectæ enim puncta _
              <emph style="sc">G</emph>
            , L,_ & </s>
            <s xml:id="echoid-s6474" xml:space="preserve">_
              <emph style="sc">F</emph>
            , K_, iungentes erunt ad
              <lb/>
            _
              <emph style="sc">De</emph>
            _, perpendiculares, cum per ſcholium in definitionibus poſitum ſecentur in _H,_
              <lb/>
            _I_, bifariam, ac propterea ad angulos rectos: </s>
            <s xml:id="echoid-s6475" xml:space="preserve">_
              <emph style="sc">E</emph>
            _runt autem _FI,
              <emph style="sc">G</emph>
            H_, ſinus re-
              <lb/>
              <note position="right" xlink:label="note-185-03" xlink:href="note-185-03a" xml:space="preserve">3. tertij.</note>
            cti arcuum _
              <emph style="sc">Df</emph>
            ,
              <emph style="sc">Dg</emph>
            ._ </s>
            <s xml:id="echoid-s6476" xml:space="preserve">_I_gitur ſi tribus rectis _ED_, ſinui toti, & </s>
            <s xml:id="echoid-s6477" xml:space="preserve">_
              <emph style="sc">F</emph>
            I_, ſinui ma-
              <lb/>
            ximæ declinationis, & </s>
            <s xml:id="echoid-s6478" xml:space="preserve">_GH_, ſinui arcus, quo datum punctum ab </s>
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