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

Table of contents

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[241.] THEOR. 7. PROPOS. 10.
Page: 187 (175)
[242.] SCHOLIVM.
Page: 189 (177)
[243.] COROLLARIVM.
Page: 189 (177)
[244.] THEOR. 8. PROPOS. II.
Page: 189 (177)
[245.] SCHOLIVM.
Page: 190 (178)
[246.] PROBL. 4. PROP. 12.
Page: 190 (178)
[247.] PROBL. 5. PROP. 13.
Page: 191 (179)
[248.] COROLLARIVM.
Page: 192 (180)
[249.] PROBL. 6. PROPOS. 14.
Page: 192 (180)
[250.] COROLLARIVM.
Page: 192 (180)
[251.] PROBL. 7. PROPOS. 15.
Page: 193 (181)
[252.] COROLLARIVM.
Page: 194 (182)
[253.] PROBL. 8. PROPOS. 16.
Page: 194 (182)
[254.] SCHOLIVM.
Page: 197 (185)
[255.] LINAE TANGENTES, atque Secantes.
Page: 200 (188)
[256.] THEOR. .9. PROPOS. 17.
Page: 201 (189)
[257.] SCHOLIVM.
Page: 202 (190)
[258.] THEOR. 10. PROPOS. 18.
Page: 203 (191)
[259.] SCHOLIVM.
Page: 204 (192)
[260.] THEOR 11. PROPOS. 19.
Page: 205 (193)
[261.] SCHOLIVM.
Page: 205 (193)
[262.] THEOR. 12. PROPOS. 20.
Page: 206 (194)
[263.] SCHOLIVM.
Page: 207 (195)
[264.] THEOR. 13. PROPOS. 21.
Page: 210 (198)
[265.] THEOR. 14. PROPOS. 22.
Page: 211 (199)
[266.] THEOR. 15. PROPOS. 23.
Page: 211 (199)
[267.] COROLLARIVM.
Page: 212 (200)
[268.] THEOR. 16. PROPOS. 24.
Page: 213 (201)
[269.] SEQVVNTVR TABVLAE TANGEN-tium atque ſecantium.
Page: 213 (201)
[270.] Gradus Quadrantis pro tangentibus
Page: 214 (202)
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          <head xml:id="echoid-head282" xml:space="preserve">LINAE TANGENTES,
            <lb/>
          atque Secantes.</head>
          <p style="it">
            <s xml:id="echoid-s7624" xml:space="preserve">QVANQVAM Aſtronomi omnia
              <lb/>
            ſua problemata, atque theoremata per ſolos ſi-
              <lb/>
            nus explicare poßint, vt communiter ab omni-
              <lb/>
            bus fieri ſolet, quia tamen multa facilius, ac bre-
              <lb/>
            uius expediuntur, ſi vnà cum ſinubus lineætan-
              <lb/>
            gentes, ſecantesque adhibeantur, vt ex doctri-
              <lb/>
            na triangulorum erit manifestum; </s>
            <s xml:id="echoid-s7625" xml:space="preserve">quas qui-
              <lb/>
            demlineas vtili ſane conſilio Recentiores exco-
              <lb/>
            gitarunt, atque in tabulas redegerunt: </s>
            <s xml:id="echoid-s7626" xml:space="preserve">viſum
              <lb/>
            est has etiam lineas paucis exponere, vt doctri-
              <lb/>
            na noſtrorum triangulorum perfectior euadat.
              <lb/>
            </s>
            <s xml:id="echoid-s7627" xml:space="preserve">Vniuerſa ſiquidem triangulorum doctrina in
              <lb/>
              <note position="left" xlink:label="note-200-01" xlink:href="note-200-01a" xml:space="preserve">Doctrina
                <lb/>
              triangulo -
                <lb/>
              rũ in quo
                <lb/>
              conſiſtat.</note>
            tribus hiſce line arum generibus, nempe in ſinu-
              <lb/>
            bus, lineis tangentibus, & </s>
            <s xml:id="echoid-s7628" xml:space="preserve">ſecantibus, potißi-
              <lb/>
            mum conſiſtere videtur. </s>
            <s xml:id="echoid-s7629" xml:space="preserve">Primum autem expli-
              <lb/>
            candum eſt, quid ſit linea tangens, & </s>
            <s xml:id="echoid-s7630" xml:space="preserve">quid ſe-
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            cans propoſiti cuiuſuis arcus.</s>
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              <emph style="sc">CVm</emph>
            ergoab altero extremo cuius libet arcus, qui quadrante minor ſit, ſemi-
              <lb/>
              <note position="left" xlink:label="note-200-02" xlink:href="note-200-02a" xml:space="preserve">Linea tan-
                <lb/>
              gens, & ſe-
                <lb/>
              cans quid.</note>
            diameter ducta fuerit, in cuius extremitate recta linea circulum tangat, & </s>
            <s xml:id="echoid-s7633" xml:space="preserve">per
              <lb/>
            alierum extremum eiuſdem arcus extendatur alia recta linea ex centro ad tangen-
              <lb/>
            tem lineam vſque: </s>
            <s xml:id="echoid-s7634" xml:space="preserve">appellatur portio lineæ tangentis inter duas rectas è centro egre-
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            dientes, Linea tangens illius arcus, quem eædẽ duæ rectæ e centro eductæ includunt:
              <lb/>
            </s>
            <s xml:id="echoid-s7635" xml:space="preserve">Recta vero altera puncto contactus oppoſita inter centrum, & </s>
            <s xml:id="echoid-s7636" xml:space="preserve">lineam tangentem, di-
              <lb/>
            citur Linea ſecans eiuſdem arcus. </s>
            <s xml:id="echoid-s7637" xml:space="preserve">Vt ſi in circulo AB, cuius centrum C, ſumatur ar-
              <lb/>
            cus AB, quadrante minor, & </s>
            <s xml:id="echoid-s7638" xml:space="preserve">in extremitate ſemidiametri
              <emph style="sc">Ac</emph>
            , ab extremitate </s>
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