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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        <div xml:id="echoid-div764" type="section" level="1" n="447">
          <head xml:id="echoid-head474" xml:space="preserve">VSVS TABVLÆ TAM TANGEN-</head>
          <head xml:id="echoid-head475" xml:space="preserve">tium, quam ſecantium.</head>
          <p style="it">
            <s xml:id="echoid-s8584" xml:space="preserve">EX vtraq; </s>
            <s xml:id="echoid-s8585" xml:space="preserve">tabula non aliter tangentes, ac ſecantes arcuum, vel complemento@
              <lb/>
              <note position="left" xlink:label="note-304-01" xlink:href="note-304-01a" xml:space="preserve">Vſus tabu-
                <lb/>
              læ tam tan
                <lb/>
              gentium,
                <lb/>
              quam ſecá-
                <lb/>
              tium.</note>
            rum arcuum inueſtigabimus, ac ſupra ſinus rectos, & </s>
            <s xml:id="echoid-s8586" xml:space="preserve">ſinus complementorum arcuum
              <lb/>
            ex ſinuum tabula eruere docuimus. </s>
            <s xml:id="echoid-s8587" xml:space="preserve">Vt ſi quæratur tam tangens, quam ſecans arcus
              <lb/>
            grad. </s>
            <s xml:id="echoid-s8588" xml:space="preserve">50. </s>
            <s xml:id="echoid-s8589" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8590" xml:space="preserve">24. </s>
            <s xml:id="echoid-s8591" xml:space="preserve">inuenietur in tabula tangentium ſub grad. </s>
            <s xml:id="echoid-s8592" xml:space="preserve">50. </s>
            <s xml:id="echoid-s8593" xml:space="preserve">in vertice tabu-
              <lb/>
            læ poſitis, è regione Min. </s>
            <s xml:id="echoid-s8594" xml:space="preserve">24. </s>
            <s xml:id="echoid-s8595" xml:space="preserve">ad ſiniſtram collocatorum tangens particularum
              <lb/>
            1 2087923. </s>
            <s xml:id="echoid-s8596" xml:space="preserve">qualium ſinus totus ponitur 10000000. </s>
            <s xml:id="echoid-s8597" xml:space="preserve">In tabula vero ſecantium repe-
              <lb/>
            rietur ſub grad. </s>
            <s xml:id="echoid-s8598" xml:space="preserve">50. </s>
            <s xml:id="echoid-s8599" xml:space="preserve">è regione Min. </s>
            <s xml:id="echoid-s8600" xml:space="preserve">24. </s>
            <s xml:id="echoid-s8601" xml:space="preserve">ſecans earundem particularum. </s>
            <s xml:id="echoid-s8602" xml:space="preserve">15688144.
              <lb/>
            </s>
            <s xml:id="echoid-s8603" xml:space="preserve">Quod ſi quæratur tam tangens, quam ſecans complementi arcus 39. </s>
            <s xml:id="echoid-s8604" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8605" xml:space="preserve">36. </s>
            <s xml:id="echoid-s8606" xml:space="preserve">repe-
              <lb/>
            rietur in priori quidem tabula ſupra grad. </s>
            <s xml:id="echoid-s8607" xml:space="preserve">39. </s>
            <s xml:id="echoid-s8608" xml:space="preserve">in ima ſede poſitos, è regione Min 36. </s>
            <s xml:id="echoid-s8609" xml:space="preserve">
              <lb/>
            ad dextram collocatorum tangens eadem, quæ prius, 12087923. </s>
            <s xml:id="echoid-s8610" xml:space="preserve">In poſteriori vero ta-
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            bula eadem ſecans 15688144. </s>
            <s xml:id="echoid-s8611" xml:space="preserve">propterea quòd complementum arcus grad. </s>
            <s xml:id="echoid-s8612" xml:space="preserve">39. </s>
            <s xml:id="echoid-s8613" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8614" xml:space="preserve">
              <lb/>
            36. </s>
            <s xml:id="echoid-s8615" xml:space="preserve">complectitur grad. </s>
            <s xml:id="echoid-s8616" xml:space="preserve">50. </s>
            <s xml:id="echoid-s8617" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8618" xml:space="preserve">24. </s>
            <s xml:id="echoid-s8619" xml:space="preserve">cui arcui dicta tangens, ac ſecans debetur, vt
              <lb/>
            patet.</s>
            <s xml:id="echoid-s8620" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s8621" xml:space="preserve">I AM verò ſi ſinus totus aſſumatur particularum tantummodo 100000. </s>
            <s xml:id="echoid-s8622" xml:space="preserve">abiectis
              <lb/>
            duabus cifris ex ſinu tote 10000000. </s>
            <s xml:id="echoid-s8623" xml:space="preserve">abijciendæ quoq; </s>
            <s xml:id="echoid-s8624" xml:space="preserve">erunt ex ſingulis tangentibus,
              <lb/>
            ac ſecantibus duæ priores figuræ ad dextram: </s>
            <s xml:id="echoid-s8625" xml:space="preserve">quemadmodum de ſinubus diximus.</s>
            <s xml:id="echoid-s8626" xml:space="preserve"/>
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          <head xml:id="echoid-head476" xml:space="preserve">SINVVM, TANGENTIVM,
            <lb/>
          ET SECANTIVM FINIS.</head>
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