Clavius, Christoph, Geometria practica

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            <s xml:id="echoid-s404" xml:space="preserve">
              <pb o="7" file="037" n="37" rhead="LIBER PRIMVS."/>
            quælibet pars contineat {10/10}@ vnius centeſimæ.) </s>
            <s xml:id="echoid-s405" xml:space="preserve">hoc eſt, {80/1000}. </s>
            <s xml:id="echoid-s406" xml:space="preserve">& </s>
            <s xml:id="echoid-s407" xml:space="preserve">{7/10}. </s>
            <s xml:id="echoid-s408" xml:space="preserve">vnius cen-
              <lb/>
            teſimæ contineant {7/1000}. </s>
            <s xml:id="echoid-s409" xml:space="preserve">comprehendet tota linea abſciſſa {87/1000}. </s>
            <s xml:id="echoid-s410" xml:space="preserve">Item ſi quis
              <lb/>
            cupiat {17/1000}. </s>
            <s xml:id="echoid-s411" xml:space="preserve">accipienda erit vna pá
              <unsure/>
            rs ipſius A F, & </s>
            <s xml:id="echoid-s412" xml:space="preserve">{7/10}. </s>
            <s xml:id="echoid-s413" xml:space="preserve">ſequentis partis ſe-
              <lb/>
            cundæ, vt paulo ante dictum eſt. </s>
            <s xml:id="echoid-s414" xml:space="preserve">Vel ſic agemus. </s>
            <s xml:id="echoid-s415" xml:space="preserve">Sumptis 7. </s>
            <s xml:id="echoid-s416" xml:space="preserve">partibus ex
              <lb/>
            K L, transferemus easin A F. </s>
            <s xml:id="echoid-s417" xml:space="preserve">vbicunque libuerit. </s>
            <s xml:id="echoid-s418" xml:space="preserve">Nam abſciſſæ partes erunt
              <lb/>
            7 {7/17}. </s>
            <s xml:id="echoid-s419" xml:space="preserve">Vna ergo pars cum {7/10}. </s>
            <s xml:id="echoid-s420" xml:space="preserve">continebit {17/1000}. </s>
            <s xml:id="echoid-s421" xml:space="preserve">Denique ſi optentur {457/1000}. </s>
            <s xml:id="echoid-s422" xml:space="preserve">ſu-
              <lb/>
            mendæ erunt exrecta A F, partes 45. </s>
            <s xml:id="echoid-s423" xml:space="preserve">cum hæ æquiualeant {450/1000}. </s>
            <s xml:id="echoid-s424" xml:space="preserve">Deinde {7/10}.
              <lb/>
            </s>
            <s xml:id="echoid-s425" xml:space="preserve">ex ſequenti parte quadrageſima ſexta, beneficio ſeptem particularum rectæ
              <lb/>
            K L, &</s>
            <s xml:id="echoid-s426" xml:space="preserve">c.</s>
            <s xml:id="echoid-s427" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s428" xml:space="preserve">5. </s>
            <s xml:id="echoid-s429" xml:space="preserve">
              <emph style="sc">Si</emph>
            ergo ſinus totus ponatur 1000. </s>
            <s xml:id="echoid-s430" xml:space="preserve">habebuntur Tangentes, vt in ta-
              <lb/>
            bula nouæ deſcriptionis horologiorum poſitæ ſunt, nulla figura abiecta. </s>
            <s xml:id="echoid-s431" xml:space="preserve">Sed
              <lb/>
              <note position="right" xlink:label="note-037-01" xlink:href="note-037-01a" xml:space="preserve">Tangentes
                <lb/>
              quo modo in-
                <lb/>
              inueniantur,
                <lb/>
              poſito ſinu toto
                <lb/>
              100.</note>
            quando Tangens maior eſt quam 1000. </s>
            <s xml:id="echoid-s432" xml:space="preserve">relictis millenis, accipendæ ſuntre-
              <lb/>
            liquæ partes milleſimæ pro Tangente, eiq; </s>
            <s xml:id="echoid-s433" xml:space="preserve">toties ſinus totus addendus, quo-
              <lb/>
              <handwritten xlink:label="hd-037-01" xlink:href="hd-037-01a" number="7"/>
            ties vnitas in millenis relictis reperitur. </s>
            <s xml:id="echoid-s434" xml:space="preserve">Vt ſi quis velit Tangentem Grad. </s>
            <s xml:id="echoid-s435" xml:space="preserve">40.
              <lb/>
            </s>
            <s xml:id="echoid-s436" xml:space="preserve">min. </s>
            <s xml:id="echoid-s437" xml:space="preserve">30. </s>
            <s xml:id="echoid-s438" xml:space="preserve">quæ in tabula eſt 854. </s>
            <s xml:id="echoid-s439" xml:space="preserve">accipiendæ ſunt in regula A F, partes 85. </s>
            <s xml:id="echoid-s440" xml:space="preserve">& </s>
            <s xml:id="echoid-s441" xml:space="preserve">
              <lb/>
            {4/10}. </s>
            <s xml:id="echoid-s442" xml:space="preserve">vnius. </s>
            <s xml:id="echoid-s443" xml:space="preserve">Ita enim Tangens continebit partes 854. </s>
            <s xml:id="echoid-s444" xml:space="preserve">ex 1000. </s>
            <s xml:id="echoid-s445" xml:space="preserve">At ſi quæratur
              <lb/>
            Tangens Grad. </s>
            <s xml:id="echoid-s446" xml:space="preserve">80. </s>
            <s xml:id="echoid-s447" xml:space="preserve">min. </s>
            <s xml:id="echoid-s448" xml:space="preserve">0. </s>
            <s xml:id="echoid-s449" xml:space="preserve">quæ in tabula eſt 5671. </s>
            <s xml:id="echoid-s450" xml:space="preserve">relictis millenis accipien-
              <lb/>
            dæ ſunt partes 67. </s>
            <s xml:id="echoid-s451" xml:space="preserve">& </s>
            <s xml:id="echoid-s452" xml:space="preserve">{1/10}. </s>
            <s xml:id="echoid-s453" xml:space="preserve">vnius partis, & </s>
            <s xml:id="echoid-s454" xml:space="preserve">Tangenti 671. </s>
            <s xml:id="echoid-s455" xml:space="preserve">addendus ſinus to-
              <lb/>
            tus quinquies.</s>
            <s xml:id="echoid-s456" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s457" xml:space="preserve">6. </s>
            <s xml:id="echoid-s458" xml:space="preserve">
              <emph style="sc">Pari</emph>
            ratione ſi adhibeatur recta M N, partium 101. </s>
            <s xml:id="echoid-s459" xml:space="preserve">diuiſa in 100. </s>
            <s xml:id="echoid-s460" xml:space="preserve">de-
              <lb/>
              <note position="right" xlink:label="note-037-02" xlink:href="note-037-02a" xml:space="preserve">Decimæ par-
                <lb/>
              tes milleſima-
                <lb/>
              rum quo mo-
                <lb/>
              do ſumantur,
                <lb/>
              etiam ſi inſtru
                <lb/>
              mentumdiui-
                <lb/>
              ſum ſit in 100.
                <lb/>
              part{es} dunta-
                <lb/>
              x{at}.</note>
            promemus ex recta A F, partes decimas milleſimarum; </s>
            <s xml:id="echoid-s461" xml:space="preserve">cum quælibet parti-
              <lb/>
            cula rectæ M N, contineat vnam particulam ipſius A F, ſemel, & </s>
            <s xml:id="echoid-s462" xml:space="preserve">inſuper
              <lb/>
            {1/100}. </s>
            <s xml:id="echoid-s463" xml:space="preserve">Ita vt quælibet particula rectæ A F, diuiſa eſſe cogitetur in 100. </s>
            <s xml:id="echoid-s464" xml:space="preserve">particu-
              <lb/>
            las; </s>
            <s xml:id="echoid-s465" xml:space="preserve">ac proinde tota A F, ſit 10000. </s>
            <s xml:id="echoid-s466" xml:space="preserve">particularum, quod eodẽ modo demon-
              <lb/>
            ſtrabitur. </s>
            <s xml:id="echoid-s467" xml:space="preserve">Eſt enim eadem proportio M N, ad vnam particulam ſuam cente-
              <lb/>
            ſimam, quæ rectæ A F, ad vnam ſuam centeſimam, &</s>
            <s xml:id="echoid-s468" xml:space="preserve">c.</s>
            <s xml:id="echoid-s469" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s470" xml:space="preserve">7. </s>
            <s xml:id="echoid-s471" xml:space="preserve">
              <emph style="sc">A@qve</emph>
            hac ratione haberi poterunt Tangentes, poſito ſinu toto
              <lb/>
            10000. </s>
            <s xml:id="echoid-s472" xml:space="preserve">abiectis nimirum tribus figuris primis ex Tangentibus tabulæ in no-
              <lb/>
            ſtro Theodoſio deſcriptæ. </s>
            <s xml:id="echoid-s473" xml:space="preserve">Vtſi velimus Tangentem Grad. </s>
            <s xml:id="echoid-s474" xml:space="preserve">78. </s>
            <s xml:id="echoid-s475" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s476" xml:space="preserve">30. </s>
            <s xml:id="echoid-s477" xml:space="preserve">quæ
              <lb/>
            in tabula (abiectis tribus figuris) eſt 49151. </s>
            <s xml:id="echoid-s478" xml:space="preserve">relictis denis millenarum, acci-
              <lb/>
              <note position="right" xlink:label="note-037-03" xlink:href="note-037-03a" xml:space="preserve">Tangent{es} p@-
                <lb/>
              ſito ſinu toto
                <lb/>
              10000 quo pa-
                <lb/>
              cto ſumãtur.</note>
            piemus partes 9151. </s>
            <s xml:id="echoid-s479" xml:space="preserve">nimirum partes 91. </s>
            <s xml:id="echoid-s480" xml:space="preserve">ex 100. </s>
            <s xml:id="echoid-s481" xml:space="preserve">regulæ A F, & </s>
            <s xml:id="echoid-s482" xml:space="preserve">{51/100}. </s>
            <s xml:id="echoid-s483" xml:space="preserve">vnius.
              <lb/>
            </s>
            <s xml:id="echoid-s484" xml:space="preserve">quod fiet, ſi partes 51. </s>
            <s xml:id="echoid-s485" xml:space="preserve">rectæ M N, transferantur in A F. </s>
            <s xml:id="echoid-s486" xml:space="preserve">Circinus enim vltra
              <lb/>
            partes 51. </s>
            <s xml:id="echoid-s487" xml:space="preserve">abſcindet {51/100}. </s>
            <s xml:id="echoid-s488" xml:space="preserve">Nam quia ſingulæ particulæ rectæ A F, concipiun-
              <lb/>
            tur ſectæ in 100. </s>
            <s xml:id="echoid-s489" xml:space="preserve">particulas, continebuntur in 91. </s>
            <s xml:id="echoid-s490" xml:space="preserve">partibus particulæ 9100. </s>
            <s xml:id="echoid-s491" xml:space="preserve">
              <lb/>
            quibus ſi addantur 51. </s>
            <s xml:id="echoid-s492" xml:space="preserve">habebitur Tangens 9151. </s>
            <s xml:id="echoid-s493" xml:space="preserve">Huic tandem apponendus
              <lb/>
            eſt ſinus totus quater, propter quatuor denas millenarum relictas, Facile au-
              <lb/>
            tem ad 91. </s>
            <s xml:id="echoid-s494" xml:space="preserve">partes adijcies particulam continentem {51/160}. </s>
            <s xml:id="echoid-s495" xml:space="preserve">vnius centeſimæ, ſi
              <lb/>
            eam, (quæ nimirum vltra partes 51. </s>
            <s xml:id="echoid-s496" xml:space="preserve">regulæ A F, exiſtit) cum vna parte regu-
              <lb/>
            læ A F, transferas, vt pes circini inter partes 91. </s>
            <s xml:id="echoid-s497" xml:space="preserve">& </s>
            <s xml:id="echoid-s498" xml:space="preserve">92. </s>
            <s xml:id="echoid-s499" xml:space="preserve">cadat, hoc eſt, ſi eam
              <lb/>
            cum vna parte transferas ex parte 90. </s>
            <s xml:id="echoid-s500" xml:space="preserve">vel cum duabus partibus, ex parte 89. </s>
            <s xml:id="echoid-s501" xml:space="preserve">
              <lb/>
            &</s>
            <s xml:id="echoid-s502" xml:space="preserve">c.</s>
            <s xml:id="echoid-s503" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s504" xml:space="preserve">8. </s>
            <s xml:id="echoid-s505" xml:space="preserve">
              <emph style="sc">Inventa</emph>
            porro Tangente in vtraqueregula A F, A G, dabit inter-
              <lb/>
              <note position="right" xlink:label="note-037-04" xlink:href="note-037-04a" xml:space="preserve">Qua ratione
                <lb/>
              ex inuenta
                <lb/>
              parte milleſi-
                <lb/>
              ma, vel deci-
                <lb/>
              {es} mill@-</note>
            uallum inter Tangentem regulæ A F, & </s>
            <s xml:id="echoid-s506" xml:space="preserve">Tangentem regulæ A G, eandem
              <lb/>
            Tangentem reſpectu ſinus totius F G.</s>
            <s xml:id="echoid-s507" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s508" xml:space="preserve">9. </s>
            <s xml:id="echoid-s509" xml:space="preserve">
              <emph style="sc">Qvando</emph>
            autem Tangens tam exigua eſt, vt eius interuallum prope
              <lb/>
            punctum A, accipinequeat, vtemur hoc artificio. </s>
            <s xml:id="echoid-s510" xml:space="preserve">Sit verbi gratia </s>
          </p>
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