Clavius, Christoph, Geometria practica

Table of Notes

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          <p>
            <s xml:id="echoid-s603" xml:space="preserve">
              <pb o="9" file="039" n="39" rhead="LIBER PRIMVS."/>
            idem fiat cum reliqua particula (ſi qua forte ſuperfuerit poſt 37. </s>
            <s xml:id="echoid-s604" xml:space="preserve">partes per-
              <lb/>
            curſas) vna cum tribus centeſimis, & </s>
            <s xml:id="echoid-s605" xml:space="preserve">inciderimus verbi gratia in particulam
              <lb/>
            34. </s>
            <s xml:id="echoid-s606" xml:space="preserve">abiectis 30. </s>
            <s xml:id="echoid-s607" xml:space="preserve">continebit ea particula {4/10}. </s>
            <s xml:id="echoid-s608" xml:space="preserve">vnius milleſimæ, hoc eſt, {4/10000}. </s>
            <s xml:id="echoid-s609" xml:space="preserve">Et
              <lb/>
            quia {207/1000} æquiualent {2070/10000}. </s>
            <s xml:id="echoid-s610" xml:space="preserve">ſi addantur {4/10000}. </s>
            <s xml:id="echoid-s611" xml:space="preserve">vltimo loco deprehenſæ, ha-
              <lb/>
            bebimus {2074/10000}. </s>
            <s xml:id="echoid-s612" xml:space="preserve">Si denique cumreliqua particula (ſi qua forte remanſerit) vna
              <lb/>
            cum tribus centeſimis idem fiat, percurſæque verbi gratia ſint 39. </s>
            <s xml:id="echoid-s613" xml:space="preserve">partes, ab-
              <lb/>
            iectis 30. </s>
            <s xml:id="echoid-s614" xml:space="preserve">ſupererunt {9/10}. </s>
            <s xml:id="echoid-s615" xml:space="preserve">vnius partis {1/10000}. </s>
            <s xml:id="echoid-s616" xml:space="preserve">hoc eſt {9/100000}. </s>
            <s xml:id="echoid-s617" xml:space="preserve">Cum ergo {2074/10000} ef-
              <lb/>
            ficiant {20740/100000} ſi addantur {9/100000}. </s>
            <s xml:id="echoid-s618" xml:space="preserve">habebimus {20749/100000}. </s>
            <s xml:id="echoid-s619" xml:space="preserve">Atque adeo ſi recta A F,
              <lb/>
            ſtatuatur ſinus totus partium 100000. </s>
            <s xml:id="echoid-s620" xml:space="preserve">erit ſegmentum 20. </s>
            <s xml:id="echoid-s621" xml:space="preserve">partium cum par-
              <lb/>
            ticula data, ſinus partium 20749. </s>
            <s xml:id="echoid-s622" xml:space="preserve">Si particula data commode per cir cinum
              <lb/>
            poſsit comprehendi, & </s>
            <s xml:id="echoid-s623" xml:space="preserve">decies repetatur, dabunt centeſimæ partes percurſæ
              <lb/>
            partes decimas vnius centeſimæ. </s>
            <s xml:id="echoid-s624" xml:space="preserve">&</s>
            <s xml:id="echoid-s625" xml:space="preserve">c. </s>
            <s xml:id="echoid-s626" xml:space="preserve">Si quo que nonnunquam nulla ſuper-
              <lb/>
            ſit particula, ita vt verbi gratia inuentæ ſint præcisè {207/2000} multiplicandus erit
              <lb/>
            tam numerator, quam denominator per 100. </s>
            <s xml:id="echoid-s627" xml:space="preserve">vt habeatur ſinus 20700. </s>
            <s xml:id="echoid-s628" xml:space="preserve">reſpe-
              <lb/>
            ctu ſinus totius 100000. </s>
            <s xml:id="echoid-s629" xml:space="preserve">quemadmodũ & </s>
            <s xml:id="echoid-s630" xml:space="preserve">40. </s>
            <s xml:id="echoid-s631" xml:space="preserve">centeſimæ conſtituunt ſinum
              <lb/>
            40000. </s>
            <s xml:id="echoid-s632" xml:space="preserve">reſpectu ſinus totius 100000. </s>
            <s xml:id="echoid-s633" xml:space="preserve">Sinamque vterque numerus minutiæ
              <lb/>
            {40/100} ducatur in 1000. </s>
            <s xml:id="echoid-s634" xml:space="preserve">fiet minutia {40000/100000}.</s>
            <s xml:id="echoid-s635" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s636" xml:space="preserve">14. </s>
            <s xml:id="echoid-s637" xml:space="preserve">
              <emph style="sc">Hoc</emph>
            eodem inſtrumento, & </s>
            <s xml:id="echoid-s638" xml:space="preserve">in eadem facie partium æqualium, ex
              <lb/>
              <note position="right" xlink:label="note-039-01" xlink:href="note-039-01a" xml:space="preserve">Ex circulo
                <lb/>
              qua ratione
                <lb/>
              abſcindatur
                <lb/>
              arc{us} datorũ
                <lb/>
              grad. ac min.</note>
            data qualibet circumferentia auferemus arcum quotuis graduum & </s>
            <s xml:id="echoid-s639" xml:space="preserve">minuto-
              <lb/>
            rum, hac arte. </s>
            <s xml:id="echoid-s640" xml:space="preserve">Sit ex quadrante, cuius ſemidiameter interuallo F G, æqualis
              <lb/>
            fit, abſcindẽdus verbigratia arcus grad. </s>
            <s xml:id="echoid-s641" xml:space="preserve">53. </s>
            <s xml:id="echoid-s642" xml:space="preserve">hoc eſt, chorda huius arcusinue-
              <lb/>
            nienda. </s>
            <s xml:id="echoid-s643" xml:space="preserve">Sumatur ex tabula ſinuum ſinus ſemiſsis propoſiti arcus, graduum
              <lb/>
            videlicet 16. </s>
            <s xml:id="echoid-s644" xml:space="preserve">min. </s>
            <s xml:id="echoid-s645" xml:space="preserve">45. </s>
            <s xml:id="echoid-s646" xml:space="preserve">quiſinus, abiectis quatuor figuris ad dexteram, eſt 450.
              <lb/>
            </s>
            <s xml:id="echoid-s647" xml:space="preserve">reſpectu ſinus totius 1000. </s>
            <s xml:id="echoid-s648" xml:space="preserve">Siergo ſinus hicreſpectu ſinus totius A F, accipia-
              <lb/>
            turinrecta A F, vſque ad 45. </s>
            <s xml:id="echoid-s649" xml:space="preserve">perea, quæſupra Num. </s>
            <s xml:id="echoid-s650" xml:space="preserve">4. </s>
            <s xml:id="echoid-s651" xml:space="preserve">& </s>
            <s xml:id="echoid-s652" xml:space="preserve">12. </s>
            <s xml:id="echoid-s653" xml:space="preserve">tradita ſunt, da-
              <lb/>
            bit interuallum inter 45. </s>
            <s xml:id="echoid-s654" xml:space="preserve">& </s>
            <s xml:id="echoid-s655" xml:space="preserve">45. </s>
            <s xml:id="echoid-s656" xml:space="preserve">ſinum quoque eundemreſpectu ſinus totius
              <lb/>
            F G, quodinteruallum duplicatum dabit chordamdupli arcus grad. </s>
            <s xml:id="echoid-s657" xml:space="preserve">26. </s>
            <s xml:id="echoid-s658" xml:space="preserve">min. </s>
            <s xml:id="echoid-s659" xml:space="preserve">
              <lb/>
            45. </s>
            <s xml:id="echoid-s660" xml:space="preserve">id eſt, chordam arcus grad. </s>
            <s xml:id="echoid-s661" xml:space="preserve">53. </s>
            <s xml:id="echoid-s662" xml:space="preserve">min. </s>
            <s xml:id="echoid-s663" xml:space="preserve">30. </s>
            <s xml:id="echoid-s664" xml:space="preserve">qui quæritur. </s>
            <s xml:id="echoid-s665" xml:space="preserve">Si ſinus totus ſtatua-
              <lb/>
            tur 10000. </s>
            <s xml:id="echoid-s666" xml:space="preserve">erit ſinus grad. </s>
            <s xml:id="echoid-s667" xml:space="preserve">26. </s>
            <s xml:id="echoid-s668" xml:space="preserve">min. </s>
            <s xml:id="echoid-s669" xml:space="preserve">45. </s>
            <s xml:id="echoid-s670" xml:space="preserve">in tabula ſinuũ 4501. </s>
            <s xml:id="echoid-s671" xml:space="preserve">abiectis nimirum
              <lb/>
            tribus figuris ad dexteram: </s>
            <s xml:id="echoid-s672" xml:space="preserve">quiin A F, capietur, vt Num. </s>
            <s xml:id="echoid-s673" xml:space="preserve">6. </s>
            <s xml:id="echoid-s674" xml:space="preserve">& </s>
            <s xml:id="echoid-s675" xml:space="preserve">12. </s>
            <s xml:id="echoid-s676" xml:space="preserve">dictum eſt.</s>
            <s xml:id="echoid-s677" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s678" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            ſi vtraque regula A F, A G, contineat 1000. </s>
            <s xml:id="echoid-s679" xml:space="preserve">partes, ſtatui poterit ſi-
              <lb/>
            nustotus 100000. </s>
            <s xml:id="echoid-s680" xml:space="preserve">& </s>
            <s xml:id="echoid-s681" xml:space="preserve">etiam plurium partium, ſi nimirum adhibeatur recta
              <lb/>
            M N, partium 101. </s>
            <s xml:id="echoid-s682" xml:space="preserve">diuiſa in 100. </s>
            <s xml:id="echoid-s683" xml:space="preserve">particulas, vel alia recta partium 1001. </s>
            <s xml:id="echoid-s684" xml:space="preserve">in 1000.
              <lb/>
            </s>
            <s xml:id="echoid-s685" xml:space="preserve">particulas ſecta.</s>
            <s xml:id="echoid-s686" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s687" xml:space="preserve">15. </s>
            <s xml:id="echoid-s688" xml:space="preserve">
              <emph style="sc">EContrario</emph>
            facile etiam cognoſcemus, quot gradus, & </s>
            <s xml:id="echoid-s689" xml:space="preserve">minu-
              <lb/>
              <note position="right" xlink:label="note-039-02" xlink:href="note-039-02a" xml:space="preserve">Quot grad{us},
                <lb/>
              ac minuta in
                <lb/>
              dato arcu cõ-
                <lb/>
              tineãtur, quo
                <lb/>
              pacto cogno-
                <lb/>
              ſcatur.</note>
            tain propoſito arcu cuiuſuis quadrantis contineantur. </s>
            <s xml:id="echoid-s690" xml:space="preserve">Sit enim in quadran-
              <lb/>
            te, cuius ſemidiameter F G, cuiæqualis ſitrecta R S, datus aliquis arcus, cuius
              <lb/>
            chordæſemiſsis ſir R T. </s>
            <s xml:id="echoid-s691" xml:space="preserve">Huic R T, æqualis inueniatur recta 40. </s>
            <s xml:id="echoid-s692" xml:space="preserve">40. </s>
            <s xml:id="echoid-s693" xml:space="preserve">inter rectas
              <lb/>
            A F, A G, ita vt puncta 40. </s>
            <s xml:id="echoid-s694" xml:space="preserve">40. </s>
            <s xml:id="echoid-s695" xml:space="preserve">vel abſcindant æquales partes, vtin dato exem-
              <lb/>
            plo, vel æqualiter diſtent à duabus partibus æqualibus. </s>
            <s xml:id="echoid-s696" xml:space="preserve">Deinde per ea, quæ
              <lb/>
            Num. </s>
            <s xml:id="echoid-s697" xml:space="preserve">13. </s>
            <s xml:id="echoid-s698" xml:space="preserve">ſcripſimus, inquiratur, quot partes ex 1000, vel 10000. </s>
            <s xml:id="echoid-s699" xml:space="preserve">vel 100000.
              <lb/>
            </s>
            <s xml:id="echoid-s700" xml:space="preserve">in ſegmento ab A, vſque ad punctum inuẽtum 40. </s>
            <s xml:id="echoid-s701" xml:space="preserve">comprehendantur. </s>
            <s xml:id="echoid-s702" xml:space="preserve">In da-
              <lb/>
            to exemplo reperiuntur partes 400. </s>
            <s xml:id="echoid-s703" xml:space="preserve">vel 4000. </s>
            <s xml:id="echoid-s704" xml:space="preserve">vel 40000. </s>
            <s xml:id="echoid-s705" xml:space="preserve">prout ſinus totus
              <lb/>
            conſtituitur 1000. </s>
            <s xml:id="echoid-s706" xml:space="preserve">vel 10000. </s>
            <s xml:id="echoid-s707" xml:space="preserve">vel 100000. </s>
            <s xml:id="echoid-s708" xml:space="preserve">atque tantus eſt ſinus 40. </s>
            <s xml:id="echoid-s709" xml:space="preserve">40. </s>
            <s xml:id="echoid-s710" xml:space="preserve">re-
              <lb/>
            ſpectu ſinus totius F G, cuireſpondent Grad. </s>
            <s xml:id="echoid-s711" xml:space="preserve">23. </s>
            <s xml:id="echoid-s712" xml:space="preserve">min. </s>
            <s xml:id="echoid-s713" xml:space="preserve">35. </s>
            <s xml:id="echoid-s714" xml:space="preserve">Duplus ergo arcus
              <lb/>
            gr. </s>
            <s xml:id="echoid-s715" xml:space="preserve">47. </s>
            <s xml:id="echoid-s716" xml:space="preserve">min. </s>
            <s xml:id="echoid-s717" xml:space="preserve">10. </s>
            <s xml:id="echoid-s718" xml:space="preserve">quichordæipſius R T, duplæ debetur, eritis, qui quæritur.</s>
            <s xml:id="echoid-s719" xml:space="preserve"/>
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