Clavius, Christoph, Geometria practica

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          <p>
            <s xml:id="echoid-s510" xml:space="preserve">
              <pb o="8" file="038" n="38" rhead="GEOMETR. PRACT."/>
            Tangens 7. </s>
            <s xml:id="echoid-s511" xml:space="preserve">partium reſpectu ſinus totius FG. </s>
            <s xml:id="echoid-s512" xml:space="preserve">Sumptis duabus Tangentibus
              <lb/>
              <note position="left" xlink:label="note-038-01" xlink:href="note-038-01a" xml:space="preserve">ſima in AF,
                <lb/>
              eadem reperi-
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              atur reſpectu
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              dati ſin{us} to-
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              ti{us}.</note>
            majoribus, quarum maior minorem ſeptem vnitatibus ſuperet, nimirum 30.
              <lb/>
            </s>
            <s xml:id="echoid-s513" xml:space="preserve">& </s>
            <s xml:id="echoid-s514" xml:space="preserve">37. </s>
            <s xml:id="echoid-s515" xml:space="preserve">vel 80. </s>
            <s xml:id="echoid-s516" xml:space="preserve">& </s>
            <s xml:id="echoid-s517" xml:space="preserve">87. </s>
            <s xml:id="echoid-s518" xml:space="preserve">&</s>
            <s xml:id="echoid-s519" xml:space="preserve">c. </s>
            <s xml:id="echoid-s520" xml:space="preserve">dabit earum differentia (ſi nimirũ vtraquein aliquam
              <lb/>
            rectam lineam transferatur) Tangentem 7. </s>
            <s xml:id="echoid-s521" xml:space="preserve">quæ quæritur: </s>
            <s xml:id="echoid-s522" xml:space="preserve">Atque ita ſemper
              <lb/>
            ſumendæ erunt duæ Tangẽtes maiores prope medium inſtrumenti quarum
              <lb/>
              <handwritten xlink:label="hd-038-01" xlink:href="hd-038-01a" number="8"/>
              <handwritten xlink:label="hd-038-01" xlink:href="hd-038-01a" number="9"/>
            differentia æqualis ſit Tangenti exiguæ propoſitæ.</s>
            <s xml:id="echoid-s523" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s524" xml:space="preserve">10. </s>
            <s xml:id="echoid-s525" xml:space="preserve">
              <emph style="sc">Si</emph>
            vtraque regula AF, AG, contineat 1000. </s>
            <s xml:id="echoid-s526" xml:space="preserve">particulas, & </s>
            <s xml:id="echoid-s527" xml:space="preserve">ſinus to-
              <lb/>
            tupropoſitus conſtituatur 1000. </s>
            <s xml:id="echoid-s528" xml:space="preserve">eique interuallũ F G, æquale ſumatur, com-
              <lb/>
            modiſsime accipientur omnes Tangentes, vtin Tabula nouæ deſcriptionis
              <lb/>
            horologiorum poſitæ ſunt. </s>
            <s xml:id="echoid-s529" xml:space="preserve">Nam verbi gratia Tangens 2430. </s>
            <s xml:id="echoid-s530" xml:space="preserve">Grad. </s>
            <s xml:id="echoid-s531" xml:space="preserve">67. </s>
            <s xml:id="echoid-s532" xml:space="preserve">min.
              <lb/>
            </s>
            <s xml:id="echoid-s533" xml:space="preserve">38. </s>
            <s xml:id="echoid-s534" xml:space="preserve">habebitur, ſi relictis millenis, ſumaturinteruallũ inter partes 430. </s>
            <s xml:id="echoid-s535" xml:space="preserve">vtriuſq; </s>
            <s xml:id="echoid-s536" xml:space="preserve">
              <lb/>
            regulæ A F, A G, eique ſinus totus F G, bis adijciatur.</s>
            <s xml:id="echoid-s537" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s538" xml:space="preserve">11. </s>
            <s xml:id="echoid-s539" xml:space="preserve">
              <emph style="sc">Et</emph>
            ſi adhibeas lineam K L, partium 11. </s>
            <s xml:id="echoid-s540" xml:space="preserve">diuiſam in 10. </s>
            <s xml:id="echoid-s541" xml:space="preserve">accipere poteris
              <lb/>
            Tangentes reſpectu ſinus totius 10000. </s>
            <s xml:id="echoid-s542" xml:space="preserve">Item ſi rectam partium 101. </s>
            <s xml:id="echoid-s543" xml:space="preserve">in 100.
              <lb/>
            </s>
            <s xml:id="echoid-s544" xml:space="preserve">particulas diſtributam adhibeas, habebis Tangentes reſpectu ſinus totius
              <lb/>
            100000. </s>
            <s xml:id="echoid-s545" xml:space="preserve">Si denique rectam partium 1001. </s>
            <s xml:id="echoid-s546" xml:space="preserve">partiaris in 1000. </s>
            <s xml:id="echoid-s547" xml:space="preserve">particulas, obti-
              <lb/>
            nebis Tangentes, poſito ſinu toto 1000000. </s>
            <s xml:id="echoid-s548" xml:space="preserve">vt ex dictis patet.</s>
            <s xml:id="echoid-s549" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s550" xml:space="preserve">12. </s>
            <s xml:id="echoid-s551" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            dictum eſt de Tangentibus, intelligendum eſt etiam de ſinu-
              <lb/>
              <handwritten xlink:label="hd-038-01" xlink:href="hd-038-01a" number="8"/>
              <handwritten xlink:label="hd-038-01" xlink:href="hd-038-01a" number="9"/>
            bus, & </s>
            <s xml:id="echoid-s552" xml:space="preserve">ſecantibus. </s>
            <s xml:id="echoid-s553" xml:space="preserve">Nam ſi interuallum F G, æquale ſit ſinuialicuitoti, ſiueis
              <lb/>
            partium ſit 100. </s>
            <s xml:id="echoid-s554" xml:space="preserve">ſiue 1000. </s>
            <s xml:id="echoid-s555" xml:space="preserve">ſiue plurium, dabunt interualla inter ſinus, vel ſe-
              <lb/>
            cantes in vtraqueregula A F, A G, acceptas, per ea, quæ Num. </s>
            <s xml:id="echoid-s556" xml:space="preserve">4. </s>
            <s xml:id="echoid-s557" xml:space="preserve">docuimus,
              <lb/>
            ſinus & </s>
            <s xml:id="echoid-s558" xml:space="preserve">ſecantes reſpectu ſinus totius F G, accepti; </s>
            <s xml:id="echoid-s559" xml:space="preserve">propterea quod per Lem-
              <lb/>
            ma 5. </s>
            <s xml:id="echoid-s560" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s561" xml:space="preserve">1. </s>
            <s xml:id="echoid-s562" xml:space="preserve">noſtri Aſtrolabij, eandem proportionem habet ſinus totus A F, ad
              <lb/>
            ſinum totum F G, quam ſinus verbi gratia A 50. </s>
            <s xml:id="echoid-s563" xml:space="preserve">ad ſinum arcus circuli, cuius
              <lb/>
            ſemidiameter F G, quiarcus arcuiſinus A 50. </s>
            <s xml:id="echoid-s564" xml:space="preserve">ſimilis eſt. </s>
            <s xml:id="echoid-s565" xml:space="preserve"> Cum ergo ſit, vt A
              <note symbol="a" position="left" xlink:label="note-038-02" xlink:href="note-038-02a" xml:space="preserve">4. ſexti.</note>
            ad F G, ita A 50. </s>
            <s xml:id="echoid-s566" xml:space="preserve">ad rectam 50. </s>
            <s xml:id="echoid-s567" xml:space="preserve">50. </s>
            <s xml:id="echoid-s568" xml:space="preserve">erit recta 50. </s>
            <s xml:id="echoid-s569" xml:space="preserve">50. </s>
            <s xml:id="echoid-s570" xml:space="preserve">ſinus arcus, quiarcuiſinus
              <lb/>
            A 50. </s>
            <s xml:id="echoid-s571" xml:space="preserve">ſimilis eſt. </s>
            <s xml:id="echoid-s572" xml:space="preserve">Eademqueratio eſt de ſecantibus.</s>
            <s xml:id="echoid-s573" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Quo pacto co-
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          gnoſcatur,
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          quot decimæ
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          in particula
            <lb/>
          cuiuſuis cen-
            <lb/>
          teſimæ partis
            <lb/>
          contineantur.</note>
          <p>
            <s xml:id="echoid-s574" xml:space="preserve">13. </s>
            <s xml:id="echoid-s575" xml:space="preserve">
              <emph style="sc">Vicissim</emph>
            cognoſcemus, quot particulas ex 1000. </s>
            <s xml:id="echoid-s576" xml:space="preserve">quælibet parti-
              <lb/>
            cula vnius partis rectæ A F, complectatur: </s>
            <s xml:id="echoid-s577" xml:space="preserve">hoc ſcilicet modo. </s>
            <s xml:id="echoid-s578" xml:space="preserve">Circino ſuma-
              <lb/>
            tur data particula, vna cum vna parte centeſima, vel duabus, vel tribus, qua-
              <lb/>
            tuorue; </s>
            <s xml:id="echoid-s579" xml:space="preserve">circinuſque decies repetatur in recta A F, diligenterque notetur ſe-
              <lb/>
            gmentum rectæ A F, quod circinus percucurrit. </s>
            <s xml:id="echoid-s580" xml:space="preserve">Nam ſi ex partibus centeſimis
              <lb/>
            in eo ſegmento contentis abijciantur to ties 10. </s>
            <s xml:id="echoid-s581" xml:space="preserve">quot partes vna cum particu-
              <lb/>
            la data ſumptę fuerũt, reliquus numerusindicabit partes decimas vnius cen-
              <lb/>
            teſimæ, hoc eſt, milleſimas in data particula comprehenſas. </s>
            <s xml:id="echoid-s582" xml:space="preserve">Et ſi cumreliqua
              <lb/>
            particula eius ſegmenti (ſi qua forte ſuperſit) ſimiliter agemus, reperiemus
              <lb/>
            partes decimas vnius milleſimæ, hoc eſt, partes {1/10000}. </s>
            <s xml:id="echoid-s583" xml:space="preserve">Et ſi iterum operatio-
              <lb/>
            nemrepetemus, inueniemus partes {1/10000}. </s>
            <s xml:id="echoid-s584" xml:space="preserve">quod quidem ad finem libelli de
              <lb/>
            fabrica, & </s>
            <s xml:id="echoid-s585" xml:space="preserve">vſu inſtrumenti horologiorum demoſtrauimus, eademq; </s>
            <s xml:id="echoid-s586" xml:space="preserve">demon-
              <lb/>
            ſtrationem breuiter capite in ſequenti Num. </s>
            <s xml:id="echoid-s587" xml:space="preserve">14. </s>
            <s xml:id="echoid-s588" xml:space="preserve">repetemus. </s>
            <s xml:id="echoid-s589" xml:space="preserve">Exempli cauſa. </s>
            <s xml:id="echoid-s590" xml:space="preserve">Si
              <lb/>
            particula data cum tribus centeſimis deciesrepetita percurrat partes 37. </s>
            <s xml:id="echoid-s591" xml:space="preserve">abie-
              <lb/>
            ctis 30. </s>
            <s xml:id="echoid-s592" xml:space="preserve">continebunturin data particula {7/10}. </s>
            <s xml:id="echoid-s593" xml:space="preserve">vnius centeſimæ. </s>
            <s xml:id="echoid-s594" xml:space="preserve">Quare ſi ea par-
              <lb/>
            ticula data fuerit V. </s>
            <s xml:id="echoid-s595" xml:space="preserve">g. </s>
            <s xml:id="echoid-s596" xml:space="preserve">poſt vigeſimam partem centeſimam, continebit illud
              <lb/>
            ſegmentum rectæ A F, {207/1000}. </s>
            <s xml:id="echoid-s597" xml:space="preserve">Nam {7/10} vniuscenteſimæ faciunt {7/1000}. </s>
            <s xml:id="echoid-s598" xml:space="preserve">& </s>
            <s xml:id="echoid-s599" xml:space="preserve">20. </s>
            <s xml:id="echoid-s600" xml:space="preserve">cen-
              <lb/>
            teſimæ, ſi ſingulæ in decem particulas congitentur eſſe ſectæ, efficiunt {200/1000}.
              <lb/>
            </s>
            <s xml:id="echoid-s601" xml:space="preserve">quippe cum omnes centum partes æqui valeant 1000. </s>
            <s xml:id="echoid-s602" xml:space="preserve">particulis. </s>
            <s xml:id="echoid-s603" xml:space="preserve">Quod </s>
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