Clavius, Christoph, Geometria practica

Table of Notes

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            <s xml:id="echoid-s865" xml:space="preserve">20. </s>
            <s xml:id="echoid-s866" xml:space="preserve">
              <emph style="sc">Non</emph>
            aliter reperiemus in diametro Aſtrolabij (quod notatu di-
              <lb/>
              <note position="right" xlink:label="note-041-01" xlink:href="note-041-01a" xml:space="preserve">Quo pacto in
                <lb/>
              diametro A-
                <lb/>
              ſtrolabij pun-
                <lb/>
              ctum cuiuſuis
                <lb/>
              declinationis
                <lb/>
              reperiatur.</note>
            gnum eſt) punctum cuiuſcunque declinationis. </s>
            <s xml:id="echoid-s867" xml:space="preserve">Poſito enim ſinu toto ſemi-
              <lb/>
            diametro Aequatoris, ſi declinatio eſt Borealis, tranferenda eſt in diametrum
              <lb/>
            ex centro Tangens ſemiſsis complementi declinationis: </s>
            <s xml:id="echoid-s868" xml:space="preserve">ſi vero auſtralis eſt,
              <lb/>
            Tangens ſemiſsis arcus ex quadrante, & </s>
            <s xml:id="echoid-s869" xml:space="preserve">declinatione compoſiti. </s>
            <s xml:id="echoid-s870" xml:space="preserve">Vt Tan-
              <lb/>
            gens grad. </s>
            <s xml:id="echoid-s871" xml:space="preserve">33. </s>
            <s xml:id="echoid-s872" xml:space="preserve">min. </s>
            <s xml:id="echoid-s873" xml:space="preserve">15. </s>
            <s xml:id="echoid-s874" xml:space="preserve">qui ſemiſſem complementi declinationis ♋. </s>
            <s xml:id="echoid-s875" xml:space="preserve">conſtitu-
              <lb/>
            unt, dabit punctumextremum ſemidiametri paralleli ♋, quod videlicet ab
              <lb/>
            Aequatore in Boream grad. </s>
            <s xml:id="echoid-s876" xml:space="preserve">23. </s>
            <s xml:id="echoid-s877" xml:space="preserve">min. </s>
            <s xml:id="echoid-s878" xml:space="preserve">30. </s>
            <s xml:id="echoid-s879" xml:space="preserve">declinat. </s>
            <s xml:id="echoid-s880" xml:space="preserve">Tangens vero grad. </s>
            <s xml:id="echoid-s881" xml:space="preserve">56.
              <lb/>
            </s>
            <s xml:id="echoid-s882" xml:space="preserve">min. </s>
            <s xml:id="echoid-s883" xml:space="preserve">45. </s>
            <s xml:id="echoid-s884" xml:space="preserve">qui ſemiſſem conſtituunt arcus ex quadrante, & </s>
            <s xml:id="echoid-s885" xml:space="preserve">declinatione ♑, cõ-
              <lb/>
            flati, dabit extremum punctum ſemidiametri paralleli ♑, quod ab Aequatore
              <lb/>
            in Auſtrum grad. </s>
            <s xml:id="echoid-s886" xml:space="preserve">23. </s>
            <s xml:id="echoid-s887" xml:space="preserve">min. </s>
            <s xml:id="echoid-s888" xml:space="preserve">30. </s>
            <s xml:id="echoid-s889" xml:space="preserve">recedit. </s>
            <s xml:id="echoid-s890" xml:space="preserve">Ratio huiuſcerei eſt, quod recta in A-
              <lb/>
            ſtrolabio ab extremitate diametri rectum Horizontem referẽtis vſque ad in-
              <lb/>
            terſectionem paralleli borealis cum altera diametro Meridianum repræſen-
              <lb/>
            tãte ducta conſtituit cũ altera diametro angulũ ſemiſsis complementi decli-
              <lb/>
            nationis borealis; </s>
            <s xml:id="echoid-s891" xml:space="preserve">ad interſectionem vero paralleli auſtralis cum eadem po-
              <lb/>
            ſteriore diametro educta effi cit angulum ſemiſsis arcus ex quadrante, & </s>
            <s xml:id="echoid-s892" xml:space="preserve">de-
              <lb/>
            clinatione auſtrali conflati: </s>
            <s xml:id="echoid-s893" xml:space="preserve">atque vtriuslibet anguli Tangens ſemidiameter
              <lb/>
            eſt paralleli, vt ex Aſtrolabio liquet.</s>
            <s xml:id="echoid-s894" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s895" xml:space="preserve">
              <emph style="sc">Eodemqve</emph>
            modo, ſi conſtiterit, quem angulum in extremitate ſemi-
              <lb/>
            diametri Aequatoris in Aſtrolabio recta ad quodcunque punctum diametri,
              <lb/>
            quæ ad illam ſemidiametrum perpendicularis eſt, ducta conſtituat, reperie-
              <lb/>
            mus punctum illud per Tangentem illius anguli, ſicut in parallelis ♋, & </s>
            <s xml:id="echoid-s896" xml:space="preserve">♑.
              <lb/>
            </s>
            <s xml:id="echoid-s897" xml:space="preserve">factum eſt.</s>
            <s xml:id="echoid-s898" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s899" xml:space="preserve">21. </s>
            <s xml:id="echoid-s900" xml:space="preserve">
              <emph style="sc">Si</emph>
            etiam quæcunque linea ex centro inſtrumenti huius egrediens
              <lb/>
              <note position="right" xlink:label="note-041-02" xlink:href="note-041-02a" xml:space="preserve">Præceptum
                <lb/>
              generale ad
                <lb/>
              diuidendam
                <lb/>
              lineam datã,
                <lb/>
              vt alia quæ-
                <lb/>
              cunque diui-
                <lb/>
              ſaest.</note>
            ſecetur quomo do cunque, vt verbi gratia extrema, & </s>
            <s xml:id="echoid-s901" xml:space="preserve">media ratione, vel
              <lb/>
            (quod operæ pretium eſſet, vt expeditius horologia deſcribantur) ſicutæ-
              <lb/>
            quinoctialis linea in horologio horizontali diuiſa eſt: </s>
            <s xml:id="echoid-s902" xml:space="preserve">ſecabitur quæuis alia ſi-
              <lb/>
            militer, ſi nimirum ei æquale interuallum F G, ſumatur, vt ex dictis liquido
              <lb/>
            conſtat. </s>
            <s xml:id="echoid-s903" xml:space="preserve">Satis tamen eſt, ſi horæ ex vna parte lineę meridianæ, nimirum vel
              <lb/>
            horæ antemeridianæ, vel pomeridianæ duntaxat in inſtrumentum transfe-
              <lb/>
            rantur.</s>
            <s xml:id="echoid-s904" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s905" xml:space="preserve">22. </s>
            <s xml:id="echoid-s906" xml:space="preserve">
              <emph style="sc">Præterea</emph>
            aperto inſtrumento quomodocunque, cognoſcemus
              <lb/>
              <note position="right" xlink:label="note-041-03" xlink:href="note-041-03a" xml:space="preserve">Qua ratione
                <lb/>
              quantitas an-
                <lb/>
              guli quem la-
                <lb/>
              tera inſtru-
                <lb/>
              menti conti-
                <lb/>
              nent cogno-
                <lb/>
              ſcatur.</note>
            quantitatem anguli F A G, in centro A, conſtituti, hoc modo. </s>
            <s xml:id="echoid-s907" xml:space="preserve">Circino ſuma-
              <lb/>
            tur interualluminter gradus 60. </s>
            <s xml:id="echoid-s908" xml:space="preserve">& </s>
            <s xml:id="echoid-s909" xml:space="preserve">60. </s>
            <s xml:id="echoid-s910" xml:space="preserve">in poſteriore inſtrumenti facie, tranſ-
              <lb/>
            feraturque ex centro in alterutram lineam chordarum. </s>
            <s xml:id="echoid-s911" xml:space="preserve">Nam quot gradus in
              <lb/>
            co interuallo includuntur, tot gradus continebit angulus F A G. </s>
            <s xml:id="echoid-s912" xml:space="preserve">Ratio eſt,
              <lb/>
            quòd arcus ex centro A, per gradus 60. </s>
            <s xml:id="echoid-s913" xml:space="preserve">& </s>
            <s xml:id="echoid-s914" xml:space="preserve">60. </s>
            <s xml:id="echoid-s915" xml:space="preserve">deſcriptus portio eſt quadran-
              <lb/>
            tis, cuius chorda eſt tota linea A F: </s>
            <s xml:id="echoid-s916" xml:space="preserve">propterea quod corda 60. </s>
            <s xml:id="echoid-s917" xml:space="preserve">graduum ſe-
              <lb/>
            midiameter eſt quadrantis dicti, cuius chorda eſt A F, vt ex inſtrumenti con-
              <lb/>
            ſtructione manifeſtum eſt. </s>
            <s xml:id="echoid-s918" xml:space="preserve">Igitur interuallum inter gr. </s>
            <s xml:id="echoid-s919" xml:space="preserve">60. </s>
            <s xml:id="echoid-s920" xml:space="preserve">& </s>
            <s xml:id="echoid-s921" xml:space="preserve">60. </s>
            <s xml:id="echoid-s922" xml:space="preserve">eſt chorda
              <lb/>
            anguli F A G, propoſiti, &</s>
            <s xml:id="echoid-s923" xml:space="preserve">c.</s>
            <s xml:id="echoid-s924" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s925" xml:space="preserve">23. </s>
            <s xml:id="echoid-s926" xml:space="preserve">
              <emph style="sc">Sed</emph>
            neque hoc omittendum eſt, (quando quidem de Tangentibus,
              <lb/>
              <note position="right" xlink:label="note-041-04" xlink:href="note-041-04a" xml:space="preserve">Quandoſinus
                <lb/>
              tot{us} tam par-
                <lb/>
              u@@ eſt, vt in
                <lb/>
              inſtrumen-
                <lb/>
              tum tranſ-</note>
            ſinubus, & </s>
            <s xml:id="echoid-s927" xml:space="preserve">ſecantibus in hoc inſtrumento reſpectu datiſinus totius accipi-
              <lb/>
            endis verba fecimus) ſinum totum interdum eſſe tam exiguum, vt ex F, in G,
              <lb/>
            transferri nequeat, etiamſi inſtrumẽtum prorſus claudatur. </s>
            <s xml:id="echoid-s928" xml:space="preserve">Vt ergo reſpectu
              <lb/>
            illius ſinus totius Tangens, ſinus, ac ſecantes accipere poſsimus ex </s>
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