Clavius, Christoph, Geometria practica

Table of Notes

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            <s xml:id="echoid-s3602" xml:space="preserve">3. </s>
            <s xml:id="echoid-s3603" xml:space="preserve">
              <emph style="sc">Similem</emph>
            tabulam gnomonicam compoſuit quoque Georgius Purba-
              <lb/>
            chius in ſuo quadrato Geometrico, poſito latere partium 1200. </s>
            <s xml:id="echoid-s3604" xml:space="preserve">eamque ad ſe-
              <lb/>
            cunda extendit: </s>
            <s xml:id="echoid-s3605" xml:space="preserve">quod etiam fecit 10. </s>
            <s xml:id="echoid-s3606" xml:space="preserve">Antonius Maginus, conſtituto quadrati
              <lb/>
            latere partium 1000. </s>
            <s xml:id="echoid-s3607" xml:space="preserve">quod quidem ſerius animaduerti. </s>
            <s xml:id="echoid-s3608" xml:space="preserve">Incidi enim caſu quo-
              <lb/>
            dam in eam, cum hanc penè meam abſolueram. </s>
            <s xml:id="echoid-s3609" xml:space="preserve">alio quin in hoc ſupputandi la-
              <lb/>
            bore ſuperſediſſem, tabulamque Magini huc tranſtuliſſem. </s>
            <s xml:id="echoid-s3610" xml:space="preserve">Itaque ſi quis in alti-
              <lb/>
            tudinibus aſtrorũ deſideret etiam ſecunda, petere ea debebit ex Maginitabula:
              <lb/>
            </s>
            <s xml:id="echoid-s3611" xml:space="preserve">
              <handwritten xlink:label="hd-125-1" xlink:href="hd-125-1a" number="54"/>
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            quæ ſanè fideliter, & </s>
            <s xml:id="echoid-s3612" xml:space="preserve">accuratè ab eo ſupputata eſt, vel certè per calculum eadem
              <lb/>
            elicere, vt ſupra Num. </s>
            <s xml:id="echoid-s3613" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3614" xml:space="preserve">docuimus in hoc probl. </s>
            <s xml:id="echoid-s3615" xml:space="preserve">Sed meo iudicio contenti eſ-
              <lb/>
              <note position="right" xlink:label="note-125-01" xlink:href="note-125-01a" xml:space="preserve">Tabulã gno-
                <lb/>
              monicam non
                <lb/>
              eſſe abſolutè
                <lb/>
              neceſſariam.</note>
            ſe poſſumus hac noſtra, quæ ad Minuta ſolum vltra gradus progreditur. </s>
            <s xml:id="echoid-s3616" xml:space="preserve">In
              <lb/>
            qua, ſi eam cumilla Maginiconferre quis volet, deprehendet, in noſtra Minu-
              <lb/>
            tis graduum additum eſſe ſemper vnum minutum, quando in ea reperiuntur
              <lb/>
            plura ſecunda, quam 30. </s>
            <s xml:id="echoid-s3617" xml:space="preserve">Sed vt verum fatear, neque noſtra, nequeilla Magini
              <lb/>
              <note position="right" xlink:label="note-125-02" xlink:href="note-125-02a" xml:space="preserve">Quo pacto
                <lb/>
              part{es} milleſi-
                <lb/>
              mæ lateris</note>
            omnino neceſſaria eſt, cumipſæmet partes milleſimę lateris quadrati, ſi appo-
              <lb/>
              <handwritten xlink:label="hd-125-1" xlink:href="hd-125-1a" number="54"/>
              <handwritten xlink:label="hd-125-1" xlink:href="hd-125-1a" number="55"/>
            nantur duæ cifræ, ſint tangentes altitudinum reſpectu ſinus totius 100.</s>
            <s xml:id="echoid-s3618" xml:space="preserve">000. </s>
            <s xml:id="echoid-s3619" xml:space="preserve">& </s>
            <s xml:id="echoid-s3620" xml:space="preserve">
              <lb/>
            eædem, ſi addantur quatuor cifræ, Tangẽtes eaſdẽ, poſito ſinutoto 10.</s>
            <s xml:id="echoid-s3621" xml:space="preserve">000.</s>
            <s xml:id="echoid-s3622" xml:space="preserve">000
              <lb/>
              <note position="right" xlink:label="note-125-03" xlink:href="note-125-03a" xml:space="preserve">Quadrati of-
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              ferant tangẽ-
                <lb/>
              t{es} poſito ſinu
                <lb/>
              toto 10000.
                <lb/>
              vel
                <lb/>
              100′00000.</note>
            exhibeant: </s>
            <s xml:id="echoid-s3623" xml:space="preserve">ac proinde ex tabula Tangentium altitudines excerpi poſsint cui-
              <lb/>
            cunque partimilleſimæ congruentes, ſi prius ei adiungantur duæ, aut quatuor
              <lb/>
            cifræ, vt ſupra ad finem Num. </s>
            <s xml:id="echoid-s3624" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3625" xml:space="preserve">oſtendimus. </s>
            <s xml:id="echoid-s3626" xml:space="preserve">Quia tamen moleſtia non caret,
              <lb/>
            per Tangentes hac ratione formatas ex tabula Tangentium angulos altitudi-
              <lb/>
            num eruere, quod rarò admodum Tangentes illę in tabula præcisè reperian-
              <lb/>
            tur, ac propterea pro illis accipiendæ ſint vel proximè minores, vel maiores, il-
              <lb/>
              <note position="right" xlink:label="note-125-04" xlink:href="note-125-04a" xml:space="preserve">Non magn{us}
                <lb/>
              error in alti-
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              tudinib{us} cõ-
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              mittitur, etiãſi
                <lb/>
              per integr{as}
                <lb/>
              milleſim{as} ta-
                <lb/>
              bula progre-
                <lb/>
              diatur, & quo
                <lb/>
              pacto error
                <lb/>
              hic corrigen-
                <lb/>
              d{us} ſit.</note>
            læ videlicet, quæ paucioribus vnitatibus ab inuentis differunt: </s>
            <s xml:id="echoid-s3627" xml:space="preserve">non abs re fue-
              <lb/>
            rit, vel tabulam hanc noſtram Gnomonicam, vel illam Magini, ſi ſecunda etiam
              <lb/>
            deſiderentur, adſciſcere.</s>
            <s xml:id="echoid-s3628" xml:space="preserve"/>
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            <s xml:id="echoid-s3629" xml:space="preserve">4. </s>
            <s xml:id="echoid-s3630" xml:space="preserve">
              <emph style="sc">Qva
                <gap/>
              is</emph>
            autem tabula Gnonomica perſolas partes milleſimas inte-
              <lb/>
            gras progrediatur; </s>
            <s xml:id="echoid-s3631" xml:space="preserve">tamen ſi quando ex do ctrina cap. </s>
            <s xml:id="echoid-s3632" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3633" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s3634" xml:space="preserve">14. </s>
            <s xml:id="echoid-s3635" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3636" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3637" xml:space="preserve">tradita
              <lb/>
            vltra milleſimas integras ſuperſit adhuc aliqua particula, non magnus error in
              <lb/>
            altitudinibus aſtrorum obſeruandis committi poteſt. </s>
            <s xml:id="echoid-s3638" xml:space="preserve">Cum enim anguli in ta-
              <lb/>
            bula creſcant ordine per tria duntaxat minuta, vel duo, vel vnum, non fiet er-
              <lb/>
            ror niſi vnius autalterius minuri, etiamſi fractio illa milleſimæ partis negligatur.
              <lb/>
            </s>
            <s xml:id="echoid-s3639" xml:space="preserve">Quod ſi errorem hunc, licet minimum, vitare cupis, conſidera fra ctionem mil-
              <lb/>
            leſimæ, an ſit tertia pars, an ſemiſsis, an verò duæ tertię partes. </s>
            <s xml:id="echoid-s3640" xml:space="preserve">quo diudicio ſen-
              <lb/>
            ſus facilè cognoſces ex particula illa, quæ vltra partes decimas circino percur-
              <lb/>
            ſas ſupereſt. </s>
            <s xml:id="echoid-s3641" xml:space="preserve">Nam vbi anguli in tabula per tria Minuta augentur, addendum
              <lb/>
            erit vnum minutum, vel duo, prout particula illa reliqua fuerit {1/3}. </s>
            <s xml:id="echoid-s3642" xml:space="preserve">vel {2/3}. </s>
            <s xml:id="echoid-s3643" xml:space="preserve">Idem
              <lb/>
            faciendum erit ſi dicta particula fuerit maior, quam {1/3}. </s>
            <s xml:id="echoid-s3644" xml:space="preserve">minortamen, quam ſe-
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            miſsis. </s>
            <s xml:id="echoid-s3645" xml:space="preserve">Tunc enim addendum erit etiam vnum Minutum. </s>
            <s xml:id="echoid-s3646" xml:space="preserve">Item quando parti-
              <lb/>
            cula illa maior fuerit, quam ſemiſsis, addipoſſunt duo minuta. </s>
            <s xml:id="echoid-s3647" xml:space="preserve">At quando an-
              <lb/>
            guli tabulæ augentur per duo Minuta, addendum erit vnum minutum pro ſe-
              <lb/>
            miſſe vnius partis milleſimæ.</s>
            <s xml:id="echoid-s3648" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3649" xml:space="preserve">DISTANTIAM interte, & </s>
            <s xml:id="echoid-s3650" xml:space="preserve">ſignum quodcunque in plano Horizon-
              <lb/>
            tis poſitum, per Quadratum Geometricum inueſtigare.</s>
            <s xml:id="echoid-s3651" xml:space="preserve"/>
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