Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

Page concordance

< >
Scan Original
111 74
112 75
113 76
114 77
115 78
116 79
117 80
118 81
119 82
120 83
121 84
122 85
123 86
124 87
125 88
126 89
127 90
128 91
129 92
130 93
131 94
132 95
133 96
134 97
135 98
136 99
137 100
138 101
139 102
140 103
< >
page |< < (81) of 525 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div205" type="section" level="1" n="67">
          <p>
            <s xml:id="echoid-s4117" xml:space="preserve">
              <pb o="81" file="117" n="118" rhead="Ioan. de Sacro Boſco."/>
            ra, & </s>
            <s xml:id="echoid-s4118" xml:space="preserve">æquiangula exiſtit, omnium eſſe maximam: </s>
            <s xml:id="echoid-s4119" xml:space="preserve">Eadem enim eſt ratio haben-
              <lb/>
            da de figuris Iſoperimetris, quæ plura latera, pluresq́ue angulos continent.
              <lb/>
            </s>
            <s xml:id="echoid-s4120" xml:space="preserve">Quamobrem, cum circulus infinita propemodum latera æqualia, infinitos
              <lb/>
            quoque angulos quodammodo æquales comprehendat, eo quòd eius circun-
              <lb/>
            ferentia ſemper curuetur æqualiter, efficitur, ut ſit inter omnes figuras Iſope-
              <lb/>
            rimetras capaciſſimus. </s>
            <s xml:id="echoid-s4121" xml:space="preserve">Atque hiſce potiſſimum rationibus nituntur nonnullĩ
              <unsure/>
              <lb/>
            auctores confirmare, circulum eſſe maxime capacem: </s>
            <s xml:id="echoid-s4122" xml:space="preserve">Ex quibus manifeſtum ar
              <lb/>
            bitror relinqui, quidnam ſibi uelit auctor noſter in ſecunda hac ratione de-
              <lb/>
            ſumpta à commoditate, in qua mentionem ſecit figurarum Iſoperimetrarum.</s>
            <s xml:id="echoid-s4123" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4124" xml:space="preserve">
              <emph style="sc">Vervm</emph>
            quoniam prædictæ rationes coniecturæ potius, quàm demonſtra-
              <lb/>
            tiones ſunt appellandæ: </s>
            <s xml:id="echoid-s4125" xml:space="preserve">Neque enim circulus angulos ullos, aut latera conti
              <lb/>
            net, ex quibus componatur, quemadmodum in præfatis rationibus aſſumeba-
              <lb/>
            tur: </s>
            <s xml:id="echoid-s4126" xml:space="preserve">Immo vero, etiamſi & </s>
            <s xml:id="echoid-s4127" xml:space="preserve">angulos, & </s>
            <s xml:id="echoid-s4128" xml:space="preserve">latera haberet propemodum infinita, nõ
              <lb/>
            eſt tamen in uniuerſum demonſtratione confirmatum, eam ſemper figurã, quę
              <lb/>
            plures habet angulos, ſiue latera, atque adeo eam, quæ & </s>
            <s xml:id="echoid-s4129" xml:space="preserve">latera & </s>
            <s xml:id="echoid-s4130" xml:space="preserve">angulos ha-
              <lb/>
            bet æquales, inter iſoperimetras figuras eſſe capaciſſimam; </s>
            <s xml:id="echoid-s4131" xml:space="preserve">ſed hoc tantum oſtẽ
              <lb/>
            ſum eſt in triangulo Iſoſcele, vel Æquilatero, ſi cum parallelogrãmo confe-
              <lb/>
            ratur, & </s>
            <s xml:id="echoid-s4132" xml:space="preserve">in parallelogrammis; </s>
            <s xml:id="echoid-s4133" xml:space="preserve">non autem in figuris, quæ plura continent late-
              <lb/>
            ra. </s>
            <s xml:id="echoid-s4134" xml:space="preserve">Idcirco non abs re me facturum iudicaui, ſi hoc loco interponam tractatio
              <lb/>
            nem perbreuem de figuris Iſoperimetris, in qua euidentiſſime demonſtratur,
              <lb/>
            circulum inter figuras planas iſoperimetras eſſe capaciſſimum; </s>
            <s xml:id="echoid-s4135" xml:space="preserve">Itemq́; </s>
            <s xml:id="echoid-s4136" xml:space="preserve">ſphæ-
              <lb/>
            ram maiorem eſſe omnibus aliis figuris ſolidis ſibi iſoperimetris. </s>
            <s xml:id="echoid-s4137" xml:space="preserve">Quamuis. </s>
            <s xml:id="echoid-s4138" xml:space="preserve">n.
              <lb/>
            </s>
            <s xml:id="echoid-s4139" xml:space="preserve">hæc omnia à Theone quoque in commentarijs, quos in Ptolemæi Almageſtũ
              <lb/>
            compoſuit, Geometrice ſint confir
              <unsure/>
            mata; </s>
            <s xml:id="echoid-s4140" xml:space="preserve">tamen quia non omnibus in promptu
              <lb/>
            habentur eius demonſtrationes, (Græcus enim tantum codex reperitur) & </s>
            <s xml:id="echoid-s4141" xml:space="preserve">
              <lb/>
            obſcure admodum, atque ſuccincte ab eo omnia demonſtrantur; </s>
            <s xml:id="echoid-s4142" xml:space="preserve">deo cona-
              <lb/>
            bor, quoad eius fieri poterit, aliquam lucem hiſce demonſtrationibus afferre,
              <lb/>
            vt uel illis ſatisfeciſſe videamur, qui plurimum demonſtrationibus Geometri-
              <lb/>
            cis delectantur. </s>
            <s xml:id="echoid-s4143" xml:space="preserve">Cæterum licet in hoctractatu ſolum demonſt@etur, ſphæram
              <lb/>
            eſſe maiorem corpore quolibet ſibi Iſoperimetro, in quo ſphæra aliqua deſcri-
              <lb/>
            bi poſſit, & </s>
            <s xml:id="echoid-s4144" xml:space="preserve">quod contineatur uel ſuperficiebus planis, uel conicis, ut ſuo loco
              <lb/>
            apparebit: </s>
            <s xml:id="echoid-s4145" xml:space="preserve">Pappus tamen idem de omnicorpore demonſtrauit 70. </s>
            <s xml:id="echoid-s4146" xml:space="preserve">propoſitio-
              <lb/>
            nibus, quas hoc loco apponere ſuperuacaneum duximus, cum breui, ut ſpero,
              <lb/>
            Pappus ipſe in latinam linguam conuerſus in lucem ſit proditurus.</s>
            <s xml:id="echoid-s4147" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div211" type="section" level="1" n="68">
          <head xml:id="echoid-head72" xml:space="preserve">DE FIGVRIS ISOPERIMETRIS.
            <lb/>
          DEFINITIONES.
            <lb/>
          I.</head>
          <p style="it">
            <s xml:id="echoid-s4148" xml:space="preserve">
              <emph style="sc">TSoperimetrae</emph>
            figurę ſunt, quæ æquales ambitus
              <lb/>
              <note position="right" xlink:label="note-117-01" xlink:href="note-117-01a" xml:space="preserve">Definitio-
                <lb/>
              nes ad tra
                <lb/>
              ctationem-
                <lb/>
              Iſoperime-
                <lb/>
              trarum fi-
                <lb/>
              gurarũ per
                <lb/>
              tinentes.</note>
            continent.</s>
            <s xml:id="echoid-s4149" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div213" type="section" level="1" n="69">
          <head xml:id="echoid-head73" xml:space="preserve">II.</head>
          <p style="it">
            <s xml:id="echoid-s4150" xml:space="preserve">
              <emph style="sc">Regvlaris</emph>
            figura dicitur ea, quæ & </s>
            <s xml:id="echoid-s4151" xml:space="preserve">æquilatera, & </s>
            <s xml:id="echoid-s4152" xml:space="preserve">
              <lb/>
            æquiangula eſt.</s>
            <s xml:id="echoid-s4153" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum