Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

Table of Notes

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            <s xml:id="echoid-s3663" xml:space="preserve">
              <pb o="71" file="107" n="108" rhead="Ioan. de Sacro Boſco."/>
            nam in Nouilunijs coniunctam cum Sole eum non occultare. </s>
            <s xml:id="echoid-s3664" xml:space="preserve">Præterea ſecun
              <lb/>
            dum Albategnium & </s>
            <s xml:id="echoid-s3665" xml:space="preserve">Tebith, & </s>
            <s xml:id="echoid-s3666" xml:space="preserve">alios Aſtronomos, diameter uiſualis Solis ad
              <lb/>
              <note position="right" xlink:label="note-107-01" xlink:href="note-107-01a" xml:space="preserve">Diametri
                <unsure/>
                <lb/>
              uiſuales a-
                <lb/>
              ſtrorum
                <lb/>
              guid.</note>
            diametrum uiſualem Veneris (ſunt autem uiſuales diametri illorum circulo-
              <lb/>
            ru
              <unsure/>
            m, qui nobis apparent in aſtris) proportionem habet decuplam. </s>
            <s xml:id="echoid-s3667" xml:space="preserve">Vnde iuxta
              <lb/>
            demonſtrationes Geometricas, circulus viſualis Solis ad circulum uiſualem
              <lb/>
            Veneris proportionem habebit centuplam. </s>
            <s xml:id="echoid-s3668" xml:space="preserve">Nam cum circuli eam inter ſe
              <lb/>
            proportionem habeant, quam diametrorum quadrata, proportio autem qua-
              <lb/>
              <note position="right" xlink:label="note-107-02" xlink:href="note-107-02a" xml:space="preserve">2. duod.</note>
            dratorum, quæ deſcribuntur ex diametris circulorum, duplicata ſit illius pro-
              <lb/>
              <note position="right" xlink:label="note-107-03" xlink:href="note-107-03a" xml:space="preserve">20. ſexti.</note>
            portionis, quam habent diametri: </s>
            <s xml:id="echoid-s3669" xml:space="preserve">ſit, ut cum diametr
              <unsure/>
            i uiſuales circulorum So
              <lb/>
            lis, ac Veneris habeant proportionem decuplam, diametrorum quadrata, atque
              <lb/>
            adeo & </s>
            <s xml:id="echoid-s3670" xml:space="preserve">circulij uiſuales, proportionem habeant centuplam: </s>
            <s xml:id="echoid-s3671" xml:space="preserve">Hæc enim illius
              <lb/>
            duplicata eſt, ut in his numeris 1. </s>
            <s xml:id="echoid-s3672" xml:space="preserve">10. </s>
            <s xml:id="echoid-s3673" xml:space="preserve">100. </s>
            <s xml:id="echoid-s3674" xml:space="preserve">qui decuplam proportionem con-
              <lb/>
            tinuam habent, perſpicuum eſt. </s>
            <s xml:id="echoid-s3675" xml:space="preserve">Nam, ut ex defin. </s>
            <s xml:id="echoid-s3676" xml:space="preserve">10. </s>
            <s xml:id="echoid-s3677" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3678" xml:space="preserve">5. </s>
            <s xml:id="echoid-s3679" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s3680" xml:space="preserve">conſtat, quando
              <lb/>
            ſunt tres magnitudines continue proportionales, dicitur tertia ad primam ha-
              <lb/>
            bere proportionem duplicatam illius proportionis, quam ſecunda habet ad pri
              <lb/>
            mam, vel tertia ad ſecundam. </s>
            <s xml:id="echoid-s3681" xml:space="preserve">Cum ergo dicti tres numeri 1. </s>
            <s xml:id="echoid-s3682" xml:space="preserve">10. </s>
            <s xml:id="echoid-s3683" xml:space="preserve">100. </s>
            <s xml:id="echoid-s3684" xml:space="preserve">conti-
              <lb/>
            nuè ſint proportionales in proportione decupla, erit proportio centupla, quã
              <lb/>
            tertius numerus 100. </s>
            <s xml:id="echoid-s3685" xml:space="preserve">ad primum 1. </s>
            <s xml:id="echoid-s3686" xml:space="preserve">hẽt, duplicata proportionis decuplæ, quã
              <lb/>
            hẽt ſecundus numerus 10. </s>
            <s xml:id="echoid-s3687" xml:space="preserve">ad primũ 1. </s>
            <s xml:id="echoid-s3688" xml:space="preserve">uel tertius 100. </s>
            <s xml:id="echoid-s3689" xml:space="preserve">ad ſecundum 10. </s>
            <s xml:id="echoid-s3690" xml:space="preserve">Ex quo
              <lb/>
            f
              <unsure/>
            it, circulum uiſualem Solis ad circulum uiſualem Veneris habere proportio-
              <lb/>
            nem centuplam, cum di
              <unsure/>
            ctorum circulorum diametri decuplam habeant pro-
              <lb/>
            portionem, & </s>
            <s xml:id="echoid-s3691" xml:space="preserve">circuli habeant proportionem duplicatam illius, quam diametri
              <lb/>
            habent, vt dictum eſt. </s>
            <s xml:id="echoid-s3692" xml:space="preserve">Eadem ratione, ſi duorum circulorum diametri habeant
              <lb/>
            proportionem duplam, habebunt ipſi circuli proportionem quadruplam. </s>
            <s xml:id="echoid-s3693" xml:space="preserve">Hæc
              <lb/>
            namque illius duplicata eſt, ut patet in his numeris 1. </s>
            <s xml:id="echoid-s3694" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3695" xml:space="preserve">4. </s>
            <s xml:id="echoid-s3696" xml:space="preserve">continue proportio
              <lb/>
            nalibus in proportione dupla. </s>
            <s xml:id="echoid-s3697" xml:space="preserve">Sic etiam ſi diametri duorum circulorum ha-
              <lb/>
            beant proportionem centuplam, habebunt circuli ipſi proportionem, quam
              <lb/>
            10000. </s>
            <s xml:id="echoid-s3698" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s3699" xml:space="preserve">ut in tribus his numeris 1. </s>
            <s xml:id="echoid-s3700" xml:space="preserve">100. </s>
            <s xml:id="echoid-s3701" xml:space="preserve">10000. </s>
            <s xml:id="echoid-s3702" xml:space="preserve">continuam proportionem
              <lb/>
            centuplam habentibus manifeſtum eſt. </s>
            <s xml:id="echoid-s3703" xml:space="preserve">Hac arte quorumlibet circulorum pro-
              <lb/>
            portionem cognoſcemus, ſi proportio, quam eorum diametri habent, fuerit co-
              <lb/>
            gnita. </s>
            <s xml:id="echoid-s3704" xml:space="preserve">Vt autem facile ſciatur, quænam proportio dicatur alterius proportio
              <lb/>
            nis duplicata, multiplicandus erit denominator proportionis in ſeipſum: </s>
            <s xml:id="echoid-s3705" xml:space="preserve">pro-
              <lb/>
            ducetur enim denominator pro portionis duplicatæ: </s>
            <s xml:id="echoid-s3706" xml:space="preserve">Vt quoniam decuplæ pro
              <lb/>
            portionis denominator eſt 10. </s>
            <s xml:id="echoid-s3707" xml:space="preserve">ſi 10. </s>
            <s xml:id="echoid-s3708" xml:space="preserve">in 10. </s>
            <s xml:id="echoid-s3709" xml:space="preserve">multiplicentur, procreabuntur 100
              <lb/>
            nempe denominator duplicatæ proportionis ipſius decuplæ. </s>
            <s xml:id="echoid-s3710" xml:space="preserve">Eadem ratione
              <lb/>
            duplicata proportio proportionis triplæ, erit noncupla, &</s>
            <s xml:id="echoid-s3711" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3712" xml:space="preserve">qua de re lege ea,
              <lb/>
            quæ in defin. </s>
            <s xml:id="echoid-s3713" xml:space="preserve">10. </s>
            <s xml:id="echoid-s3714" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3715" xml:space="preserve">5. </s>
            <s xml:id="echoid-s3716" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s3717" xml:space="preserve">ſcripſimus. </s>
            <s xml:id="echoid-s3718" xml:space="preserve">Hinc perſpicuum eſt, Venerem nullo
              <lb/>
            modo poſſe Solem obtegere, etiamſi interponatur inter noſtrum aſpectum, & </s>
            <s xml:id="echoid-s3719" xml:space="preserve">
              <lb/>
            Solem: </s>
            <s xml:id="echoid-s3720" xml:space="preserve">quoniam occultabit ſolum centeſimam,
              <unsure/>
            partem ipſius, quæ nullius eſt
              <lb/>
            momenti, & </s>
            <s xml:id="echoid-s3721" xml:space="preserve">uix animaduerti poteſt. </s>
            <s xml:id="echoid-s3722" xml:space="preserve">A fortiori igitur neque Mercurius id ef-
              <lb/>
            ficere poterit, cum eius diameter uiſualis ſit longe minor diametro uiſuali Ve-
              <lb/>
            neris. </s>
            <s xml:id="echoid-s3723" xml:space="preserve">Quòd ſi quis roget, cur igitur Luna e uiſu nobis Solem quandoque eri
              <lb/>
            pit, cum tamen mirum in modum minor ſit Luna ipſo Sole? </s>
            <s xml:id="echoid-s3724" xml:space="preserve">Reſpondendum
              <lb/>
              <note position="right" xlink:label="note-107-04" xlink:href="note-107-04a" xml:space="preserve">Cur Luna
                <lb/>
              Solem in-
                <lb/>
              terdũ ecli-
                <lb/>
              pſet, cũ ta
                <lb/>
              mẽ multo
                <lb/>
              minor ipſo
                <lb/>
              ſit.</note>
            eſt, id euenire ob nimiam vicinitatem Lunæ ad terram, & </s>
            <s xml:id="echoid-s3725" xml:space="preserve">maximam illius di-
              <lb/>
            ſtantiam à Sole. </s>
            <s xml:id="echoid-s3726" xml:space="preserve">Hinc enim efficitur, ut diameter uiſualis Lunæ appar
              <unsure/>
            eat no-
              <lb/>
            bis maior diametro
              <unsure/>
            uiſuali Solis, & </s>
            <s xml:id="echoid-s3727" xml:space="preserve">propterea tota Luna maior conſpiciatur.
              <lb/>
            </s>
            <s xml:id="echoid-s3728" xml:space="preserve">quam Sol. </s>
            <s xml:id="echoid-s3729" xml:space="preserve">Vnde mirum non eſt, quod Luna Solem poſſit contegere aliquan-
              <lb/>
            do, ita ut cerni non poſſit.</s>
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