Ibn-al-Haitam, al-Hasan Ibn-al-Hasan; Witelo; Risner, Friedrich, Opticae thesavrvs Alhazeni Arabis libri septem, nunc primùm editi. Eivsdem liber De Crepvscvlis & Nubium ascensionibus. Item Vitellonis Thuvringopoloni Libri X. Omnes instaurati, figuris illustrati & aucti, adiectis etiam in Alhazenum commentarijs, a Federico Risnero, 1572

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        <div xml:id="echoid-div652" type="section" level="0" n="0">
          <head xml:id="echoid-head571" xml:space="preserve">VITELLONIS FI-
            <lb/>
          LII THVRINGORVM ET PO-
            <lb/>
          LONORVM OPTICAE LIBER PRIMVS.</head>
          <head xml:id="echoid-head572" xml:space="preserve" style="it">DEFINITIONES.</head>
          <p>
            <s xml:id="echoid-s20415" xml:space="preserve">OVAE uerò per modum principiorum huic primo libro præ-
              <lb/>
            mittimus, ſuntiſta.</s>
            <s xml:id="echoid-s20416" xml:space="preserve"> 1.</s>
            <s xml:id="echoid-s20417" xml:space="preserve"> Cathetum dicimus lineam perpendi-
              <lb/>
            cularẽ ſuper ſuperficiem aliquam, erctam.</s>
            <s xml:id="echoid-s20418" xml:space="preserve"> 2.</s>
            <s xml:id="echoid-s20419" xml:space="preserve"> Polum dicimus
              <lb/>
            omnem punctum lineæ ſuper ſuperficiem circuli à centro or-
              <lb/>
            thogonaliter erectæ.</s>
            <s xml:id="echoid-s20420" xml:space="preserve"> 3.</s>
            <s xml:id="echoid-s20421" xml:space="preserve"> Conuexam lineam uel ſuperficiem di-
              <lb/>
            cimus, quæ extrinſecus aliquam regularem curuitatem habet.</s>
            <s xml:id="echoid-s20422" xml:space="preserve">
              <lb/>
            4.</s>
            <s xml:id="echoid-s20423" xml:space="preserve"> Lineam cõcauam uel ſuperficiem dicimus, quæ intrinſecus
              <lb/>
            aliquam regularem curuitatem habet.</s>
            <s xml:id="echoid-s20424" xml:space="preserve"> 5.</s>
            <s xml:id="echoid-s20425" xml:space="preserve"> Lineam ſuper ſuperficiem conuexam uel
              <lb/>
            concauam perpendicularem dicimus, quæ ſuper planam ſuperficiẽ in puncto ſuæ
              <lb/>
            incidentiæ ſuperficiem conuexam uel concauam contingentem eſt erecta.</s>
            <s xml:id="echoid-s20426" xml:space="preserve"> 6.</s>
            <s xml:id="echoid-s20427" xml:space="preserve"> Cir-
              <lb/>
            culi ſeinuicem ſecantes dicuntur, quorum diametris eſt aliqua linea communis, u-
              <lb/>
            no reliquum non continente.</s>
            <s xml:id="echoid-s20428" xml:space="preserve"> 7.</s>
            <s xml:id="echoid-s20429" xml:space="preserve"> Circulus magnus ſphęræ dicitur, qui tranſiens cen
              <lb/>
            trum ſphæræ, diuiditipſam in duo æqualia.</s>
            <s xml:id="echoid-s20430" xml:space="preserve"> 8.</s>
            <s xml:id="echoid-s20431" xml:space="preserve"> Minor uerò circulus ſphæræ dicitur,
              <lb/>
            qui neque tranſit centrum ſphæræ, neque diuiditipſam in duo æqualia.</s>
            <s xml:id="echoid-s20432" xml:space="preserve"> 9.</s>
            <s xml:id="echoid-s20433" xml:space="preserve"> Sphæras
              <lb/>
            æquales dicimus, quarum diametri ſunt æquales.</s>
            <s xml:id="echoid-s20434" xml:space="preserve"> 10.</s>
            <s xml:id="echoid-s20435" xml:space="preserve"> Sphæras uel circulos ſeinui-
              <lb/>
            cem continentes, ęquidiſtantes dicimus, inter quas à centro maioris ductæ lineæ
              <lb/>
            à conuexo minoris ad concauum maioris ſunt æquales.</s>
            <s xml:id="echoid-s20436" xml:space="preserve"> 11.</s>
            <s xml:id="echoid-s20437" xml:space="preserve"> Sphæras ſe inuicem cõ
              <lb/>
            tingentes dicimus, quæ ſe tangentes extrinſecus uelintrinſecus nõ ſecant.</s>
            <s xml:id="echoid-s20438" xml:space="preserve"> 12.</s>
            <s xml:id="echoid-s20439" xml:space="preserve"> Sphę
              <lb/>
            ras ſeinuicem interſecantes dicimus, cùm ſphęris ſe non continentibus, diameter
              <lb/>
            unius per alteram reſecatur.</s>
            <s xml:id="echoid-s20440" xml:space="preserve"> 13.</s>
            <s xml:id="echoid-s20441" xml:space="preserve"> Sphęras intrinſecus ſe interſecantes dicimus, qua-
              <lb/>
            rum maior pars unius in altera continetur.</s>
            <s xml:id="echoid-s20442" xml:space="preserve"> 14.</s>
            <s xml:id="echoid-s20443" xml:space="preserve"> Superficiem planam ſphæram con-
              <lb/>
            tingere dicimus, quæ cum ſphæram tangat, ad omnem partem educta, non ſecat.</s>
            <s xml:id="echoid-s20444" xml:space="preserve">
              <lb/>
            15.</s>
            <s xml:id="echoid-s20445" xml:space="preserve"> Denominatio proportionis primi ad ſecundum, dicitur quantitas, quę ducta in
              <lb/>
            minorem producit maiorem:</s>
            <s xml:id="echoid-s20446" xml:space="preserve"> uel quæ maiorem diuidit ſecundum minorem.</s>
            <s xml:id="echoid-s20447" xml:space="preserve">
              <lb/>
            16.</s>
            <s xml:id="echoid-s20448" xml:space="preserve"> Proportio dicitur componi ex duabus proportionibus, quando denominatio
              <lb/>
            illius proportionis producitur ex ductu denominationum illarum proportio-
              <lb/>
            num, unius in alteram.</s>
            <s xml:id="echoid-s20449" xml:space="preserve"/>
          </p>
          <figure number="256">
            <variables xml:id="echoid-variables242" xml:space="preserve">b a c d</variables>
          </figure>
        </div>
        <div xml:id="echoid-div653" type="section" level="0" n="0">
          <head xml:id="echoid-head573" xml:space="preserve" style="it">PETITIONES.</head>
          <p>
            <s xml:id="echoid-s20450" xml:space="preserve">Petimus autem hæc.</s>
            <s xml:id="echoid-s20451" xml:space="preserve"> 1.</s>
            <s xml:id="echoid-s20452" xml:space="preserve"> Aequales angulos ſuperidem
              <lb/>
            punctum conſtitutos, æqualem continere diſtantiam æ-
              <lb/>
            qualium linearum:</s>
            <s xml:id="echoid-s20453" xml:space="preserve"> ut ſi anguli a b c, & c b d ſint æquales,
              <lb/>
            & linea a b & b d ſint æquales:</s>
            <s xml:id="echoid-s20454" xml:space="preserve"> tantum diſtabit linea a b à li-
              <lb/>
            nea b c, quãtum linea b d diſtat ab eadem linea b c.</s>
            <s xml:id="echoid-s20455" xml:space="preserve"> 2.</s>
            <s xml:id="echoid-s20456" xml:space="preserve"> Item
              <lb/>
            inter quælibet duo puncta lineam, & inter quaslibet duas
              <lb/>
            lineas ſuperficiem poſſe extendi.</s>
            <s xml:id="echoid-s20457" xml:space="preserve"> 3.</s>
            <s xml:id="echoid-s20458" xml:space="preserve"> Item, cum duæ planæ
              <lb/>
            ſuperficies ſe contingunt, unã ex eis fieri ſuperficiem.</s>
            <s xml:id="echoid-s20459" xml:space="preserve"> 4.</s>
            <s xml:id="echoid-s20460" xml:space="preserve"> I-
              <lb/>
            tem duas planas ſuperficies corpus non includere.</s>
            <s xml:id="echoid-s20461" xml:space="preserve"> 5.</s>
            <s xml:id="echoid-s20462" xml:space="preserve"> Item
              <lb/>
            omnes eaſdem proportiones ex ſimilibus proportioni-
              <lb/>
            bus componi, & in ſimiles proportiones diuidi, & eaſdem habe-
              <lb/>
            re denominationes.</s>
            <s xml:id="echoid-s20463" xml:space="preserve"/>
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