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-div426" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s12146" xml:space="preserve">
              <pb o="181" file="0187" n="187" rhead="OPTICAE LIBER V."/>
            fieri reflexio à duobus punctis arcus interiacentis diametros, aut à tribus.</s>
            <s xml:id="echoid-s12147" xml:space="preserve"> Palàm etiam [per 73.</s>
            <s xml:id="echoid-s12148" xml:space="preserve"> 75
              <lb/>
            n] quòd ab uno tantùm puncto arcus oppoſiti [n d] fiet reflexio.</s>
            <s xml:id="echoid-s12149" xml:space="preserve"> Et
              <lb/>
              <figure xlink:label="fig-0187-01" xlink:href="fig-0187-01a" number="142">
                <variables xml:id="echoid-variables132" xml:space="preserve">f e t b m f a g d n</variables>
              </figure>
            ita in hoc ſitu, aliquando à tribus, aliquando à quatuor punctis fiet
              <lb/>
            reflexio.</s>
            <s xml:id="echoid-s12150" xml:space="preserve"> Si uerò unum punctorum fuerit intra circulũ, aliud in cir-
              <lb/>
            cumferentia, uel extra:</s>
            <s xml:id="echoid-s12151" xml:space="preserve"> ſecabit circulus arcum interiacentem in uni-
              <lb/>
            co puncto:</s>
            <s xml:id="echoid-s12152" xml:space="preserve"> & reſtabit unus arcus tantùm.</s>
            <s xml:id="echoid-s12153" xml:space="preserve"> Et omnes anguli facti in
              <lb/>
            parte illius arcus, incluſa à ſecante circulo:</s>
            <s xml:id="echoid-s12154" xml:space="preserve"> erũt maiores angulo dia-
              <lb/>
            metrorũ [per 22 p 3.</s>
            <s xml:id="echoid-s12155" xml:space="preserve"> 13.</s>
            <s xml:id="echoid-s12156" xml:space="preserve"> 21 p 1.</s>
            <s xml:id="echoid-s12157" xml:space="preserve">] Et poterit fieri reflexio à duobus pun-
              <lb/>
            ctis illius partis, uel ab uno [per 80 n.</s>
            <s xml:id="echoid-s12158" xml:space="preserve">] Omnes uerò anguli alterius
              <lb/>
            partis interiacentis [quæ eſt tl] erunt minores angulo diametro-
              <lb/>
            rum [ut oſtenſum eſt.</s>
            <s xml:id="echoid-s12159" xml:space="preserve">] Et ab uno tantùm pũcto illius partis fiet re-
              <lb/>
            flexio [per 80 n.</s>
            <s xml:id="echoid-s12160" xml:space="preserve">] Etita, cũ ab uno puncto arcus oppoſiti [n d] ſem-
              <lb/>
            per fiat reflexio in hoc ſitu:</s>
            <s xml:id="echoid-s12161" xml:space="preserve"> [per 73.</s>
            <s xml:id="echoid-s12162" xml:space="preserve">75 n] aliquãdo à tribus, aliquan-
              <lb/>
            do à quatuor:</s>
            <s xml:id="echoid-s12163" xml:space="preserve"> & nõ à pluribus poterit eſſe reflexio.</s>
            <s xml:id="echoid-s12164" xml:space="preserve"> Palàm ergo, quòd
              <lb/>
            puncta inæqualis longitudinis à centro, aliquando ab uno puncto
              <lb/>
            tantùm:</s>
            <s xml:id="echoid-s12165" xml:space="preserve"> aliquando à duobus:</s>
            <s xml:id="echoid-s12166" xml:space="preserve"> aliquando à tribus:</s>
            <s xml:id="echoid-s12167" xml:space="preserve"> aliquando à qua-
              <lb/>
            tuor:</s>
            <s xml:id="echoid-s12168" xml:space="preserve"> nunquam à pluribus reflectuntur.</s>
            <s xml:id="echoid-s12169" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div428" type="section" level="0" n="0">
          <head xml:id="echoid-head390" xml:space="preserve" style="it">87. Sirecta linea connectens duo puncta in diuerſis diametris circuli (quieſt communis ſe-
            <lb/>
          ctio ſuperficierum, reflexionis & ſpeculi ſphærici caui) à centro æquabiliter diſtantia, cõtinua-
            <lb/>
          ta eundẽ ſecet: poſſunt dicta puncta ab uno, duobus uel quatuor punctis ſpeculi inter ſe reflecti:
            <lb/>
          nunquam uerò à tribus tantùm. 41 p 8.</head>
          <p>
            <s xml:id="echoid-s12170" xml:space="preserve">CVm autem puncta eiuſdẽ longitudinis fuerint:</s>
            <s xml:id="echoid-s12171" xml:space="preserve"> poterit fieri reflexio aut ab uno tantûm pun
              <lb/>
            cto;</s>
            <s xml:id="echoid-s12172" xml:space="preserve"> [ut oſtenſum eſt 70 n] aut à duobus:</s>
            <s xml:id="echoid-s12173" xml:space="preserve"> [ut 71 n] aut à quatuor:</s>
            <s xml:id="echoid-s12174" xml:space="preserve"> [ut 72 n] nunquam uerò
              <lb/>
            à tribus.</s>
            <s xml:id="echoid-s12175" xml:space="preserve"> [Quia ſi reflexio fiat à tribus punctis, fiet etiam à quatuor.</s>
            <s xml:id="echoid-s12176" xml:space="preserve"> Nam cum è tribus iſtis
              <lb/>
            reflexionum punctis duo in eandẽ peripheriam ca-
              <lb/>
              <figure xlink:label="fig-0187-02" xlink:href="fig-0187-02a" number="143">
                <variables xml:id="echoid-variables133" xml:space="preserve">l m a b g n d</variables>
              </figure>
            dant, ut in præcedentibus numeris patuit:</s>
            <s xml:id="echoid-s12177" xml:space="preserve"> periphe-
              <lb/>
            ria igitur inter duo illa reflexionũ puncta interiecta,
              <lb/>
            per 30 p 3 bifariam ſecta, ductisq́;</s>
            <s xml:id="echoid-s12178" xml:space="preserve"> rectis à centro, &
              <lb/>
            datis punctis, in diuerſis diametris ęquabiliter à cẽ-
              <lb/>
            tro diſtantibus, ad ſectionis punctum:</s>
            <s xml:id="echoid-s12179" xml:space="preserve"> erunt anguli
              <lb/>
            ad ipſum facti æquales per 27 p 3.</s>
            <s xml:id="echoid-s12180" xml:space="preserve"> 4 p 1.</s>
            <s xml:id="echoid-s12181" xml:space="preserve"> Quare ipſum
              <lb/>
            eſt reflexionis punctum per 12 n 4:</s>
            <s xml:id="echoid-s12182" xml:space="preserve"> atqui in periphe-
              <lb/>
            ria priori l m oppoſita, ſcilicet n d, eſt etiam unũ re-
              <lb/>
            flexionis punctũ per 73.</s>
            <s xml:id="echoid-s12183" xml:space="preserve"> 75 n.</s>
            <s xml:id="echoid-s12184" xml:space="preserve"> A
              <gap/>
            quatuor igitur pun-
              <lb/>
            ctis, nõ à tribus tantùm fit reflexio.</s>
            <s xml:id="echoid-s12185" xml:space="preserve">] Vbi ab uno pun
              <lb/>
            cto fit reflexio, una apparet imago:</s>
            <s xml:id="echoid-s12186" xml:space="preserve"> ibi â duobus,
              <lb/>
            duæ:</s>
            <s xml:id="echoid-s12187" xml:space="preserve"> ubi à tribus, tres:</s>
            <s xml:id="echoid-s12188" xml:space="preserve"> ibi à quatuor, quatuor.</s>
            <s xml:id="echoid-s12189" xml:space="preserve"> Siue-
              <lb/>
            rò punctum uiſum & cẽtrum uiſus fuerintin eadem
              <lb/>
            diametro:</s>
            <s xml:id="echoid-s12190" xml:space="preserve"> fiet reflexio à circulo toto:</s>
            <s xml:id="echoid-s12191" xml:space="preserve"> & locus imagi-
              <lb/>
            nis erit cẽtrum uiſus [ut oſtenſum eſt 65 n.</s>
            <s xml:id="echoid-s12192" xml:space="preserve">] Verùm
              <lb/>
            ſi centrum uiſus fuerit in centro ſpeculi:</s>
            <s xml:id="echoid-s12193" xml:space="preserve"> nihil uidet
              <lb/>
            [præter ſe ipſum, ut patuit 44 n 4.</s>
            <s xml:id="echoid-s12194" xml:space="preserve"> 62 n.</s>
            <s xml:id="echoid-s12195" xml:space="preserve">] Si uerò pũ-
              <lb/>
            ctum uiſum fuerit in centro ſpeculi:</s>
            <s xml:id="echoid-s12196" xml:space="preserve"> non uidebitur:</s>
            <s xml:id="echoid-s12197" xml:space="preserve">
              <lb/>
            quoniam forma eius accedet ad ſpeculum ſuper perpendicularem, nec reflecti poterit, niſi ſuper
              <lb/>
            perpendicularem [per 11 n 4.</s>
            <s xml:id="echoid-s12198" xml:space="preserve">] Cum autem centrum uiſus & punctum uiſum fuerint in diuerſis li-
              <lb/>
            neis extra centrum:</s>
            <s xml:id="echoid-s12199" xml:space="preserve"> lineæ illę ad centrum productæ, ſecabunt in diuerſis partibus ex circulo ſphæ-
              <lb/>
            ræ duos arcus:</s>
            <s xml:id="echoid-s12200" xml:space="preserve"> ab uno puncto unius tantùm fiet reflexio:</s>
            <s xml:id="echoid-s12201" xml:space="preserve"> ab alio forſitan à quatuor.</s>
            <s xml:id="echoid-s12202" xml:space="preserve"> Quòd ſi cẽtrum
              <lb/>
            ſphæræ fuerit ex una parte:</s>
            <s xml:id="echoid-s12203" xml:space="preserve"> centrum uiſus & punctum uiſum ex una:</s>
            <s xml:id="echoid-s12204" xml:space="preserve"> arcus, quem ſecant diametri,
              <lb/>
            propter oppoſitionem capitis abſcondetur.</s>
            <s xml:id="echoid-s12205" xml:space="preserve"> Vnde tunc à tribus tantùm punctis fiet reflexio.</s>
            <s xml:id="echoid-s12206" xml:space="preserve"> Et ſi
              <lb/>
            dirigatur in hoc ſitu uiſus ad arcum unius reflexionis tantùm:</s>
            <s xml:id="echoid-s12207" xml:space="preserve"> abſcondetur alius trium reflexionũ,
              <lb/>
            & unica apparebit imago.</s>
            <s xml:id="echoid-s12208" xml:space="preserve"> Item:</s>
            <s xml:id="echoid-s12209" xml:space="preserve"> Si integrum fuerit ſpeculum:</s>
            <s xml:id="echoid-s12210" xml:space="preserve"> nõ erit ibi perceptio:</s>
            <s xml:id="echoid-s12211" xml:space="preserve"> oportet igitur,
              <lb/>
            ut in eo ſit abſciſsio.</s>
            <s xml:id="echoid-s12212" xml:space="preserve"> Et accidet nonnunquam arcum interiacẽtem diametros abſciſſum eſſe:</s>
            <s xml:id="echoid-s12213" xml:space="preserve"> & tunc
              <lb/>
            nihil in eo uideri.</s>
            <s xml:id="echoid-s12214" xml:space="preserve"> Quare rarò eueniet quatuor imagines in hoc ſpeculo comprehendi.</s>
            <s xml:id="echoid-s12215" xml:space="preserve"> Vnde ſi quis
              <lb/>
            hanc pluralitatem imaginum uoluerit uidere:</s>
            <s xml:id="echoid-s12216" xml:space="preserve"> diſponat uiſum intra ſpeculum circa ipſum, ut modi
              <lb/>
            cam partem eius abſcondat mole capitis, & totam ſpeculi ſuperficiem uiſu diſcurrat.</s>
            <s xml:id="echoid-s12217" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div430" type="section" level="0" n="0">
          <head xml:id="echoid-head391" xml:space="preserve" style="it">88. In ſpeculo ſphærico cauo imago eiuſdem uiſibilis utrog uiſu aliâs una, aliâs gemina uide-
            <lb/>
          tur. 59 p 8.</head>
          <p>
            <s xml:id="echoid-s12218" xml:space="preserve">CVm autem aliquid in hoc ſpeculo percipietur duplici uiſu:</s>
            <s xml:id="echoid-s12219" xml:space="preserve"> ſi linea reflexionis fuerit æqui-
              <lb/>
            diſtans perpendiculari:</s>
            <s xml:id="echoid-s12220" xml:space="preserve"> [incidentiæ] erit locus imaginis punctum reflexionis [per 60 n.</s>
            <s xml:id="echoid-s12221" xml:space="preserve">]
              <lb/>
            Et cum diſtant à ſe puncta reflexionis reſpectu duorum uiſuum:</s>
            <s xml:id="echoid-s12222" xml:space="preserve"> apparebũt duobus uiſibus
              <lb/>
            duæ imagines eiuſdem puncti:</s>
            <s xml:id="echoid-s12223" xml:space="preserve"> & locus cuiuſq;</s>
            <s xml:id="echoid-s12224" xml:space="preserve"> imaginis eſt in puncto ſuæ reflexionis.</s>
            <s xml:id="echoid-s12225" xml:space="preserve"> Si uerò linea
              <lb/>
            reflexionis non ſit æquidiſtans perpendiculari:</s>
            <s xml:id="echoid-s12226" xml:space="preserve"> [incidentiæ] & punctum uiſum tantùm diſtet ab
              <lb/>
            </s>
          </p>
        </div>
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    </echo>
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