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

Table of figures

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[251] e d a n b g m q t k z h l
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[252] f g k h d c e a b
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[253] h d a m e c k z g b
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[254] n a d p e q o r f k h g b l c m
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[Figure 255]
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[256] b a c d
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[257] a c b d
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[258] c a b d e
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[259] a b c d e f
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[260] a e b f g
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[261] a b c d g c d g f
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[262] a b c d
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[263] a b e c d
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[264] a b c d e f
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[265] a b c d
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[266] a b c d
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[267] a b e c d
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[268] a b e c d
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[269] a b c e d
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[270] a b g d e z
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[271] e a b c d f
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[272] a d e c b
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[273] a c f d b e
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[274] g d a h b c f k
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[275] g d e a z b f c
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[Figure 276]
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[277] a b c d e f
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[278] e a b k l f g h m c d
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[Figure 279]
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[280] a b c e f g h d i
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          <p>
            <s xml:id="echoid-s17222" xml:space="preserve">
              <pb o="245" file="0251" n="251" rhead="OPTICAE LIBER VII."/>
            experiri refractiones lucis de uitro ad aerem, & ad aquam:</s>
            <s xml:id="echoid-s17223" xml:space="preserve"> applicet uitrum è contrario primi ſitus:</s>
            <s xml:id="echoid-s17224" xml:space="preserve">
              <lb/>
            ſcilicet, ut ponat conuexum eius ex parte duorum foraminum, & ponat medium communis diffe-
              <lb/>
            rentiæ, quæ eſt in uitro, ſuper centrum laminæ.</s>
            <s xml:id="echoid-s17225" xml:space="preserve"> Tunc ergo lux, quæ tranſit per centra duorum fora-
              <lb/>
            minum, peruenit rectè ad cẽtrum uitri, & refringitur apud illud de uitro ad aerem.</s>
            <s xml:id="echoid-s17226" xml:space="preserve"> Deinde diuidat
              <lb/>
            arcus ſucceſsiuè, & mutet poſitionem uitri:</s>
            <s xml:id="echoid-s17227" xml:space="preserve"> & ſic habebit angulos refractionũ particulares, & pro-
              <lb/>
            portiones eorum ad angulos, quos continet prima linea, per quam extenditur lux, cum linea per-
              <lb/>
            pendiculari ſuper ſuperficiem contingentẽ ſuperficiem uitri.</s>
            <s xml:id="echoid-s17228" xml:space="preserve"> Et cum experimẽtator expertus fue-
              <lb/>
            rit hos duos prædictos ſitus:</s>
            <s xml:id="echoid-s17229" xml:space="preserve"> uidebit quòd quãtitates angulorum refractionis de aere ad uitrum, &
              <lb/>
            de uitro ad aerem ſemper erunt æquales:</s>
            <s xml:id="echoid-s17230" xml:space="preserve"> cum angulus, quem continet linea, per quam extenditur
              <lb/>
            lux ad locum refractionis cum linea perpendiculari, cum refringitur de aere ad uitrum, æqualis ſit
              <lb/>
            angulo, quem cõtinet linea, per quam extenditur lux à loco refractionis cum perpendiculari, cum
              <lb/>
            reflectitur à uitro ad aerem.</s>
            <s xml:id="echoid-s17231" xml:space="preserve"> Et ſi quis uoluerit experiri quantitates angulorũ refractionis, qui ſunt
              <lb/>
            apud conuexum uitri:</s>
            <s xml:id="echoid-s17232" xml:space="preserve"> diuidat de circumferentia medij circuli ex parte cẽtri foraminis, quod eſt in
              <lb/>
            ora inſtrumenti, arcum, cuius quantitas ſit 10 partium, & extrahat ab extremitate eius perpendicu-
              <lb/>
            larem ſuper ſuperficiem laminæ in ſuperficie oræ inſtrumenti, ſicut prius fecerat:</s>
            <s xml:id="echoid-s17233" xml:space="preserve"> deinde diuidat ex
              <lb/>
            hac linea incipiens à centro laminæ lineam æqualem ſemidiametro uitri, & ab extremitate huius
              <lb/>
            lineæ extrahat perpẽdicularem ſuper diametrum laminæ, ſuper cuius extremitates ſunt duæ lineæ
              <lb/>
            perpendiculares in ora inſtrumenti:</s>
            <s xml:id="echoid-s17234" xml:space="preserve"> & protrahat hãc perpendicularem in utramq;</s>
            <s xml:id="echoid-s17235" xml:space="preserve"> partem:</s>
            <s xml:id="echoid-s17236" xml:space="preserve"> deinde
              <lb/>
            ſuperponat uitrum ſuper ſuperficiẽ laminæ, & ſuper-
              <lb/>
              <figure xlink:label="fig-0251-01" xlink:href="fig-0251-01a" number="215">
                <variables xml:id="echoid-variables202" xml:space="preserve">k n b l
                  <gap/>
                o q f g u z</variables>
              </figure>
            ponat differentiam eius cõmunem prędictæ perpen-
              <lb/>
            diculari, & ponat medium differẽtiæ cõmunis ſuper
              <lb/>
            punctum, à quo extracta fuerit perpendicularis:</s>
            <s xml:id="echoid-s17237" xml:space="preserve"> & ſic
              <lb/>
            erit centrum uitri in ſuperficie medij circuli, & linea,
              <lb/>
            quæ tranſit per centra duorũ foraminum, erit perpen
              <lb/>
            dicularis ſuper ſuperficiẽ uitri æqualẽ:</s>
            <s xml:id="echoid-s17238" xml:space="preserve"> [per 8 p 11] eſt
              <lb/>
            enim æquidiſtans diametro laminæ, quæ eſt perpen-
              <lb/>
            dicularis ſuper illam ſuperficiem & differẽtiam com-
              <lb/>
            munem, quę eſt in uitro:</s>
            <s xml:id="echoid-s17239" xml:space="preserve"> & centrum circuli medij erit
              <lb/>
            in conuexo uitri.</s>
            <s xml:id="echoid-s17240" xml:space="preserve"> Nam linea, quæ exit à centro circuli
              <lb/>
            medij ad cẽtrum laminæ, eſt æqualis lineæ exeunti à
              <lb/>
            centro uitri ad mediũ differentiæ cõmunis:</s>
            <s xml:id="echoid-s17241" xml:space="preserve"> & utraq;</s>
            <s xml:id="echoid-s17242" xml:space="preserve">
              <lb/>
            iſtarum linearũ eſt perpẽdicularis ſuper ſuperficiem
              <lb/>
            laminæ:</s>
            <s xml:id="echoid-s17243" xml:space="preserve"> ergo duæ lineæ ſunt æquales & æquidiſtãtes:</s>
            <s xml:id="echoid-s17244" xml:space="preserve">
              <lb/>
            [per 33 p 1] & linea, quę copulat centrũ ultri cũ centro
              <lb/>
            circuli medij, eſt æqualis lineæ, quę copulat centrũ la-
              <lb/>
            minæ, & mediũ differentiæ cõmunis, quæ eſt in uitro:</s>
            <s xml:id="echoid-s17245" xml:space="preserve">
              <lb/>
            hæc autem linea æqualis poſita fuit ſemidiametro uitri.</s>
            <s xml:id="echoid-s17246" xml:space="preserve"> Centrum ergo medij circuli eſt in conuexo
              <lb/>
            uitri.</s>
            <s xml:id="echoid-s17247" xml:space="preserve"> Linea ergo, quę tranſit per centra duorum foraminum, quæ tranſit per medij circuli centrum,
              <lb/>
            tenet cum linea, exeunte à centro uitri, angulum æqualem angulo, qui eſt apud centrũ laminæ.</s>
            <s xml:id="echoid-s17248" xml:space="preserve"> Ex-
              <lb/>
            tendantur ergo duæ lineæ in imaginatione rectè in utramq;</s>
            <s xml:id="echoid-s17249" xml:space="preserve"> partẽ, ſcilicet diameter prædicta uitri,
              <lb/>
            & linea, quæ tranſit per centra duorum foraminum:</s>
            <s xml:id="echoid-s17250" xml:space="preserve"> peruenient ergo ad circumferẽtiam medij cir-
              <lb/>
            culi:</s>
            <s xml:id="echoid-s17251" xml:space="preserve"> ſunt enim ambæ in ſuperficie medij circuli.</s>
            <s xml:id="echoid-s17252" xml:space="preserve"> Ergo duę lineæ diuident à circũferentia medij cir-
              <lb/>
            culi ex utraq;</s>
            <s xml:id="echoid-s17253" xml:space="preserve"> parte arcum, cuius quantitas eſt 10 partium:</s>
            <s xml:id="echoid-s17254" xml:space="preserve"> & extremitates lineæ, quę tranſit per cen
              <lb/>
            tra duorũ foraminum, ſunt notæ:</s>
            <s xml:id="echoid-s17255" xml:space="preserve"> altera enim earũ eſt centrum foraminis, & altera punctũ oppoſi-
              <lb/>
            tum centro foraminis:</s>
            <s xml:id="echoid-s17256" xml:space="preserve"> & altera duarũ extremitatum lineæ, quę tranſit per centrũ uitri, eſt extremi-
              <lb/>
            tas arcus, quẽ ſeparauerat à circũferentia medij circuli, qui diſtat à cẽtro foraminis 10 partibus:</s>
            <s xml:id="echoid-s17257" xml:space="preserve"> re-
              <lb/>
            liqua ergo extremitas lineæ, quę tranſit per centrũ uitri, diſtat à linea, quę tranſit per centra duorũ
              <lb/>
            foraminũ, decẽ partibus in parte oppoſita primo ſigno.</s>
            <s xml:id="echoid-s17258" xml:space="preserve"> Signemus ergo extremitatẽ huius diame-
              <lb/>
            tri, & extremitatẽ lineæ, quę tranſit per centra duorũ foraminum, quoniã locus iſte eſt notus:</s>
            <s xml:id="echoid-s17259" xml:space="preserve"> quia
              <lb/>
            eſt ſuper lineã perpendicularem in ora inſtrumenti:</s>
            <s xml:id="echoid-s17260" xml:space="preserve"> & intueatur experimentator ſignũ:</s>
            <s xml:id="echoid-s17261" xml:space="preserve"> & inueniet
              <lb/>
            illud remotius ab extremitate lineæ, quæ tranſit per centra duorũ foraminum.</s>
            <s xml:id="echoid-s17262" xml:space="preserve"> Hæc ergo refractio
              <lb/>
            eſt ad partem contrariam perpendiculari à loco refractionis:</s>
            <s xml:id="echoid-s17263" xml:space="preserve"> quia perpẽdicularis exiens à loco re-
              <lb/>
            fractionis, eſt linea, quæ tranſit per centrũ uitri:</s>
            <s xml:id="echoid-s17264" xml:space="preserve"> & arcus circumferentiæ medij circuli, qui eſt inter
              <lb/>
            cẽtrum lucis & extremitatem lineæ, quę tranſit per centra duorũ foraminum, eſt quantitas anguli
              <lb/>
            refractionis:</s>
            <s xml:id="echoid-s17265" xml:space="preserve"> angulus enim refractionis eſt apud centrum medij circuli.</s>
            <s xml:id="echoid-s17266" xml:space="preserve"> Lux enim extenditur ſuper
              <lb/>
            lineam tranſeuntem per centra duorum foraminum rectè, donec perueniat ad conuexum uitri &
              <lb/>
            ſphęricum.</s>
            <s xml:id="echoid-s17267" xml:space="preserve"> Angulus ergo refractionis erit apud centrũ circuli medij, qui eſt ſuper conuexum uitri:</s>
            <s xml:id="echoid-s17268" xml:space="preserve">
              <lb/>
            & arcus, qui eſt inter cẽtrum lucis & extremitatem lineæ, quę tranſit per centra duorũ foraminum,
              <lb/>
            eſt ille, qui chordat angulũ refractionis, qui eſt 10 partium.</s>
            <s xml:id="echoid-s17269" xml:space="preserve"> Deinde oportet experimentatorẽ euel-
              <lb/>
            lere uitrum, & diuidere à centro foraminis arcum, qui ſit 20 partium, & procedat ut prius:</s>
            <s xml:id="echoid-s17270" xml:space="preserve"> & ſic ha-
              <lb/>
            bebit quantitatẽ anguli refractionis differentem à quantitate anguli, qui eſt 20 partium.</s>
            <s xml:id="echoid-s17271" xml:space="preserve"> Et ſic diui-
              <lb/>
            dat alios arcus ſucceſsiuè:</s>
            <s xml:id="echoid-s17272" xml:space="preserve"> & experiatur refractiones eorum ſicut in primis:</s>
            <s xml:id="echoid-s17273" xml:space="preserve"> & habebit quantitates
              <lb/>
            angulorum refractionis, qui ſunt apud conuexum uitri.</s>
            <s xml:id="echoid-s17274" xml:space="preserve"> Et eædem ſunt quantitates angulorum re.</s>
            <s xml:id="echoid-s17275" xml:space="preserve">
              <lb/>
            fractionis lucis de aere ad uitrum:</s>
            <s xml:id="echoid-s17276" xml:space="preserve"> hoc enim declaratum eſt in prædictis experimentationibus:</s>
            <s xml:id="echoid-s17277" xml:space="preserve"> ſed
              <lb/>
            </s>
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