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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[141] f e t h k o b m a g n d
[142] f e t b m f a g d n
[143] l m a b g n d
[144] e b g q m d a o z h k
[145] a s c p c f d d e b
[146] e b g q l m d o a z n h k
[147] d z b t m l q r p h k f g e a
[148] s z o r x a h k g m u b d e t l f q p n
[149] a b h
[150] a l c q g d b h
[151] a g e u m q d o n z h p l
[152] a e u g d o p h q n k z i s t f
[153] f f e a z b h d g
[154] a f b m k q n e t h d z
[155] b a e p g d
[156] a b h z e p g d
[157] o z l h m n q t d a b e
[158] z i l m h n t d z a k g y c f b z r s u p a e x
[159] i u r c z h t m g b n q f a
[160] i u r k c z l b d t m g n q f a
[161] l u r c z o d t m g b n k q f a s p x e s
[162] d t e h s n q b l q m f p a g
[163] e c h m z b d a
[164] e n c z b d g a
[165] c h z b d g a
[166] b e a d h z m g
[167] p o b c e l m t n a q k f d g
[168] b d a e h t z g f
[169] e b f a d m h t z g
[170] q e a b d m h z
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          <p>
            <s xml:id="echoid-s17277" xml:space="preserve">
              <pb o="246" file="0252" n="252" rhead="ALHAZEN"/>
            refractio de aere ad uitrũ eſt ad partẽ քpẽdicularis:</s>
            <s xml:id="echoid-s17278" xml:space="preserve"> refractio uerò de uitro ad aerẽ eſt ad partẽ cõtra
              <lb/>
            riam perpẽdiculari.</s>
            <s xml:id="echoid-s17279" xml:space="preserve"> Et ſi quis uoluerit experiri uitrum & aquã, & à cõuexo uitri & à ſuperficie eius
              <lb/>
            æquali, habebit quãtitates angulorũ refractionis de uitro ad aquã:</s>
            <s xml:id="echoid-s17280" xml:space="preserve"> aqua enim ponitur in loco aeris.</s>
            <s xml:id="echoid-s17281" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div568" type="section" level="0" n="0">
          <head xml:id="echoid-head492" xml:space="preserve" style="it">12. Magnitudines angulorum refractionis ab aere uel aqua ad uitrum cauum, & contrà,
            <lb/>
          organo refractionis inueſtigare. 7. 8 p 10.</head>
          <p>
            <s xml:id="echoid-s17282" xml:space="preserve">ET ſi quis uoluerit experiri quãtitates angulorũ refractionis apud concauũ uitri:</s>
            <s xml:id="echoid-s17283" xml:space="preserve"> accipiat ui-
              <lb/>
            trum concauum concauitate columnari in quantitate ſemicolumnę:</s>
            <s xml:id="echoid-s17284" xml:space="preserve"> & ſit figura uniuerſi ui-
              <lb/>
            tri æquidiſtãtium ſuperficierũ:</s>
            <s xml:id="echoid-s17285" xml:space="preserve"> & longitudo eius ſit maior diametro uitri ſphærici uno grano
              <lb/>
            hordei:</s>
            <s xml:id="echoid-s17286" xml:space="preserve"> & latitudo eius ſit ſimiliter:</s>
            <s xml:id="echoid-s17287" xml:space="preserve"> & ſpiſsitudo eius ſit dupla diametri foraminis, quod eſt in ora
              <lb/>
            inſtrumẽti:</s>
            <s xml:id="echoid-s17288" xml:space="preserve"> & concauitas ſit in uno ſuorũ laterum:</s>
            <s xml:id="echoid-s17289" xml:space="preserve"> columnaris ſcilicet in ſuperficie una quadrata:</s>
            <s xml:id="echoid-s17290" xml:space="preserve"> &
              <lb/>
            longitudo columnæ ſit in lõgitudine uitri:</s>
            <s xml:id="echoid-s17291" xml:space="preserve"> & ſemidiameter baſis columnæ ſit in quãtitate ſemidia-
              <lb/>
            metri uitri ſphęrici:</s>
            <s xml:id="echoid-s17292" xml:space="preserve"> & ſint fines uitri lineæ rectę ueriſsimæ.</s>
            <s xml:id="echoid-s17293" xml:space="preserve"> Hoc autẽ inſtrumentum ſic bene poteſt
              <lb/>
            fieri ſuper formam:</s>
            <s xml:id="echoid-s17294" xml:space="preserve"> ita ut forma fiat eadẽ doctrina prædicta, & diſſoluatur uitrũ, & infundatur ſuper
              <lb/>
            formam prædictam.</s>
            <s xml:id="echoid-s17295" xml:space="preserve"> Si ergo experimentator uoluerit experiri refractionem hoc inſtrumẽto:</s>
            <s xml:id="echoid-s17296" xml:space="preserve"> diui-
              <lb/>
            dat de circumferentia medij circuli arcum, cuius quãtitas ſit illa, quam uult experiri, & extrahat ab
              <lb/>
            extremitate arcus perpendicularẽ ſuper ſuperficiẽ laminę, ut prędictũ eſt, & copulet extrem t
              <gap/>
            tem
              <lb/>
            perpendicularis cũ centro laminæ linea recta, quam protrahat in alteram partẽ, & diuidat ex hac li-
              <lb/>
            nea in altera parte, ſcilicet in qua ſunt duo foramina, lineam æqualẽ ſemidiametro baſis columnæ,
              <lb/>
            & extrahat ab extremitate eius perpendicularẽ ſuper diametrũ laminę, & protrahat illã in utramq;</s>
            <s xml:id="echoid-s17297" xml:space="preserve">
              <lb/>
            partem.</s>
            <s xml:id="echoid-s17298" xml:space="preserve"> Deinde ſuperponat uitrum laminę, & ponat dorſum cõcauitatis ex parte duorũ foraminũ,
              <lb/>
            & ſuperponat duas ſuperfluitates, quę ſuperfluunt ſuper diametrũ columnæ, huic perpendiculari,
              <lb/>
            obſeruetq́;</s>
            <s xml:id="echoid-s17299" xml:space="preserve">, ut ſint diſtantiæ duarũ extremitatum diametri baſis cõcauitatis à puncto, à quo exiuit
              <lb/>
            perpendicularis, diſtantiæ æquales.</s>
            <s xml:id="echoid-s17300" xml:space="preserve"> Erit ergo centrũ baſis cõcauitatis columnaris ſuper punctum,
              <lb/>
            à quo exiuit perpendicularis, ſuperq́;</s>
            <s xml:id="echoid-s17301" xml:space="preserve"> punctum, cuius diſtantia à centro laminæ, eſt in quantitate
              <lb/>
            ſemidiametri baſis cõcauitatis.</s>
            <s xml:id="echoid-s17302" xml:space="preserve"> Hoc ſitu obſeruato, applicet uitrum fixa applicatione:</s>
            <s xml:id="echoid-s17303" xml:space="preserve"> & erit ſuper-
              <lb/>
            ficies medij circuli ſecãs foramen columnæ & æqui
              <lb/>
              <figure xlink:label="fig-0252-01" xlink:href="fig-0252-01a" number="216">
                <variables xml:id="echoid-variables203" xml:space="preserve">k n m b l d p o q f g u
                  <gap/>
                </variables>
              </figure>
            diſtans baſi eius:</s>
            <s xml:id="echoid-s17304" xml:space="preserve"> nã baſis eius in hac dιſpoſitione eſt
              <lb/>
            in ſuperficie laminæ.</s>
            <s xml:id="echoid-s17305" xml:space="preserve"> Superficies ergo circuli medij
              <lb/>
            facit in ſuperficie columnari concaua ſemicirculum
              <lb/>
            [per 5 th.</s>
            <s xml:id="echoid-s17306" xml:space="preserve"> cylindricorum Sereni] & eſt diameter hu-
              <lb/>
            ius ſemicirculi æquidiſtans diametro baſis concaui-
              <lb/>
            tatis.</s>
            <s xml:id="echoid-s17307" xml:space="preserve"> Erit ergo linea, quæ egrediturà cẽtro huius ſe-
              <lb/>
            micirculi ad centrum baſis concauitatis, quę eſt per-
              <lb/>
            pendicularis ſuper ſuperficiem laminæ, æqualis per-
              <lb/>
            pendiculari exeunti à cẽtro circuli medij perpendi-
              <lb/>
            culari ſuper ſuperficiem laminę:</s>
            <s xml:id="echoid-s17308" xml:space="preserve"> & perpendicularis,
              <lb/>
            quę exit à centro circuli medij ad cẽtrum laminę, eſt
              <lb/>
            æqualis ſemidiametro baſis colũnæ.</s>
            <s xml:id="echoid-s17309" xml:space="preserve"> Ergo linea, quæ
              <lb/>
            exit à centro circuli medij ad cẽtrum ſemicirculi, qui
              <lb/>
            fit in ſuperficie columnæ, eſt æqualis ſemidiametro
              <lb/>
            huius ſemicirculi [per 33 p 1.</s>
            <s xml:id="echoid-s17310" xml:space="preserve">] Centrum ergo circuli
              <lb/>
            medij eſt in circumferentia ſemicirculi facti:</s>
            <s xml:id="echoid-s17311" xml:space="preserve"> eſt ergo
              <lb/>
            in concauo columnæ.</s>
            <s xml:id="echoid-s17312" xml:space="preserve"> Et quia terminus uitri ſuper-
              <lb/>
            ponitur lineę perpẽdiculari ſuper punctũ laminę:</s>
            <s xml:id="echoid-s17313" xml:space="preserve"> erit diameter laminę perpẽdicularis ſuper ſuper-
              <lb/>
            ficiem uitri æqualem.</s>
            <s xml:id="echoid-s17314" xml:space="preserve"> Nã ſuperficies uitri æquales, ſunt perpẽdiculares inter ſe.</s>
            <s xml:id="echoid-s17315" xml:space="preserve"> Erit ergo linea, quę
              <lb/>
            tranſit per centra duorũ foraminum perpẽdicularis ſuper ſuperficiẽ uitri æqualem, quę eſt in parte
              <lb/>
            conuexa uitri [per 8 p 11] quia eſt æquidiſtans diametro laminę:</s>
            <s xml:id="echoid-s17316" xml:space="preserve"> & hęc ſuperficies uitri æqualis, eſt
              <lb/>
            ex parte foraminum.</s>
            <s xml:id="echoid-s17317" xml:space="preserve"> In hoc ergo ſitu lux, quę extenditur ſuper lineã, quę tranſit per cẽtra duorum
              <lb/>
            foraminũ, extenditur in corpore uitri rectè, donec perueniat ad concauum uitri:</s>
            <s xml:id="echoid-s17318" xml:space="preserve"> & tũc refringitur
              <lb/>
            apud concauum uitri:</s>
            <s xml:id="echoid-s17319" xml:space="preserve"> cum non tranſeat per centrum circuli, qui eſt in concauo uitri:</s>
            <s xml:id="echoid-s17320" xml:space="preserve"> neq;</s>
            <s xml:id="echoid-s17321" xml:space="preserve"> eſt per-
              <lb/>
            pendicularis ſuper concauum uitri:</s>
            <s xml:id="echoid-s17322" xml:space="preserve"> ergo refringitur in concauo uitri:</s>
            <s xml:id="echoid-s17323" xml:space="preserve"> ergo differẽtia cõmunis huic
              <lb/>
            lineæ & concauo uitri eſt centrum circuli medij.</s>
            <s xml:id="echoid-s17324" xml:space="preserve"> Ergo lux, quę extenditur ſuper lineam, quę tranſit
              <lb/>
            per centra duorum foraminũ, refringitur apud centrum medij circuli:</s>
            <s xml:id="echoid-s17325" xml:space="preserve"> ergo arcus, qui eſt inter cen-
              <lb/>
            trum lucis & extremitatem lineæ, quę tranſit per centra duorum foraminum, chordat angulum re-
              <lb/>
            fractionis.</s>
            <s xml:id="echoid-s17326" xml:space="preserve"> Hac igitur uia poſſet quis experiri quantitates angulorum refractionis, qui fiunt in con-
              <lb/>
            cauo uitri, addendo in arcubus parum.</s>
            <s xml:id="echoid-s17327" xml:space="preserve"> Et hæc refractio eſt à uitro concauo ad aerem:</s>
            <s xml:id="echoid-s17328" xml:space="preserve"> & eruntan-
              <lb/>
            guli acquiſiti hac refractione ijdem illis, qui fiunt ex aere ad uitrum in concauo uitri.</s>
            <s xml:id="echoid-s17329" xml:space="preserve"> Declaratum
              <lb/>
            eſt autem paulò antè, quòd angulus refractionis à uitro ad aerem, & ab aere ad uitrum, eſt idem
              <lb/>
            cum angulo, quem continet prima linea, per quam extenditur lux, & perpendicularis exiens à lo-
              <lb/>
            co refractionis.</s>
            <s xml:id="echoid-s17330" xml:space="preserve"> Hac ergo uia poſſet quis habere quantitates angulorum refractionis de aere ad
              <lb/>
            aquam, & de aere ad uitrum, & de uitro ad aerem, & de uitro ad aquam à ſuperficie æquali, & con-
              <lb/>
            caua & conuexa.</s>
            <s xml:id="echoid-s17331" xml:space="preserve"> His ergo angulis experimentatis & proportionibus eorum notis, experimẽtator
              <lb/>
            inueniet duos angulos, quorum utrumq;</s>
            <s xml:id="echoid-s17332" xml:space="preserve"> continet prima linea, per quã extenditur lux, & perpẽdi-
              <lb/>
            </s>
          </p>
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