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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[Figure 211]
[212] a h e d c b k q l g f
[213] a d c g b e f
[214] k n m x b l p f s u z y t
[215] k n b l o q f g u z
[216] k n m b l d p o q f g u
[217] k b d o f u g z r e a
[218] k h b m z d e a t i g
[219] h m k o n q e f p g i
[220] a k h g p d b c l
[221] a p h f l g e o k a n m e z q b
[222] a f h p g o e k d m n c q z b
[223] a f h p l g o e k d b m c q z n
[224] a f l p g e o k d b n m c z
[225] h a b g e f d e z
[226] h a b e d c z
[227] e a b d f c
[228] a r c p e h b z b d
[229] a n r l c x m h e p z g b b f d o k
[230] a l g h e z d k b t
[231] e a g e z b
[232] k o g e c n a d z f h m l p b
[233] e o k a c n g d z h m l p b
[234] a k r q c n g h l m d p z b
[235] ad m g p h l k q bn z c
[236] a d e i f p m h l k b z q o c
[237] a p k d m e l o g h b z c
[238] a q p k d m e g l o b z f c
[239] a d p m h e ſ g o k b n z c
[240] a h m g e n k z b c ſ d
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          <p>
            <s xml:id="echoid-s18086" xml:space="preserve">
              <pb o="260" file="0266" n="266" rhead="ALHAZEN"/>
            parte uiſus:</s>
            <s xml:id="echoid-s18087" xml:space="preserve"> & ſit ſuperficies corporis diaphani, quod eſt ex parte b, ſuperficies circularis cõuexa ex
              <lb/>
            parte uiſus.</s>
            <s xml:id="echoid-s18088" xml:space="preserve"> Ergo ք duo pũcta, a, b tranſit ſuperficies perpendicularis ſuper ſuperficiẽ corporis dia-
              <lb/>
            phani, [per 9 n:</s>
            <s xml:id="echoid-s18089" xml:space="preserve"> quia ſuperficies per a & b educta, eſt ſuperficies refractionis:</s>
            <s xml:id="echoid-s18090" xml:space="preserve">] & non tranſit per illa,
              <lb/>
            ſuperficies perpendicularis ſuper ſuperficiẽ corporis, in qua refringitur forma b ad a, niſi una tan-
              <lb/>
            tùm.</s>
            <s xml:id="echoid-s18091" xml:space="preserve"> Hãc ergo ſuperficiẽ corporis diaphani ſignet circulus c e d:</s>
            <s xml:id="echoid-s18092" xml:space="preserve"> cuius centrum ſit z:</s>
            <s xml:id="echoid-s18093" xml:space="preserve"> & continue-
              <lb/>
            mus a c z d:</s>
            <s xml:id="echoid-s18094" xml:space="preserve"> linea ergo c z d erit perpẽdicularis ſuper ſuperficiẽ corporis diaphani [per 4 th 1 ſphę-
              <lb/>
            ricorum:</s>
            <s xml:id="echoid-s18095" xml:space="preserve"> quia perpendicularis eſt plano tangenti.</s>
            <s xml:id="echoid-s18096" xml:space="preserve">] Punctum autẽ b aut erit extra lineam c d:</s>
            <s xml:id="echoid-s18097" xml:space="preserve"> aut in
              <lb/>
            ipſa.</s>
            <s xml:id="echoid-s18098" xml:space="preserve"> Si igitur b fuerit in linea c d:</s>
            <s xml:id="echoid-s18099" xml:space="preserve"> tunc uiſus a comprehendet b rectè, & ſine refractione [per 13 n.</s>
            <s xml:id="echoid-s18100" xml:space="preserve">]
              <lb/>
            Nam forma, quæ extenditur per lineam c d, extenditur rectè in corpore diaphano, quod eſt ex par-
              <lb/>
            te uiſus:</s>
            <s xml:id="echoid-s18101" xml:space="preserve"> quia linea c d eſt perpendicularis ſuper ſuperficiem corporis diaphani, quod eſt ex parte
              <lb/>
            uiſus.</s>
            <s xml:id="echoid-s18102" xml:space="preserve"> Viſus ergo a comprehendit b in ſuo loco, & rectè.</s>
            <s xml:id="echoid-s18103" xml:space="preserve"> Dico ergo, quòd forma punctib, quod eſt
              <lb/>
            in c d linea, nunquam refringetur ad a.</s>
            <s xml:id="echoid-s18104" xml:space="preserve"> Quoniam punctum b aut
              <lb/>
              <figure xlink:label="fig-0266-01" xlink:href="fig-0266-01a" number="228">
                <variables xml:id="echoid-variables215" xml:space="preserve">a r c p e h b z b d</variables>
              </figure>
            erit in centro:</s>
            <s xml:id="echoid-s18105" xml:space="preserve"> aut extra centrum.</s>
            <s xml:id="echoid-s18106" xml:space="preserve"> Si ergo fuerit in centro:</s>
            <s xml:id="echoid-s18107" xml:space="preserve"> tunc o-
              <lb/>
            mnis linea, per quam extenditur forma b ad circumferẽtiam c e d,
              <lb/>
            extenditur in rectitudine eius in corpore diaphano, quod eſt ex
              <lb/>
            parte uiſus.</s>
            <s xml:id="echoid-s18108" xml:space="preserve"> Nam omnis linea exiens à centro circuli c e d eſt per-
              <lb/>
            pendicularis ſuper ſuperficiem corporis diaphani, [ut oſtenſum
              <lb/>
            eſt 25 n 4:</s>
            <s xml:id="echoid-s18109" xml:space="preserve">] & non exit à centro circuli c e d ad uiſum a linea recta,
              <lb/>
            niſi linea z a.</s>
            <s xml:id="echoid-s18110" xml:space="preserve"> Ergo forma puncti b, quod eſt in centro, non refringi-
              <lb/>
            tur ad a ex circumferentia c e d.</s>
            <s xml:id="echoid-s18111" xml:space="preserve"> Ergo forma b nunquam refringe-
              <lb/>
            tur ad a, ſi b fuerit in centro.</s>
            <s xml:id="echoid-s18112" xml:space="preserve"> Si uerò fuerit extra centrum:</s>
            <s xml:id="echoid-s18113" xml:space="preserve"> aut erit
              <lb/>
            in linea z c, aut in z d:</s>
            <s xml:id="echoid-s18114" xml:space="preserve"> ſit ergo primò in linea z c.</s>
            <s xml:id="echoid-s18115" xml:space="preserve"> Dico, quòd forma b
              <lb/>
            non refringatur ad a.</s>
            <s xml:id="echoid-s18116" xml:space="preserve"> Quod ſi fuerit poſsibile:</s>
            <s xml:id="echoid-s18117" xml:space="preserve"> refringatur ex ipſo
              <lb/>
            e:</s>
            <s xml:id="echoid-s18118" xml:space="preserve"> & continuemus b e:</s>
            <s xml:id="echoid-s18119" xml:space="preserve"> & extrahamus illud ad h:</s>
            <s xml:id="echoid-s18120" xml:space="preserve"> & continuemus
              <lb/>
            z e:</s>
            <s xml:id="echoid-s18121" xml:space="preserve"> & extrahamus ipſam ad p:</s>
            <s xml:id="echoid-s18122" xml:space="preserve"> erit ergo linea z e p perpendicu-
              <lb/>
            laris ſuper ſuperficiem corporis diaphani [per 25 n 4,] quod eſt
              <lb/>
            ex parte uiſus.</s>
            <s xml:id="echoid-s18123" xml:space="preserve"> Forma ergo b, quan do extenditur ad lineam b e, &
              <lb/>
            refringitur in puncto e:</s>
            <s xml:id="echoid-s18124" xml:space="preserve"> tranſit à perpendiculari p e ad partem h
              <lb/>
            contrariam illi, in qua eſt perpendicularis [per 14 n:</s>
            <s xml:id="echoid-s18125" xml:space="preserve">] forma ergo
              <lb/>
            b non perueniet ad a ſecũdum refractionem, ſi b fuerit in linea z c.</s>
            <s xml:id="echoid-s18126" xml:space="preserve">
              <lb/>
            Item ſit b in linea d z.</s>
            <s xml:id="echoid-s18127" xml:space="preserve"> Dico ergo, quòd forma b non refringetur ad
              <lb/>
            a.</s>
            <s xml:id="echoid-s18128" xml:space="preserve"> Quod ſi eſt poſsibile:</s>
            <s xml:id="echoid-s18129" xml:space="preserve"> refringatur ex e:</s>
            <s xml:id="echoid-s18130" xml:space="preserve"> & continuemus b e:</s>
            <s xml:id="echoid-s18131" xml:space="preserve"> & extrahamus b e lineam ad r:</s>
            <s xml:id="echoid-s18132" xml:space="preserve"> & co
              <gap/>
              <lb/>
            tinuemus z e, & extrahamus lineam uſque ad p:</s>
            <s xml:id="echoid-s18133" xml:space="preserve"> & refringatur forma b ad a per lineam e a:</s>
            <s xml:id="echoid-s18134" xml:space="preserve"> Sic ergo
              <lb/>
            angulus r e a erit angulus refractionis:</s>
            <s xml:id="echoid-s18135" xml:space="preserve"> angulus autem r e p erit angulus, quem continet linea, per
              <lb/>
            quam extenditur forma, & perpendicularis exiens à loco refractionis:</s>
            <s xml:id="echoid-s18136" xml:space="preserve"> angulus ergo r e a eſt minor
              <lb/>
            angulo r e p [per 12 n] & linea b z aut eſt minor linea z e, aut æqualis ei:</s>
            <s xml:id="echoid-s18137" xml:space="preserve"> nam b aut eſt inter duo
              <lb/>
            puncta d, z:</s>
            <s xml:id="echoid-s18138" xml:space="preserve"> aut in puncto d:</s>
            <s xml:id="echoid-s18139" xml:space="preserve"> ergo angulus e b z aut eſt maior angulo b e z [per 18 p 1] aut æqualis
              <lb/>
            ei:</s>
            <s xml:id="echoid-s18140" xml:space="preserve"> [per 5 p 1] ſed [per 16 p 1] angulus a e r eſt maior angulo e b z:</s>
            <s xml:id="echoid-s18141" xml:space="preserve"> ergo angulus a e r eſt maior angu
              <lb/>
            lo r e p.</s>
            <s xml:id="echoid-s18142" xml:space="preserve"> [Nam quia a e r maior eſt e b z, qui maior eſt, uel æqualis ipſi b e z:</s>
            <s xml:id="echoid-s18143" xml:space="preserve"> erit etiam maior ipſo
              <lb/>
            b e z:</s>
            <s xml:id="echoid-s18144" xml:space="preserve"> at ipſi b e z æquatur r e p per 15 p 1:</s>
            <s xml:id="echoid-s18145" xml:space="preserve"> quare a e r maior eſt r e p] quo prius erat minor:</s>
            <s xml:id="echoid-s18146" xml:space="preserve"> quod eſt
              <lb/>
            impoſsibile.</s>
            <s xml:id="echoid-s18147" xml:space="preserve"> Ergo forma b non refringetur ad a ex e:</s>
            <s xml:id="echoid-s18148" xml:space="preserve"> nec ex alio puncto circumferentiæ c e d:</s>
            <s xml:id="echoid-s18149" xml:space="preserve"> ne-
              <lb/>
            que ex alia circumferentia circulorum, qui fiunt in ſuperficie corporis diaphani, in quo eſt b.</s>
            <s xml:id="echoid-s18150" xml:space="preserve"> Igitur
              <lb/>
            b exiſtente in linea c d:</s>
            <s xml:id="echoid-s18151" xml:space="preserve"> non comprehendetur ipſum à uiſu per refractionem.</s>
            <s xml:id="echoid-s18152" xml:space="preserve"> Quare non compre-
              <lb/>
            henditur, niſi unum ſolum punctum.</s>
            <s xml:id="echoid-s18153" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div592" type="section" level="0" n="0">
          <head xml:id="echoid-head510" xml:space="preserve" style="it">27. Si communis ſectio ſuperficierum, refractionis & refractiui conuexi denſioris fuerit
            <lb/>
          peripheria: uiſibιle extra perpendicularem à uiſu ſuper refractiuum ductam, ab uno puncto re
            <lb/>
          fringetur, unam́ habebit imaginem, uariè, pro uaria uiſ{us} uel uiſibilis poſitione, ſitam.
            <lb/>
          23 p 10.</head>
          <p>
            <s xml:id="echoid-s18154" xml:space="preserve">ITem:</s>
            <s xml:id="echoid-s18155" xml:space="preserve"> ſit b extra lineam c d:</s>
            <s xml:id="echoid-s18156" xml:space="preserve"> & extrahamus ſuperficiem, in qua eſt perpẽdicularis, & punctum b.</s>
            <s xml:id="echoid-s18157" xml:space="preserve">
              <lb/>
            Hæc ergo ſuperficies erit perpendicularis ſuper ſuperficiem corporis diaphani:</s>
            <s xml:id="echoid-s18158" xml:space="preserve"> [per 9 n:</s>
            <s xml:id="echoid-s18159" xml:space="preserve"> quia
              <lb/>
            planum ductum per perpendicularẽ a c d & uiſibile b, eſt planum refractionis] & punctum b
              <lb/>
            non refringetur ad a, niſi in hac ſuperficie:</s>
            <s xml:id="echoid-s18160" xml:space="preserve"> non enim tranſit per duo puncta a, b ſuperficies perpen-
              <lb/>
            dicularis ſuper ſuperficiem corporis diaphani, niſi illa, quæ tranſit per lineam a d:</s>
            <s xml:id="echoid-s18161" xml:space="preserve"> & non exit ex
              <lb/>
            linea a d ſuperficies, quæ tranſit per b, niſi una tantùm.</s>
            <s xml:id="echoid-s18162" xml:space="preserve"> Hæc ergo ſuperficies ſignet in ſuperficie
              <lb/>
            corporis diaphani circulum c e d:</s>
            <s xml:id="echoid-s18163" xml:space="preserve"> forma ergo b non refringetur ad a, niſi ex circumferentia c e d:</s>
            <s xml:id="echoid-s18164" xml:space="preserve">
              <lb/>
            refringatur ergo ex e.</s>
            <s xml:id="echoid-s18165" xml:space="preserve"> Dico ergo, quòd nõ refringetur ex alio puncto quàm e.</s>
            <s xml:id="echoid-s18166" xml:space="preserve"> Refringatur enim (ſi
              <lb/>
            poſsibile eſt) ex alio puncto:</s>
            <s xml:id="echoid-s18167" xml:space="preserve"> quod, ut dictũ eſt, erit in circũferentia c e d:</s>
            <s xml:id="echoid-s18168" xml:space="preserve"> Sit ergo m:</s>
            <s xml:id="echoid-s18169" xml:space="preserve"> & cõtinuemus
              <lb/>
            lineas b e, e a, b m, m a, z e, z m:</s>
            <s xml:id="echoid-s18170" xml:space="preserve"> & ſecẽt ſe lineæ b m, z e in pũcto g:</s>
            <s xml:id="echoid-s18171" xml:space="preserve"> & extrahamus b e uſq;</s>
            <s xml:id="echoid-s18172" xml:space="preserve"> ad h:</s>
            <s xml:id="echoid-s18173" xml:space="preserve"> & b m
              <lb/>
            ad n:</s>
            <s xml:id="echoid-s18174" xml:space="preserve"> & e z ad p:</s>
            <s xml:id="echoid-s18175" xml:space="preserve"> & z m a d l.</s>
            <s xml:id="echoid-s18176" xml:space="preserve"> Erit ergo angulus h e p ille, quem continet linea, per quam extenditur
              <lb/>
            forma, & perpendicularis exiens à loco refractionis:</s>
            <s xml:id="echoid-s18177" xml:space="preserve"> & angulus h e a erit angulus refractionis:</s>
            <s xml:id="echoid-s18178" xml:space="preserve"> &
              <lb/>
            n m l angulus ille, quem continet linea, per quam extenditur ſorma, & perpendicularis exiens à
              <lb/>
            loco refractionis:</s>
            <s xml:id="echoid-s18179" xml:space="preserve"> & angulus n m a erit angulus refractionis.</s>
            <s xml:id="echoid-s18180" xml:space="preserve"> Angulus igitur h e p aut erit æqua-
              <lb/>
            lis angulo n m l:</s>
            <s xml:id="echoid-s18181" xml:space="preserve"> aut erit minor:</s>
            <s xml:id="echoid-s18182" xml:space="preserve"> aut maior.</s>
            <s xml:id="echoid-s18183" xml:space="preserve"> Si æqualis:</s>
            <s xml:id="echoid-s18184" xml:space="preserve"> angulus h e a, qui eſt angulus refractionis:</s>
            <s xml:id="echoid-s18185" xml:space="preserve">
              <lb/>
            </s>
          </p>
        </div>
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