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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[31] a b h c
[32] a d b k ſ c
[33] b ſ a u f d c h n g r k s x q p
[34] f d d e r b g c h i p ſ q s n k
[35] f a r d e b g c h p ſ s n k
[36] ſ g d f h b a
[37] a d f t e b
[38] d b c e f g b d
[39] a f b c d e
[40] a f b c d e g
[41] h t a d ſ s g k b e
[42] a b h e d z
[43] b a g q t d z e h
[44] a g b e d z t q h
[45] b g a t z d h
[46] a h b e g p d z n q
[47] h a b e g p d z n q
[48] a h b e g p f d z n q
[49] x e g k z a d
[50] g m h z p b d a k
[51] t g p b h i z d a k s
[52] g z f h a b d c q e k ſ r
[53] m t n q h b f e z p d a g
[54] b ſ d h f r g z q t e a
[55] a d q c m x b g p o k t f z h
[56] a d k u m r h b g i l f e o z t y
[57] a d u m b g o e q s z h p
[58] a d u m c g b o t q p n z h
[59] b k a p f m e l z g t r o q h n d
[60] b k u a p e g t q n d
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page |< < (123) of 778 > >|
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        <div xml:id="echoid-div266" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s7226" xml:space="preserve">
              <pb o="123" file="0129" n="129" rhead="OPTICAE LIBER IIII."/>
            pyramidis, per punctum illud tranſeuntem [ut antè patuit:</s>
            <s xml:id="echoid-s7227" xml:space="preserve">] ſed linea ab acumine pyramidis intel-
              <lb/>
            lectæ ad punctũ circuli, per quod tranſit illa linea longitudinis, abſq;</s>
            <s xml:id="echoid-s7228" xml:space="preserve"> dubio eſt perpendicularis ſu-
              <lb/>
            per eam.</s>
            <s xml:id="echoid-s7229" xml:space="preserve"> Quare alia angulum tenet acutum cum hac linea, non rectum.</s>
            <s xml:id="echoid-s7230" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0129-01" xlink:href="fig-0129-01a" number="35">
                <variables xml:id="echoid-variables25" xml:space="preserve">f a r d e b g c h p ſ s n k</variables>
              </figure>
            [ſecus tres anguli trianguli rectilinei maiores eſſent duobus rectis cõ-
              <lb/>
            tra 32 p 1:</s>
            <s xml:id="echoid-s7231" xml:space="preserve"> quod tamen abſurdum ex angulis c r i, cir rectis concluſis
              <lb/>
            ſequitur.</s>
            <s xml:id="echoid-s7232" xml:space="preserve">] Si uerò ſuperficies reflexionis ſecet intellectualem pyrami-
              <lb/>
            dem:</s>
            <s xml:id="echoid-s7233" xml:space="preserve"> ſecabit circulum, qui eſt baſis, in duobus punctis.</s>
            <s xml:id="echoid-s7234" xml:space="preserve"> [Quia enim cõ-
              <lb/>
            munis ſectio ellipſis (quæ ex theſi eſt reflexionis ſuperficies) & circuli
              <lb/>
            (qui eſt fictæ pyramidis baſis) eſt linea recta per 3 p 11, duobus punctis
              <lb/>
            terminata:</s>
            <s xml:id="echoid-s7235" xml:space="preserve"> ellipſis igitur ſecat circulũ in duobus punctis, nempe lineæ
              <lb/>
            rectæ terminis.</s>
            <s xml:id="echoid-s7236" xml:space="preserve">] Dico, quòd hæc ſola ſunt puncta in tota ſectione com-
              <lb/>
            muni, à quibus fieri poſsit reflexio in eadẽ ſuperficie.</s>
            <s xml:id="echoid-s7237" xml:space="preserve"> Quoniã ab utroq;</s>
            <s xml:id="echoid-s7238" xml:space="preserve">
              <lb/>
            iſtorum punctorũ linea ducta ad acumen intellectæ pyramidis, eſt per-
              <lb/>
            pendicularis ſuper lineam longitudinis ſuper punctum ſuũ tranſeun-
              <lb/>
            tem.</s>
            <s xml:id="echoid-s7239" xml:space="preserve"> À
              <unsure/>
            quocunq;</s>
            <s xml:id="echoid-s7240" xml:space="preserve"> enim ſectionis puncto alio ducatur linea ad acumen
              <lb/>
            illius pyramidis:</s>
            <s xml:id="echoid-s7241" xml:space="preserve"> tenebit angulum acutum cum linea longitudinis per
              <lb/>
            ipſum tranſeunte, cũ perpendicularis cum eadẽ longitudinis linea an-
              <lb/>
            gulum rectum teneat in circulo.</s>
            <s xml:id="echoid-s7242" xml:space="preserve"> Et lineæ ductæ ab acumine pyramidis
              <lb/>
            intellectæ ad puncta ſectionis, quæ intercidunt inter ſpeculi acumen &
              <lb/>
            circulum:</s>
            <s xml:id="echoid-s7243" xml:space="preserve"> facient angulos obtuſos cum lineis longitudinis uerſus par-
              <lb/>
            tem acuminis pyramιdis totalis:</s>
            <s xml:id="echoid-s7244" xml:space="preserve"> & quæ ducuntur ad puncta inter cir-
              <lb/>
            culum & baſim ſpeculi interiacentia, faciẽt cum linea longitudinis an-
              <lb/>
            gulos acutos ex parte acuminis ſpeculi, obtuſos ex parte baſis.</s>
            <s xml:id="echoid-s7245" xml:space="preserve"> Ergo à nullo iſtorũ punctorum po-
              <lb/>
            teſt fieri reflexio.</s>
            <s xml:id="echoid-s7246" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div268" type="section" level="0" n="0">
          <head xml:id="echoid-head291" xml:space="preserve" style="it">44. Si uiſ{us} fuerit in caua ſpeculi ſphærici ſuperficie: uidebit totam: ſi intra uel extra: aliâs
            <lb/>
          hemiſp hærium, aliâs pl{us}, aliâs min{us}: ſi in centro: ſe ipſum tantùm uidebit. 71. 72 p 4. 4 p 8.</head>
          <p>
            <s xml:id="echoid-s7247" xml:space="preserve">IN ſpeculis ſphæricis concauis ſi uiſus fuerit intra concauitatem ſpeculi:</s>
            <s xml:id="echoid-s7248" xml:space="preserve"> tota ſpeculi ſuperficies
              <lb/>
            apparebit ei:</s>
            <s xml:id="echoid-s7249" xml:space="preserve"> quod ſi extra fuerit:</s>
            <s xml:id="echoid-s7250" xml:space="preserve"> poterit comprehendere portionem eius maiorem medietate,
              <lb/>
            quam ſcilicet fecit circulus ſphæræ, quem contingunt duo radij à centro uiſus ducti:</s>
            <s xml:id="echoid-s7251" xml:space="preserve"> uiſu autem
              <lb/>
            in centro huius ſpeculi exiſtente, non fiet ab aliquo puncto ſpeculi reflexio, niſi in ſe.</s>
            <s xml:id="echoid-s7252" xml:space="preserve"> Quoniã enim
              <lb/>
            quælibet linea à centro ſphæræ ad ſphæram ducta perpendicularis eſt ſuper ſuperficiem, ſphæram
              <lb/>
            in puncto illo tangentem [per 25 n uel 4 th.</s>
            <s xml:id="echoid-s7253" xml:space="preserve"> 1 ſphæricorum:</s>
            <s xml:id="echoid-s7254" xml:space="preserve">] ergo in hoc ſitu non comprehendet
              <lb/>
            uiſus per reflexionem, niſi ſe tantùm [per 11 n.</s>
            <s xml:id="echoid-s7255" xml:space="preserve">]</s>
          </p>
        </div>
        <div xml:id="echoid-div269" type="section" level="0" n="0">
          <head xml:id="echoid-head292" xml:space="preserve" style="it">45. Si uiſ{us} ſit extra centrum ſpeculi ſphærici caui: uiſibile à quolibet ei{us} puncto ad uiſum
            <lb/>
          reflecti poteſt: excepto eo, in quod recta à uiſu per centrum ſpeculi ducta, cadit. 6. 3 p 8.</head>
          <p>
            <s xml:id="echoid-s7256" xml:space="preserve">SI uerò ſtatuatur uiſus extra centrum ſphæræ:</s>
            <s xml:id="echoid-s7257" xml:space="preserve"> poterit fieri reflexio alterius rei uiſibilis à quo-
              <lb/>
            cunq;</s>
            <s xml:id="echoid-s7258" xml:space="preserve"> ſpeculi puncto:</s>
            <s xml:id="echoid-s7259" xml:space="preserve"> præterquam ab eo, in quod cadit diameter, à centro uiſus ad ſphæram
              <lb/>
            per centrum ſphæræ ducta:</s>
            <s xml:id="echoid-s7260" xml:space="preserve"> quoniam diameter cadit ſuper ſuperficiem contingentem ſphæ-
              <lb/>
            ram, orthogonaliter [per 25 n, ideoq́;</s>
            <s xml:id="echoid-s7261" xml:space="preserve"> reflectitur in ſeipſam per 11 n.</s>
            <s xml:id="echoid-s7262" xml:space="preserve">] Sumpto autẽ alio puncto, du-
              <lb/>
            catur ad ipſum diameter à centro ſphæræ, & linea à
              <lb/>
              <figure xlink:label="fig-0129-02" xlink:href="fig-0129-02a" number="36">
                <variables xml:id="echoid-variables26" xml:space="preserve">ſ g d f h b a
                  <gap/>
                </variables>
              </figure>
            centro uiſus.</s>
            <s xml:id="echoid-s7263" xml:space="preserve"> Ex his ergo lineis acutus includetur
              <lb/>
            angulus:</s>
            <s xml:id="echoid-s7264" xml:space="preserve"> quoniam linea uiſualis cadit inter diame-
              <lb/>
            trum & ſuperficiem contingentem punctum, quæ
              <lb/>
            ſcilicet eſt extra ſphæram:</s>
            <s xml:id="echoid-s7265" xml:space="preserve"> & ſiue ſit oculus intra ſpe
              <lb/>
            culum, ſiue extra, cadit uiſualis linea intra ſpecu-
              <lb/>
            lum:</s>
            <s xml:id="echoid-s7266" xml:space="preserve"> quia cadit inter lineas uiſuales contingentes
              <lb/>
            circulum portionis ſphæræ.</s>
            <s xml:id="echoid-s7267" xml:space="preserve"> [Itaq;</s>
            <s xml:id="echoid-s7268" xml:space="preserve"> ſi diameter g b &
              <lb/>
            linea reflexionis g a in peripheriam cõtinuatæ, con-
              <lb/>
            nectantur:</s>
            <s xml:id="echoid-s7269" xml:space="preserve"> erit angulus a g b acutus per 31 p 3.</s>
            <s xml:id="echoid-s7270" xml:space="preserve">32 p 1.</s>
            <s xml:id="echoid-s7271" xml:space="preserve">]
              <lb/>
            Cum igitur diameter angulum rectum teneat cum
              <lb/>
            contingẽte [per 18 p 3:</s>
            <s xml:id="echoid-s7272" xml:space="preserve">] ſecetur ex eo acutus, æqua-
              <lb/>
            lis prædicto in eadem ſuperficie:</s>
            <s xml:id="echoid-s7273" xml:space="preserve"> dico ergo, quòd li-
              <lb/>
            nea reflexionis cadit intra ſpeculum:</s>
            <s xml:id="echoid-s7274" xml:space="preserve"> quoniam com
              <lb/>
            munis linea ſpeculi & ſuperficiei reflexionis, eſt cir-
              <lb/>
            culus, tenens cum diametro angulum acutum ma-
              <lb/>
            iorem omni rectilineo acuto [per 31 p 3.</s>
            <s xml:id="echoid-s7275" xml:space="preserve">] Et in ſin-
              <lb/>
            gulis punctis erit hic modus reflexionis.</s>
            <s xml:id="echoid-s7276" xml:space="preserve"> Palàm ex
              <lb/>
            his, quòd in omni ſuperficie reflexionis erunt centrum uiſus:</s>
            <s xml:id="echoid-s7277" xml:space="preserve"> centrum ſpeculi:</s>
            <s xml:id="echoid-s7278" xml:space="preserve"> punctum reflexio-
              <lb/>
            nis:</s>
            <s xml:id="echoid-s7279" xml:space="preserve"> punctum uiſum:</s>
            <s xml:id="echoid-s7280" xml:space="preserve"> terminus diametri à centro uiſus per centrum ſphæræ ductæ:</s>
            <s xml:id="echoid-s7281" xml:space="preserve"> & quòd com-
              <lb/>
            munis omnium ſuperficierum reflexionis linea cum ſuperficie ſpeculi, eſt circulus:</s>
            <s xml:id="echoid-s7282" xml:space="preserve"> & quòd à quo-
              <lb/>
            libet lineæ communis puncto poteſt fieri in eadem ſuperficie reflexio.</s>
            <s xml:id="echoid-s7283" xml:space="preserve"/>
          </p>
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