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

Page concordance

< >
Scan Original
341 39
342 40
343 41
344 42
345 43
346 44
347 45
348 46
349 47
350 48
351 49
352 50
353 51
354 52
355 53
356 54
357 55
358 56
359 57
360 58
361 59
362 60
363 61
364 62
365 63
366 64
367 65
368 66
369 67
370 68
< >
page |< < (149) of 778 > >|
    <echo version="1.0RC">
      <text xml:lang="lat" type="free">
        <div xml:id="echoid-div1155" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s29018" xml:space="preserve">
              <pb o="149" file="0451" n="451" rhead="LIBER QVARTVS"/>
            per 31 p 1.</s>
            <s xml:id="echoid-s29019" xml:space="preserve"> Et quia diameter ſphęrę ex hypotheſi eſt minor quàm linea b g, palàm quoniam lineæ b e
              <lb/>
            & g d ultra diametrum fh concurrent per 16 th.</s>
            <s xml:id="echoid-s29020" xml:space="preserve"> 1 huius concurrant ergo in puncto z.</s>
            <s xml:id="echoid-s29021" xml:space="preserve"> Quia ergo ab
              <lb/>
            uno puncto z ducuntur duę lineę contingentes circulum, ſcilicet e z & z d:</s>
            <s xml:id="echoid-s29022" xml:space="preserve"> palàm, quia portio cir-
              <lb/>
            culi, quæ eſt e c d eſt minor ſemicirculo per 58 th.</s>
            <s xml:id="echoid-s29023" xml:space="preserve"> 1 huius:</s>
            <s xml:id="echoid-s29024" xml:space="preserve"> ergo portio eiuſdem circuli reliqua, quæ
              <lb/>
            eſt e i d eſt m aior ſemicirculo:</s>
            <s xml:id="echoid-s29025" xml:space="preserve"> hęc autem portio eſt illa, quę uidetur.</s>
            <s xml:id="echoid-s29026" xml:space="preserve"> Et quia idem eſt de omnib.</s>
            <s xml:id="echoid-s29027" xml:space="preserve"> cir-
              <lb/>
            culis magnis in tota ſphęra ſignatis:</s>
            <s xml:id="echoid-s29028" xml:space="preserve"> palàm, quia maius hemiſphęrio eſt, qđ de ſuperficie ſphęrica,
              <lb/>
            hypotheſi tali exiſtente, uidetur.</s>
            <s xml:id="echoid-s29029" xml:space="preserve"> Et hoc eſt propoſitum.</s>
            <s xml:id="echoid-s29030" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1156" type="section" level="0" n="0">
          <figure number="498">
            <variables xml:id="echoid-variables478" xml:space="preserve">f a h b y i d e z</variables>
          </figure>
          <head xml:id="echoid-head918" xml:space="preserve" style="it">70. Linea connectens centra amborum uiſuum, ſi diametro ſphæ
            <lb/>
          ræ conuexæ minor fuerit: minus hemiſphærio eſt, quod uidetur. Eu- clides 28 th. opt.</head>
          <p>
            <s xml:id="echoid-s29031" xml:space="preserve">Sit ſphęra data, cuius centrum a:</s>
            <s xml:id="echoid-s29032" xml:space="preserve"> & circuli eius magni diameter ſit
              <lb/>
            f h:</s>
            <s xml:id="echoid-s29033" xml:space="preserve"> ſintq́;</s>
            <s xml:id="echoid-s29034" xml:space="preserve"> centra oculorum d & e:</s>
            <s xml:id="echoid-s29035" xml:space="preserve"> & producatur linea d e, connectens
              <lb/>
            centra oculorum minor exiſtens diametro ſ h:</s>
            <s xml:id="echoid-s29036" xml:space="preserve"> ducanturq́;</s>
            <s xml:id="echoid-s29037" xml:space="preserve"> lineæ illũ
              <lb/>
            circulum cõtingentes, quę ſint d b & e g.</s>
            <s xml:id="echoid-s29038" xml:space="preserve"> Dico, quòd minus hemiſphę
              <lb/>
            rio eſt illud, quod uidetur.</s>
            <s xml:id="echoid-s29039" xml:space="preserve"> Protrahantur enim lineę b d & g e.</s>
            <s xml:id="echoid-s29040" xml:space="preserve"> Et quo-
              <lb/>
            niam linea d e, eſt minor diametro f h, palàm per 16 th.</s>
            <s xml:id="echoid-s29041" xml:space="preserve"> 1 huius, quoniã
              <lb/>
            lineæ b d & g e, concurrent ultra ambos uiſus:</s>
            <s xml:id="echoid-s29042" xml:space="preserve"> ſit ergo concurſus pun
              <lb/>
            ctus z Palàm per 58 th.</s>
            <s xml:id="echoid-s29043" xml:space="preserve"> 1 huius, quoniam cum à puncto z ducãtur duę
              <lb/>
            lineæ unum circulum contingentes, quæ ſunt z b & z g, quòd arcus b
              <lb/>
            i g eſt minor ſemicirculo:</s>
            <s xml:id="echoid-s29044" xml:space="preserve"> minus ergo ſemicirculo b g uidetur ſub ocu
              <lb/>
            lis d & e.</s>
            <s xml:id="echoid-s29045" xml:space="preserve"> Ergo, ut prius, minus hemiſphærio uidebitur ſub oculis d &
              <lb/>
            e.</s>
            <s xml:id="echoid-s29046" xml:space="preserve"> Et hoc eſt, quod proponebatur.</s>
            <s xml:id="echoid-s29047" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1157" type="section" level="0" n="0">
          <head xml:id="echoid-head919" xml:space="preserve" style="it">71. Centro for aminis uueæ in ſuperficie ſphæræ concauæ illumina
            <lb/>
          tæ exiſtente, tota ſphæræ intrinſeca ſuperficies uidetur. Alha-
            <lb/>
          zen 44 n 4.</head>
          <p>
            <s xml:id="echoid-s29048" xml:space="preserve">Eſto centrum ſoraminis uueæ punctus a:</s>
            <s xml:id="echoid-s29049" xml:space="preserve"> & ſit ſphæra data, cuius maior circulus ſit b a g tranſiẽs
              <lb/>
            per centrum a.</s>
            <s xml:id="echoid-s29050" xml:space="preserve"> Patet ergo per 52 huius, quoniam ſic uiſu diſpoſito to-
              <lb/>
            tus circulus b a g poterit uideri.</s>
            <s xml:id="echoid-s29051" xml:space="preserve"> Et quia plurimi circuli magni ſphęræ
              <lb/>
              <figure xlink:label="fig-0451-02" xlink:href="fig-0451-02a" number="499">
                <variables xml:id="echoid-variables479" xml:space="preserve">a b g</variables>
              </figure>
            ſe ſecant ſuper polos ſphęrę, quilibet autem punctus ſphęræ eſt polus
              <lb/>
            ſphæræ:</s>
            <s xml:id="echoid-s29052" xml:space="preserve"> palàm, quia omnes circuli magni ſphærę datę, qui per omnia
              <lb/>
            puncta ſuperficiei ſphęrę imagin ari poſſunt, tranſeuntes ſe interſeca-
              <lb/>
            bunt ſuper punctum a:</s>
            <s xml:id="echoid-s29053" xml:space="preserve"> erit ergo punctum a, quod eſt centrum ſorami
              <lb/>
            nis ipſius uueæ in quolibet illorum magnorum circulorũ:</s>
            <s xml:id="echoid-s29054" xml:space="preserve"> omnes aũt
              <lb/>
            illi circuli magni ſphæræ totam ſphæræ ſuperficiem euacuant:</s>
            <s xml:id="echoid-s29055" xml:space="preserve"> quia
              <lb/>
            non eſt dare punctum in ſphærę ſuperficie, quem aliquis circulus ma-
              <lb/>
            gnus non tranſeat.</s>
            <s xml:id="echoid-s29056" xml:space="preserve"> Viſu ergo taliter diſpoſito, tota concaua ſphærę ſu
              <lb/>
            perficies uidebitur.</s>
            <s xml:id="echoid-s29057" xml:space="preserve"> Et hoc eſt propoſitum.</s>
            <s xml:id="echoid-s29058" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1159" type="section" level="0" n="0">
          <head xml:id="echoid-head920" xml:space="preserve" style="it">72. Centro for aminis uueæ intra ſphæræ concauæ illuminatæ ſuperficiem, uel extra illam exi
            <lb/>
          ſtente, portio circularis ſphæræ uidebitur, cui incidunt æquales lineæ à centro uiſus ductæ: erit́
            <lb/>
          uiſum quando hemiſphærium: quando mairo portio: quando minor. Alhazen 44 n 4.</head>
          <p>
            <s xml:id="echoid-s29059" xml:space="preserve">Eſto centrum foraminis uueę punctum a, & ſit ſphęra concaua, cuius circulus magnus ſit b c d:</s>
            <s xml:id="echoid-s29060" xml:space="preserve"> &
              <lb/>
            centrum ſphærę ſit punctum e.</s>
            <s xml:id="echoid-s29061" xml:space="preserve"> Si ergo centrum uiſus ſuerit in puncto e centro ſphæræ, quod eſt e-
              <lb/>
            tiam centrum circuli magni, qui eſt b c d, per definitionem circuli magni:</s>
            <s xml:id="echoid-s29062" xml:space="preserve"> tunc manifeſtum eſt per
              <lb/>
            52 huius, quòd totus circulus b c d uidebitur:</s>
            <s xml:id="echoid-s29063" xml:space="preserve"> ſed & per eandẽ 52 hu-
              <lb/>
            ius, omnes alij circuli ſubiecti hemiſphærij æquidiſtantes circulo b
              <lb/>
              <figure xlink:label="fig-0451-03" xlink:href="fig-0451-03a" number="500">
                <variables xml:id="echoid-variables480" xml:space="preserve">b c a e d</variables>
              </figure>
            c d uidebuntur, quoniam omnium illorum polus erit centrum
              <lb/>
            uιſus:</s>
            <s xml:id="echoid-s29064" xml:space="preserve"> omnes quoq;</s>
            <s xml:id="echoid-s29065" xml:space="preserve"> lineę rectæ ductę à polo ad peripheriam ſui cir-
              <lb/>
            culi ſunt æquales per 65 th.</s>
            <s xml:id="echoid-s29066" xml:space="preserve"> 1 huius:</s>
            <s xml:id="echoid-s29067" xml:space="preserve"> & quoniam hi omnes circu-
              <lb/>
            li totum hemiſphęrium exhauriunt:</s>
            <s xml:id="echoid-s29068" xml:space="preserve"> patet, quòd in hoc ſitu exiſten-
              <lb/>
            te uiſu, totum hemiſphęrium uidebitur.</s>
            <s xml:id="echoid-s29069" xml:space="preserve"> Quòd ſi punctum a, cen-
              <lb/>
            trum foraminis uueæ ſit ſub centro ſphæræ, quod eſt punctum e,
              <lb/>
            tunc per eadem minus hemiſphęrio uidebitur:</s>
            <s xml:id="echoid-s29070" xml:space="preserve"> ſi ſit ſupra centrum e,
              <lb/>
            ſiue ſit intra ſphęram, ſiue extra:</s>
            <s xml:id="echoid-s29071" xml:space="preserve"> tũc ſimiliter per 2 th.</s>
            <s xml:id="echoid-s29072" xml:space="preserve"> 3 huius, omnes
              <lb/>
            circuli, ad quorum circum ferentias poſſunt produci lineę rectę, ui-
              <lb/>
            debuntur:</s>
            <s xml:id="echoid-s29073" xml:space="preserve"> maius ergo hemiſphęrio uidebitur.</s>
            <s xml:id="echoid-s29074" xml:space="preserve"> Et ſi linea à centro ui-
              <lb/>
            ſus ad ſuperficem ſphæræ ducta, obliquè incidat ſuperficiei ipſius
              <lb/>
            ſphęrę:</s>
            <s xml:id="echoid-s29075" xml:space="preserve"> tunc palàm, quòd etiam ſuperficiebus multorum circulorũ obliquè incidet:</s>
            <s xml:id="echoid-s29076" xml:space="preserve"> & poteſt acci-
              <lb/>
            dere, quòd tota figura ſphærę uidebitur inęqualis, ſuorum circulorum peripherijs quibuſdam ten
              <lb/>
            dentibus ad figuram ſectionis columnaris per 55 & 56 huius.</s>
            <s xml:id="echoid-s29077" xml:space="preserve"> Patet ergo propoſitum.</s>
            <s xml:id="echoid-s29078" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum