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 |< < (64) of 778 > >|
    <echo version="1.0RC">
      <text xml:lang="lat" type="free">
        <div xml:id="echoid-div885" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s24156" xml:space="preserve">
              <pb o="64" file="0366" n="366" rhead="VITELLONIS OPTICAE"/>
            mathematicã, quę eſt in medio lineę ſenſibilis, & ſecundum lineas extremas ęquidiſtãtes lineę me-
              <lb/>
            diæ:</s>
            <s xml:id="echoid-s24157" xml:space="preserve"> neq;</s>
            <s xml:id="echoid-s24158" xml:space="preserve"> cadit lux minima in punctum mathematicum corporis oppoſiti, ſed in punctum ſenſibilẽ
              <lb/>
            correſpondentẽ omnibus punctis mathematicis indiuiſibilibus, ad quos lineæ mathematicæ ipſi-
              <lb/>
            us lineæ ſenſibilis poſſunt terminari:</s>
            <s xml:id="echoid-s24159" xml:space="preserve"> & ob hoc utemur in demonſtrandis paſsionibus lucis figura-
              <lb/>
            tione linearum mathematicarum in proceſſu.</s>
            <s xml:id="echoid-s24160" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div886" type="section" level="0" n="0">
          <head xml:id="echoid-head719" xml:space="preserve" style="it">4. Corpora diaphana ſunt apta penetrationi luminis & coloris ſine eſſentiali ſui tranſmuta
            <lb/>
          tione. Alhazen 28 n 1.</head>
          <p>
            <s xml:id="echoid-s24161" xml:space="preserve">Hęc enim corpora ꝓprietatẽ habẽt, ut nõ ꝓhibeant formas lucis & coloris ſe penetrare:</s>
            <s xml:id="echoid-s24162" xml:space="preserve"> attamẽ
              <lb/>
            nõ mutantur à lucibus uel coloribus, nec alterantur ab eis alteratione fixa:</s>
            <s xml:id="echoid-s24163" xml:space="preserve"> ſed fit per illa diffuſio lu
              <lb/>
            cis & coloris ſecundum lineas rectas per 1 huius:</s>
            <s xml:id="echoid-s24164" xml:space="preserve"> quarum aliquæ ſunt ęquidiſtãtes, aliquę ſecantes
              <lb/>
            ſe, & quæ dã diuerſi ſitus:</s>
            <s xml:id="echoid-s24165" xml:space="preserve"> & omnium iſtarum linearum diſtinctio fit per diſtinctum ſitum corporis
              <lb/>
            luminoſi, à quo fit diffuſio illius lucis uel coloris.</s>
            <s xml:id="echoid-s24166" xml:space="preserve"> Formæ itaq;</s>
            <s xml:id="echoid-s24167" xml:space="preserve"> lucis & coloris extẽſæ à corporibus
              <lb/>
            diuerſis in e o dẽ diaphano, extenduntur quęlibet ipſarum ſecundum lineam rectã, & pertranſeunt
              <lb/>
            ad corpora oppoſita.</s>
            <s xml:id="echoid-s24168" xml:space="preserve"> Corpus uero diaphanũ nõ tingitur per luces uel colores, ſed ſolùm penetra-
              <lb/>
            tur:</s>
            <s xml:id="echoid-s24169" xml:space="preserve"> neq;</s>
            <s xml:id="echoid-s24170" xml:space="preserve"> enim talia corpora propter luces & colores perdunt ſuas formas, neq;</s>
            <s xml:id="echoid-s24171" xml:space="preserve"> tinguntur per luces
              <lb/>
            & colores tinctura fixa:</s>
            <s xml:id="echoid-s24172" xml:space="preserve"> quia in eis non remanent formę lucis uel coloris poſt receſſum lucis uel co
              <lb/>
            loris ab ipſorum oppoſitione.</s>
            <s xml:id="echoid-s24173" xml:space="preserve"> Non ergo tranſmutantur illa corpora eſſentiali tranſmutatione per
              <lb/>
            luces & colores.</s>
            <s xml:id="echoid-s24174" xml:space="preserve"> Quod eſt propoſitum.</s>
            <s xml:id="echoid-s24175" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div887" type="section" level="0" n="0">
          <head xml:id="echoid-head720" xml:space="preserve" style="it">5. Luces & colores in corporib{us} diaphanis non admiſcentur adinuicem, ſed penetrant di-
            <lb/>
          ſtincti. Alhazen 29 n 1.</head>
          <p>
            <s xml:id="echoid-s24176" xml:space="preserve">Huius rei experimẽtaliter declarãdæ cauſſa, ponãtur in loco aliquo candelæ multæ localiter di-
              <lb/>
            ſtinctæ:</s>
            <s xml:id="echoid-s24177" xml:space="preserve"> & ſint oẽs oppoſitę uni foramini pertrãſeunti ad locũ obſcurum, & opponatur foramini in
              <lb/>
            loco obſcuro aliquod corpus non diaphanum.</s>
            <s xml:id="echoid-s24178" xml:space="preserve"> Luces itaq;</s>
            <s xml:id="echoid-s24179" xml:space="preserve"> cãdelarum apparent ſuper illud corpus
              <lb/>
            diſtinctè ſecundum numerum candelarũ, & quælibet illarum apparet oppoſita uni candelę ſecun-
              <lb/>
            dum lineã rectã tranſeuntẽ per foramẽ & per medium luminis candelæ:</s>
            <s xml:id="echoid-s24180" xml:space="preserve"> & ſi cooperiatur una cãde-
              <lb/>
            la, deſtruetur unum lumẽ oppoſitum illi cãdelæ tantùm, & diſcooperta cãdela, reuertitur lumẽ.</s>
            <s xml:id="echoid-s24181" xml:space="preserve"> Pa
              <lb/>
            làm itaq;</s>
            <s xml:id="echoid-s24182" xml:space="preserve">, qđ luces in medio foraminis, ubi ſe interſecãt oẽs uel plures in puncto uno, nõ admiſcen
              <lb/>
            tur in eodẽ puncto, ſed ſunt diſtinctæ per ſui ipſarum eſſentias:</s>
            <s xml:id="echoid-s24183" xml:space="preserve"> & ob hoc cum ulterius ꝓtẽduntur,
              <lb/>
            tunc ſecundum locorum, quibus incidũt, diuerſitatẽ localiter diſtinguuntur.</s>
            <s xml:id="echoid-s24184" xml:space="preserve"> Et quoniã luxres co-
              <lb/>
            loratas pertranſiẽs, illarum coloribus coloratur, ut ſuppoſitum eſt:</s>
            <s xml:id="echoid-s24185" xml:space="preserve"> palàm, ſi lumẽ penetrat diſtin-
              <lb/>
            ctum, & colores, qui feruntur cum lumine, penetrabunt diſtincti.</s>
            <s xml:id="echoid-s24186" xml:space="preserve"> Patet ergo propoſitum.</s>
            <s xml:id="echoid-s24187" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div888" type="section" level="0" n="0">
          <head xml:id="echoid-head721" xml:space="preserve" style="it">6. Proportio uirtutis toti{us} corporis luminoſi ad totum corp{us} luminoſum eſt, ſicut determi-
            <lb/>
          natæ partis uirtutis ad partem corporis ſibi proportionalem.</head>
          <p>
            <s xml:id="echoid-s24188" xml:space="preserve">Sit corpus aliquod luminoſum a b.</s>
            <s xml:id="echoid-s24189" xml:space="preserve"> Dico, quòd ꝓportio uirtutis totius corporis a b ad totũ cor
              <lb/>
            pus a b eſt, ſicut proportio partis uirtutis, quæ
              <lb/>
              <figure xlink:label="fig-0366-01" xlink:href="fig-0366-01a" number="403">
                <variables xml:id="echoid-variables386" xml:space="preserve">a b g d</variables>
              </figure>
            eſt a, ad partẽ corporis, quę eſt a.</s>
            <s xml:id="echoid-s24190" xml:space="preserve"> Si enim non
              <lb/>
            eſt iſtorum eadẽ ꝓportio:</s>
            <s xml:id="echoid-s24191" xml:space="preserve"> aut ergo maior, aut
              <lb/>
            minor:</s>
            <s xml:id="echoid-s24192" xml:space="preserve"> ſit primũ maior:</s>
            <s xml:id="echoid-s24193" xml:space="preserve"> & ſit uirtus totius cor
              <lb/>
            poris a b ſignata per lineã g d:</s>
            <s xml:id="echoid-s24194" xml:space="preserve"> ſitq́;</s>
            <s xml:id="echoid-s24195" xml:space="preserve"> g uirtus partis corporis, quæ eſt a, & d ſit uirtus partis corporis,
              <lb/>
            quæ eſt b:</s>
            <s xml:id="echoid-s24196" xml:space="preserve"> quę eſt ergo proportio g ad a, eadẽ eſt ꝓportio d ad b:</s>
            <s xml:id="echoid-s24197" xml:space="preserve"> ergo per 18 p 5 erit cõiunctim g d
              <lb/>
            ad a b, ſicut g a d a.</s>
            <s xml:id="echoid-s24198" xml:space="preserve"> Si ergo ꝓportio g ad a eſt maior ꝓportione g d ad a b:</s>
            <s xml:id="echoid-s24199" xml:space="preserve"> erit quoq;</s>
            <s xml:id="echoid-s24200" xml:space="preserve"> maior ꝓportio
              <lb/>
            g d ad a b, ꝗ̃ g d ad a b:</s>
            <s xml:id="echoid-s24201" xml:space="preserve"> quod eſt impoſsibile:</s>
            <s xml:id="echoid-s24202" xml:space="preserve"> nõ enim poterunt eſſe unius rei ad aliã duę ꝓportiões,
              <lb/>
            quarum una ſit maior alia.</s>
            <s xml:id="echoid-s24203" xml:space="preserve"> Idẽ quoq;</s>
            <s xml:id="echoid-s24204" xml:space="preserve"> accidit impoſsibile danti, qđ minor ſit ꝓportio g partis uirtu
              <lb/>
            tis ad partẽ corporis, quę eſt a, ꝗ̃ g d uirtutis ad a b corpus.</s>
            <s xml:id="echoid-s24205" xml:space="preserve"> Si enim minor eſt proportio g ad a, ꝗ̃ g d
              <lb/>
            ad a b:</s>
            <s xml:id="echoid-s24206" xml:space="preserve"> & quę eſt g ad a, eadẽ eſt d ad b:</s>
            <s xml:id="echoid-s24207" xml:space="preserve"> erit ergo per 18 p 5 cõiunctim proportio totius uirtutis, quæ
              <lb/>
            eſt g d, ad corpus a b, minor proportione g d ad a b:</s>
            <s xml:id="echoid-s24208" xml:space="preserve"> quod eſt impoſsibile.</s>
            <s xml:id="echoid-s24209" xml:space="preserve"> Eſt ergo proportio g ad a,
              <lb/>
            ſicut g d ad a b.</s>
            <s xml:id="echoid-s24210" xml:space="preserve"> Et hoc eſt propoſitum:</s>
            <s xml:id="echoid-s24211" xml:space="preserve"> & eſt uniuerſale, niſi fortè aliquid cõferat unio uirtuti:</s>
            <s xml:id="echoid-s24212" xml:space="preserve"> quo-
              <lb/>
            niam uirtus unita ſemper eſt fortior ſe ipſa diuiſa:</s>
            <s xml:id="echoid-s24213" xml:space="preserve"> unde tenet noſtra demonſtratio, quando partes
              <lb/>
            non diuiſæ à toto, agunt in ipſo toto non actualiter diſtinctę:</s>
            <s xml:id="echoid-s24214" xml:space="preserve"> cum enim diſtinctæ ſunt à toto, tunc
              <lb/>
            non ſunt partes:</s>
            <s xml:id="echoid-s24215" xml:space="preserve"> quia nomen partis, id quod dicit philoſophus, ſignat potentiam, non actum:</s>
            <s xml:id="echoid-s24216" xml:space="preserve"> & de
              <lb/>
            hoc completus in alijs ſermo fuit.</s>
            <s xml:id="echoid-s24217" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div890" type="section" level="0" n="0">
          <figure number="404">
            <variables xml:id="echoid-variables387" xml:space="preserve">a b g c d</variables>
          </figure>
          <head xml:id="echoid-head722" xml:space="preserve" style="it">7. Omnis corporis luminoſi intr anſmutabilis ſecun
            <lb/>
          dũ formã & ſitũ, in corp{us} aliud æquale et homogeneũ
            <lb/>
          idẽ immediatè uel per medium uniforme oppoſitũ, eſt ſemper actio æqualis & uniformis.</head>
          <p>
            <s xml:id="echoid-s24218" xml:space="preserve">Sit enim dati alicuius corporis luminoſi uirtus a:</s>
            <s xml:id="echoid-s24219" xml:space="preserve"> & ſit
              <lb/>
            corpus æquale & homogeneũ eidẽ oppoſitũ b g:</s>
            <s xml:id="echoid-s24220" xml:space="preserve"> & ſit im
              <lb/>
            preſsio uirtutis a in b g corpus ſignata ք c.</s>
            <s xml:id="echoid-s24221" xml:space="preserve"> Dico, quòd a
              <lb/>
            ſemper imprimit in corpus b g impreſsionẽ c, quę eſt ſem
              <lb/>
            per æqualis ſibijpſi & uniformis.</s>
            <s xml:id="echoid-s24222" xml:space="preserve"> Si enim detur, quòd a
              <lb/>
            quãdoq;</s>
            <s xml:id="echoid-s24223" xml:space="preserve"> imprimit in corpus b g impreſsionem, quę eſt c,
              <lb/>
            quãdoq;</s>
            <s xml:id="echoid-s24224" xml:space="preserve"> uerò nõ imprimit c, ſed aliud maius uel minus ipſo c, ut d:</s>
            <s xml:id="echoid-s24225" xml:space="preserve"> tũc cũ corpus obiectũ ſit homo
              <lb/>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum