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

< >
[321] a o c d f e b
Page: 324
[322] f m a h k d p e o c l g n b q
Page: 325
[323] a h b g e f d c
Page: 325
[324] h a b e d z c
Page: 326
[325] e a b d f c
Page: 326
[326] g d f a e c h b
Page: 326
[327] d a g b f e c
Page: 327
[328] e b a g c f d
Page: 327
[329] f h g a e b d c
Page: 328
[330] f g g m b p h c a k d b e
Page: 328
[331] a e g b d c f
Page: 329
[332] g f h k b l a c e m d n
Page: 329
[333] g b c a f d e
Page: 329
[334] g f c b d a
Page: 329
[335] e a d b c
Page: 330
[336] b z g a e d
Page: 330
[337] b f c a d g e
Page: 330
[338] d f b c e d
Page: 331
[339] c a d b
Page: 331
[340] g h e b f d a
Page: 332
[341] a c e h d b
Page: 332
[342] l h g b e c k a d f
Page: 334
[343] f c c l a
Page: 334
[344] b c a
Page: 335
[345] c f b e d a
Page: 335
[346] a b d c
Page: 335
[347] a b d c e
Page: 336
[348] a d b c
Page: 336
[349] a b d c
Page: 337
[350] d e a b c
Page: 337
< >
page |< < (28) of 778 > >|
    <echo version="1.0RC">
      <text xml:lang="lat" type="free">
        <div xml:id="echoid-div765" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s21880" xml:space="preserve">
              <pb o="28" file="0330" n="330" rhead="VITELLONIS OPTICAE"/>
            minoris ductæ ad peripheriam, & baſis a c eſt æqualis baſi a d:</s>
            <s xml:id="echoid-s21881" xml:space="preserve"> quoniam ſunt ex centro circuli maio
              <lb/>
            ris.</s>
            <s xml:id="echoid-s21882" xml:space="preserve"> Ergo per 8 p 1 anguli æquis lateribus contenti ſunt ęquales:</s>
            <s xml:id="echoid-s21883" xml:space="preserve"> angulus ergo c a b eſt æqualis angu
              <lb/>
            lo d a b:</s>
            <s xml:id="echoid-s21884" xml:space="preserve"> ergo per 26 p 3 arcus c g eſt ęqualis arcui d g:</s>
            <s xml:id="echoid-s21885" xml:space="preserve"> reliqui ergo arcus ſemicirculorum, qui ſunt a c
              <lb/>
            & a d, ſunt ęquales.</s>
            <s xml:id="echoid-s21886" xml:space="preserve"> Arcus ergo c a d diuiditur per æqualia in puncto a:</s>
            <s xml:id="echoid-s21887" xml:space="preserve"> quod eſt propoſitum.</s>
            <s xml:id="echoid-s21888" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div766" type="section" level="0" n="0">
          <figure number="335">
            <variables xml:id="echoid-variables319" xml:space="preserve">e a d b c</variables>
          </figure>
          <head xml:id="echoid-head639" xml:space="preserve" style="it">65. Omnes lineæ rectæ ductæ à polo ad peripheriam ſui circuli
            <lb/>
          ſunt æquales. 5 def. 1 ſphæ. Theodo.</head>
          <p>
            <s xml:id="echoid-s21889" xml:space="preserve">Eſto circulus a b c, cuius centrum d:</s>
            <s xml:id="echoid-s21890" xml:space="preserve"> & erigatur perpendiculariter
              <lb/>
            ſuper circulum à centro linea d e, ita, ut per definitionem polus cir-
              <lb/>
            culi ſit punctũ e:</s>
            <s xml:id="echoid-s21891" xml:space="preserve"> & ducantur lineæ e a, e b, e c.</s>
            <s xml:id="echoid-s21892" xml:space="preserve"> Dico, quòd ipſæ oẽs
              <lb/>
            ſunt æquales.</s>
            <s xml:id="echoid-s21893" xml:space="preserve"> Ducantur enim lineę a d, b d, c d.</s>
            <s xml:id="echoid-s21894" xml:space="preserve"> Quia itaq;</s>
            <s xml:id="echoid-s21895" xml:space="preserve"> quadratũ
              <lb/>
            lineę a e eſt ęquale quadrato lineę e d & lineę d a:</s>
            <s xml:id="echoid-s21896" xml:space="preserve"> quadratum quoq;</s>
            <s xml:id="echoid-s21897" xml:space="preserve">
              <lb/>
            lineæ b e æquale eſt quadrato lineæ e d & lineæ d b per 47 p 1:</s>
            <s xml:id="echoid-s21898" xml:space="preserve"> qua-
              <lb/>
            dratum uerò lineæ e d eſt æquale ſibijpſi, & quadratũ lineę d a ęqua-
              <lb/>
            le quadrato lineæ d b per circuli definitionem:</s>
            <s xml:id="echoid-s21899" xml:space="preserve"> palàm quia quadra-
              <lb/>
            tum lineæ a e eſt æquale quadrato lineę b e, & ſimiliter quadrato li-
              <lb/>
            neæ c e.</s>
            <s xml:id="echoid-s21900" xml:space="preserve"> Palàm ergo, quoniam lineę a e, b e, c e, & quæcunq;</s>
            <s xml:id="echoid-s21901" xml:space="preserve"> ſimiliter
              <lb/>
            ductæ, ſunt æquales:</s>
            <s xml:id="echoid-s21902" xml:space="preserve"> & hoc eſt propoſitum.</s>
            <s xml:id="echoid-s21903" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div767" type="section" level="0" n="0">
          <head xml:id="echoid-head640" xml:space="preserve" style="it">66. Omnis linea centrum ſphæræ cum centro circuli non magni
            <lb/>
          illius ſphæræ continuans eſt perpẽdicularis ſuper ſuperficiem illius
            <lb/>
          circuli. 7 & 23 th. 1 ſphæ. Theodo.</head>
          <p>
            <s xml:id="echoid-s21904" xml:space="preserve">Sit centrum ſphærę punctum z, ſitq́;</s>
            <s xml:id="echoid-s21905" xml:space="preserve"> punctum e centrum circuli non magni illius ſphæræ, qui ſit
              <lb/>
            a b g d, & ducatur linea z e.</s>
            <s xml:id="echoid-s21906" xml:space="preserve"> Dico, quòd linea z e eſt perpendicularis ſuper ſuperficiem circuli a b g d.</s>
            <s xml:id="echoid-s21907" xml:space="preserve">
              <lb/>
            Ducantur enim lineę a e, b e, quę productæ cõpleant duas
              <lb/>
              <figure xlink:label="fig-0330-02" xlink:href="fig-0330-02a" number="336">
                <variables xml:id="echoid-variables320" xml:space="preserve">b z g a e d</variables>
              </figure>
            diametros circuli, quæ ſint a g, & b d:</s>
            <s xml:id="echoid-s21908" xml:space="preserve"> & ducantur lineę z a
              <lb/>
            & z b & z d & z g, quę omnes erunt æquales per definitio-
              <lb/>
            nem ſphæræ:</s>
            <s xml:id="echoid-s21909" xml:space="preserve"> ſed & lineæ e a, e b, e d, e g ſunt æquales per
              <lb/>
            definitionem circuli:</s>
            <s xml:id="echoid-s21910" xml:space="preserve"> linea itaq;</s>
            <s xml:id="echoid-s21911" xml:space="preserve"> z e exiſtente communi, pa
              <lb/>
            tet quòd trigona z a e, z b e, z d e, z g e omnia ſunt ęquilate-
              <lb/>
            ra:</s>
            <s xml:id="echoid-s21912" xml:space="preserve"> ergo per 8 p 1 ipſorum anguli ęqualibus laterib.</s>
            <s xml:id="echoid-s21913" xml:space="preserve"> conten-
              <lb/>
            ti ſunt ęquales.</s>
            <s xml:id="echoid-s21914" xml:space="preserve"> Oęs ergo anguli z e a, z e g, z e b, z e d ſunt
              <lb/>
            ęquales:</s>
            <s xml:id="echoid-s21915" xml:space="preserve"> ſunt ergo recti.</s>
            <s xml:id="echoid-s21916" xml:space="preserve"> Eodemq́;</s>
            <s xml:id="echoid-s21917" xml:space="preserve"> modo poteſt demõſtra.</s>
            <s xml:id="echoid-s21918" xml:space="preserve">
              <lb/>
            ri de omnibus angulis contentis ſub linea z e & omni ſemi
              <lb/>
            diametro circuli a b g d.</s>
            <s xml:id="echoid-s21919" xml:space="preserve"> Linea ergo z e eſt perpendicularis
              <lb/>
            ſuper ſuperficiem circuli a b g d:</s>
            <s xml:id="echoid-s21920" xml:space="preserve"> & hoc eſt propoſitum.</s>
            <s xml:id="echoid-s21921" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div769" type="section" level="0" n="0">
          <head xml:id="echoid-head641" xml:space="preserve" style="it">67. À
            <unsure/>
          centro ſphæræ ductã perpendicularẽ ſuք ſuper-
            <lb/>
          ficiẽ circuli non magni ipſius ſphæræ, eiuſdẽ circuli cẽtro
            <lb/>
          incidere eſt neceſſe. Cõſectariũ ſecundũ 1 th. 1 ſphæ. Theo.</head>
          <p>
            <s xml:id="echoid-s21922" xml:space="preserve">Sit, ut in præmiſſa, centrum ſphęræ punctum z:</s>
            <s xml:id="echoid-s21923" xml:space="preserve"> ſitq́;</s>
            <s xml:id="echoid-s21924" xml:space="preserve"> punctum e centrum circuli non magni illius
              <lb/>
            ſphęrę, qui ſit a b g d:</s>
            <s xml:id="echoid-s21925" xml:space="preserve"> & ducatur à puncto z centro ſphærę linea perpendiculariter ſuper ſuperficiẽ
              <lb/>
            circuli a b g d, quæ ſit z e.</s>
            <s xml:id="echoid-s21926" xml:space="preserve"> Dico, quòd punctum e eſt centrum circuli a b g d.</s>
            <s xml:id="echoid-s21927" xml:space="preserve"> Ducantur enim lineæ
              <lb/>
            z a, z b, z g, quæ erũt ęquales per definitionẽ ſphęrę.</s>
            <s xml:id="echoid-s21928" xml:space="preserve"> Quoniã ergo anguli a e z, b e z, d e z, g e z ſunt re
              <lb/>
            cti:</s>
            <s xml:id="echoid-s21929" xml:space="preserve"> patet per 47 p 1 quoniam quadratũ lineę z a ualet quadrata linearum a e & z e, & quadratum li-
              <lb/>
            neę z b ualet ambo quadrata linearum b e & z e:</s>
            <s xml:id="echoid-s21930" xml:space="preserve"> & ſimiliter quadratũ lineę z g ualet ambo quadra-
              <lb/>
            ta linearum g e & z e:</s>
            <s xml:id="echoid-s21931" xml:space="preserve"> lineę uerò z a, z b, z g ſunt ęquales, & quadrata ipſarum ęqualia:</s>
            <s xml:id="echoid-s21932" xml:space="preserve"> ablato itaque
              <lb/>
            quadrato lineę z e omnib.</s>
            <s xml:id="echoid-s21933" xml:space="preserve"> cõmuni, relinquitur ut quadrata linearum
              <lb/>
              <figure xlink:label="fig-0330-03" xlink:href="fig-0330-03a" number="337">
                <variables xml:id="echoid-variables321" xml:space="preserve">b f c a d g e</variables>
              </figure>
            a e, b e, g e ſint ęqualia:</s>
            <s xml:id="echoid-s21934" xml:space="preserve"> ergo & ipſę lineę a e, b e, g e ſunt ęquales.</s>
            <s xml:id="echoid-s21935" xml:space="preserve"> Ergo
              <lb/>
            per 9 p 3 punctum e eſt centrum circuli a b g d:</s>
            <s xml:id="echoid-s21936" xml:space="preserve"> quod eſt propoſitum.</s>
            <s xml:id="echoid-s21937" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div771" type="section" level="0" n="0">
          <head xml:id="echoid-head642" xml:space="preserve" style="it">68. Aequidiſtantium in ſphæra circulorum centra in eadẽ dia
            <lb/>
          metro ſphæræ conſiſtere eſt neceſſe. Ex quo patet, quòd omnes circu-
            <lb/>
          li in ſphæra æquidiſtantes eoſdem habent polos: & ſi eoſdem habent
            <lb/>
          polos, ſunt æquidiſtantes. 1 & 2 th. 2 ſphæ. Theodo.</head>
          <p>
            <s xml:id="echoid-s21938" xml:space="preserve">Sit ſphęra, cuius centrũ ſit punctũ a, & in ipſa ſint duo circuli ęquidi
              <lb/>
            ſtãtes:</s>
            <s xml:id="echoid-s21939" xml:space="preserve"> b c, cuius cẽtrũ ſit f:</s>
            <s xml:id="echoid-s21940" xml:space="preserve"> & d e, cuius cẽtrũ g:</s>
            <s xml:id="echoid-s21941" xml:space="preserve"> & ducatur linea a f, quę
              <lb/>
            ꝓducta erit diameter ſphęrę, cũ ipſa trãſeat centrũ ſphęrę a:</s>
            <s xml:id="echoid-s21942" xml:space="preserve"> ergo ք 66
              <lb/>
            huius lineá a f eſt erecta ſup ſupficiẽ circuli b c:</s>
            <s xml:id="echoid-s21943" xml:space="preserve"> ergo ք 23 huius erit ea
              <lb/>
            dẽ diameter erecta ſuք ſuքficiẽ circuli d e:</s>
            <s xml:id="echoid-s21944" xml:space="preserve"> ergo ք pmiſſam ipſa trãſit ք
              <lb/>
            centrũ circuli d e.</s>
            <s xml:id="echoid-s21945" xml:space="preserve"> Sunt ergo centra illorũ circulorũ in eadẽ diametro
              <lb/>
            ſphęrę:</s>
            <s xml:id="echoid-s21946" xml:space="preserve"> qđ eſt ꝓpoſitũ.</s>
            <s xml:id="echoid-s21947" xml:space="preserve"> Et exhoc patet, qđ illi circuli eoſdẽ habẽt po-
              <lb/>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum