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

List of thumbnails

< >
291
291 (285) 		292
292 (286)
293
293 (287) 		294
294 (288)
295
295 		296
296
297
297 		298
298
299
299 		300
300
< >
page |< < (286) of 778 > >|
    <echo version="1.0RC">
      <text xml:lang="lat" type="free">
        <div xml:id="echoid-div640" type="section" level="0" n="0">
          <p>
            <s xml:id="echoid-s19844" xml:space="preserve">
              <pb o="286" file="0292" n="292" rhead="ALHAZEN"/>
            & cõtinuabo m cũ a.</s>
            <s xml:id="echoid-s19845" xml:space="preserve"> Angulus igitur trianguli a n m eſt rectus:</s>
            <s xml:id="echoid-s19846" xml:space="preserve"> & iá protractú eſt latus n m ſecundú
              <lb/>
            rectitudiné uſq;</s>
            <s xml:id="echoid-s19847" xml:space="preserve"> ad t, & prouenit angulus a m t extra triangulũ, qui eſt maior recto [per 16 p 1] ſcili-
              <lb/>
            cet angulo n.</s>
            <s xml:id="echoid-s19848" xml:space="preserve"> Et quãdo protrahitur ab extremitate diametri circuli linea, quæ cũ ipla cõtineat plus
              <lb/>
            angulo recto:</s>
            <s xml:id="echoid-s19849" xml:space="preserve"> tũc illa linea nõ ſecat circulũ, nec cadit de ea intra ipſum aliquid:</s>
            <s xml:id="echoid-s19850" xml:space="preserve"> ergo de linea m t nó
              <lb/>
            cadit in circulo a m aliquid.</s>
            <s xml:id="echoid-s19851" xml:space="preserve"> Ergo punctũ m facie ad facié reſpicit circulũ z, & nõ abſcondit aliquid
              <lb/>
            ei:</s>
            <s xml:id="echoid-s19852" xml:space="preserve"> quoniã quando nõ abſcondit ei aliquid ex corpore iſtiuſmetſphæræ a m:</s>
            <s xml:id="echoid-s19853" xml:space="preserve"> tunc nulla alia res tegit
              <lb/>
            illud:</s>
            <s xml:id="echoid-s19854" xml:space="preserve"> quoniá nos poſuimus, ut inter duas ſphæras nõ ſit corpus aliud ab eis, quod tegat unam earũ
              <lb/>
            alteri.</s>
            <s xml:id="echoid-s19855" xml:space="preserve"> Et ſimiliter oſtẽdetur hoc in omni pũcto ſuք arcũ h t k.</s>
            <s xml:id="echoid-s19856" xml:space="preserve"> Et dico iterũ, quòd nõ eſt in arcu b e d
              <lb/>
            punctú, quod appareat circulo z:</s>
            <s xml:id="echoid-s19857" xml:space="preserve"> nec eſt poſsibile, ut continuetur cũ aliquo de circulo z p ք lineá, niſt
              <lb/>
            & illa linea ſecet circulũ a b, & cadat intra ipſum.</s>
            <s xml:id="echoid-s19858" xml:space="preserve"> Quod ſi poſsibile eſt:</s>
            <s xml:id="echoid-s19859" xml:space="preserve"> ꝓtrahamus à pũcto e lineam
              <lb/>
            peruenienté ad aliꝗ d de circũferentia circuli h t k l:</s>
            <s xml:id="echoid-s19860" xml:space="preserve"> & nó ſecet aliꝗd de circulo a e d:</s>
            <s xml:id="echoid-s19861" xml:space="preserve"> & ſi fuerit poſ-
              <lb/>
            ſibile, ſit linea e q l:</s>
            <s xml:id="echoid-s19862" xml:space="preserve"> & ꝓtrahá lineá d k in utraſq;</s>
            <s xml:id="echoid-s19863" xml:space="preserve"> partes duarũ extremitatũ eius:</s>
            <s xml:id="echoid-s19864" xml:space="preserve"> neceſſe eſt ergo, ut
              <lb/>
            occurrat lineæ e q l in duob.</s>
            <s xml:id="echoid-s19865" xml:space="preserve"> locis:</s>
            <s xml:id="echoid-s19866" xml:space="preserve"> quoniá linea d k, quá iá poſuimus contingenté duos circulos, nõ
              <lb/>
            eſt poſsibile, ut ſecet unũ duorũ circulorum, nec cadat inter utroſq;</s>
            <s xml:id="echoid-s19867" xml:space="preserve"> [per 16 p 3:</s>
            <s xml:id="echoid-s19868" xml:space="preserve">] & quoniã nó cadit
              <lb/>
            inter ipſos, tunc ſecabit lineam e l in duobus locis:</s>
            <s xml:id="echoid-s19869" xml:space="preserve"> ergo iam ſunt duæ lineæ rectæ continentes ſu-
              <lb/>
            perficiem:</s>
            <s xml:id="echoid-s19870" xml:space="preserve">illud autem eſt contrarium & impoſsibile [per 12 axioma.</s>
            <s xml:id="echoid-s19871" xml:space="preserve">]</s>
          </p>
        </div>
        <div xml:id="echoid-div641" type="section" level="0" n="0">
          <head xml:id="echoid-head551" xml:space="preserve" style="it">5. Deperipheria maximi in terra circuli ſol illuminat partes 180, ſcrupula prima 27, ſcru-
            <lb/>
          pula ſecunda 52. Vitell. 59 p 10.</head>
          <p>
            <s xml:id="echoid-s19872" xml:space="preserve">QVod aũt oportet nos facere ſecundũ illud, quod pręmiſimus, ut inueniamus, quãta ſit quã-
              <lb/>
            titas arcus terræ illuminati à ſole:</s>
            <s xml:id="echoid-s19873" xml:space="preserve"> quã iã poſuimus maiorẽ eſſe medietate terræ:</s>
            <s xml:id="echoid-s19874" xml:space="preserve"> ponã ergo
              <lb/>
            duos circulos ſolis & terræ, ſuper quos ſecat utroſq;</s>
            <s xml:id="echoid-s19875" xml:space="preserve"> una ſuperficies plana, quales ſunt a b c
              <lb/>
            d e, f h g.</s>
            <s xml:id="echoid-s19876" xml:space="preserve"> Circulus ergo a ſit terræ, & circulus ſolis f:</s>
            <s xml:id="echoid-s19877" xml:space="preserve"> & protrahã duas lineas contingẽtes unũquenq;</s>
            <s xml:id="echoid-s19878" xml:space="preserve">
              <lb/>
            eorũ, ſicut diximus, quæ ſint duæ lineæ b h & e g.</s>
            <s xml:id="echoid-s19879" xml:space="preserve"> Igitur portio b c d e exterra, eſt illuminata à ſole,
              <lb/>
            ſicut iam oſtendimus [3 n] & illud eſt plus me-
              <lb/>
              <figure xlink:label="fig-0292-01" xlink:href="fig-0292-01a" number="252">
                <variables xml:id="echoid-variables239" xml:space="preserve">f g k h d c e a b</variables>
              </figure>
            dietate circuli.</s>
            <s xml:id="echoid-s19880" xml:space="preserve"> Quando ergo uolumus ſcire
              <lb/>
            quantitatẽ eius, tũc nos cõtinuabimus a cum b
              <lb/>
            & cũ f, & f cũ h:</s>
            <s xml:id="echoid-s19881" xml:space="preserve"> ergo b a & h fſunt æquidiſtãtes
              <lb/>
            [per 28 p 1] quoniã utræq;</s>
            <s xml:id="echoid-s19882" xml:space="preserve"> ſunt perpẽdiculares
              <lb/>
            ſuper lineã b h, contingentẽ duos circulos [per
              <lb/>
            18 p 3.</s>
            <s xml:id="echoid-s19883" xml:space="preserve">] Et ſecabo ex linea h f, quod ſit æquale li-
              <lb/>
            neæ b a [id uerò fieri poteſt, quia f h ex theſi ma
              <lb/>
            ior eſt a b] & ſit linea h k:</s>
            <s xml:id="echoid-s19884" xml:space="preserve"> & continuabo a cũ k:</s>
            <s xml:id="echoid-s19885" xml:space="preserve">
              <lb/>
            ergo a k eſt perpẽdicularis ſuper h f [per 29 p 1]
              <lb/>
            quoniã eſt æquidiſtãs ipſi b h:</s>
            <s xml:id="echoid-s19886" xml:space="preserve"> cũ cõtinuet totũ,
              <lb/>
            quod eſt inter extremitates duarũ linearũ b a,
              <lb/>
            & h k æqualiũ & æquidiſtantiũ:</s>
            <s xml:id="echoid-s19887" xml:space="preserve"> ergo angulus k
              <lb/>
            eſt rectus.</s>
            <s xml:id="echoid-s19888" xml:space="preserve"> Et ꝓpterea quòd linea h f eſt quinq;</s>
            <s xml:id="echoid-s19889" xml:space="preserve">
              <lb/>
            partes & medιetas partis, ք quãtitatẽ, qua linea
              <lb/>
            b a eſt pars una [ut dictũ eſt 1 n] remanet linea
              <lb/>
            k f quatuor partium & medietatis unius partis
              <lb/>
            ex illa quãtitate:</s>
            <s xml:id="echoid-s19890" xml:space="preserve"> & per eandẽ inuenitur linea a
              <lb/>
            f 1110, in medijs lõgitudinibus [ſole cõſtituto.</s>
            <s xml:id="echoid-s19891" xml:space="preserve">]
              <lb/>
            Ergo per quantitatẽ, qua linea a f ſubtẽſa angu-
              <lb/>
            lo recto, eſt 60 grad.</s>
            <s xml:id="echoid-s19892" xml:space="preserve"> eſt linea k f 14 minuta &
              <lb/>
            tres quintæ unius minuti:</s>
            <s xml:id="echoid-s19893" xml:space="preserve"> ergo angulus k a f eſt
              <lb/>
            14 min.</s>
            <s xml:id="echoid-s19894" xml:space="preserve"> excepta tertia parte ꝗntæ partis unius
              <lb/>
            minuti, [id eſt 13 minu.</s>
            <s xml:id="echoid-s19895" xml:space="preserve"> & 56 ſec.</s>
            <s xml:id="echoid-s19896" xml:space="preserve"> Nam ſecũdum
              <lb/>
            pręcepta arithmetices quin cunx ſeu ꝗnta pars
              <lb/>
            unius minuti ſunt 12 ſecunda, quorũ tertia pars
              <lb/>
            per diuiſionẽ inuẽta, ſunt 4 ſecun.</s>
            <s xml:id="echoid-s19897" xml:space="preserve"> quibus ſub-
              <lb/>
            ductis à 14 minutis, rectã 13 minuta & 56 ſecun-
              <lb/>
            da] per quãtitatem, qua angulus rectus eſt 90
              <lb/>
            grad.</s>
            <s xml:id="echoid-s19898" xml:space="preserve"> & illud eſt quãtitas arcus c d:</s>
            <s xml:id="echoid-s19899" xml:space="preserve"> ſed arcus b c
              <lb/>
            eſt 90 grad.</s>
            <s xml:id="echoid-s19900" xml:space="preserve"> quoniã angulus b a c eſt rectus.</s>
            <s xml:id="echoid-s19901" xml:space="preserve"> Er-
              <lb/>
            go arcus b d eſt 90 grad.</s>
            <s xml:id="echoid-s19902" xml:space="preserve"> 14 min.</s>
            <s xml:id="echoid-s19903" xml:space="preserve"> excepta tertia
              <lb/>
            parte quintæ partis unius minuti:</s>
            <s xml:id="echoid-s19904" xml:space="preserve"> & arcus d e
              <lb/>
            eſt ęqualis arcui b d.</s>
            <s xml:id="echoid-s19905" xml:space="preserve"> [Ducta enim à pũcto a pa-
              <lb/>
            rallela ip̀ſi e g:</s>
            <s xml:id="echoid-s19906" xml:space="preserve"> erit angulus à ſemidiametro e a & parallela cõprehenſus, rectus per 29 p 1, & æqualis
              <lb/>
            angulo b a c per 10 ax.</s>
            <s xml:id="echoid-s19907" xml:space="preserve"> Et quia ducta parallela ſecat de ſemidiametro f g uerſus f æqualẽ ipſi f k ք 15
              <lb/>
            d.</s>
            <s xml:id="echoid-s19908" xml:space="preserve"> 34 p 1.</s>
            <s xml:id="echoid-s19909" xml:space="preserve"> 1 ax:</s>
            <s xml:id="echoid-s19910" xml:space="preserve"> & angulus à parallela & ſemidiametro f g cõprehẽſus, rectus eſt per 29 uel 34 p 1:</s>
            <s xml:id="echoid-s19911" xml:space="preserve"> ęqua-
              <lb/>
            buntur quadrata parallelæ & ſectæ de ſemidiametro f g uerſus f, quadrato f a per 47 p 1, cui per ean-
              <lb/>
            dem æquantur quadrata ipſarũ a k & k f:</s>
            <s xml:id="echoid-s19912" xml:space="preserve"> ſubductis igitur quadratis æqualibus ipſarũ f k & ſectæ d e
              <lb/>
            ſemidiametro f g uerſus f, relinquẽtur quadrata ipſarũ a k & ductæ parallelæ æqualia, ideoq́;</s>
            <s xml:id="echoid-s19913" xml:space="preserve"> recta
              <lb/>
            a k æqualis erit ductæ parallelæ:</s>
            <s xml:id="echoid-s19914" xml:space="preserve"> & per 8 p 1 angulus d a c æquabitur angulo ab f a & parallela ad cẽ-
              <lb/>
            trum a cõprehenſo.</s>
            <s xml:id="echoid-s19915" xml:space="preserve"> ſed angulo c ab æqualis cõcluſus eſt angulus à ſemidiametro e a & parallela cõ-
              <lb/>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum