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

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          <head xml:id="echoid-head609" xml:space="preserve" style="it">
            <pb o="15" file="0317" n="317" rhead="LIBER I."/>
          partis b aſis remotioris ad propinquiorem. 5 p geometriæ Iordani.</head>
          <p>
            <s xml:id="echoid-s20973" xml:space="preserve">Sit trigonum orthogonium a b c, cuius angulus b a c ſit rectus:</s>
            <s xml:id="echoid-s20974" xml:space="preserve"> & à puncto b ducatur ad latus
              <lb/>
            a c (quod eſt baſis anguli a b c) linea recta, quæ ſit b d.</s>
            <s xml:id="echoid-s20975" xml:space="preserve"> Dico, quòd minor eſt proportio anguli
              <lb/>
            c b d remotioris ab angulo recto, ad angulum d b a propinquiorem ipſi recto, quàm partis baſis
              <lb/>
            remotioris ab angulo recto (quæ eſt c d) ad latus d a propinquius ipſi angulo recto.</s>
            <s xml:id="echoid-s20976" xml:space="preserve"> Quoniam
              <lb/>
            enim angulus b a c eſt rectus, patet, quia angulus b d a eſt acutus per
              <lb/>
              <figure xlink:label="fig-0317-01" xlink:href="fig-0317-01a" number="297">
                <variables xml:id="echoid-variables281" xml:space="preserve">c d f e a b</variables>
              </figure>
            32 p 1:</s>
            <s xml:id="echoid-s20977" xml:space="preserve"> ergo per 13 p 1, angulus b d c eſt obtuſus:</s>
            <s xml:id="echoid-s20978" xml:space="preserve"> ergo per 19 p 1 latus
              <lb/>
            b d eſt maius latere a b, & minus latere b c.</s>
            <s xml:id="echoid-s20979" xml:space="preserve"> A' centro itaque b ſe-
              <lb/>
            cundum quantitatem ſemidiametri b d deſcribatur arcus circuli ſe-
              <lb/>
            cans lineam b c in puncto e:</s>
            <s xml:id="echoid-s20980" xml:space="preserve"> & ad ipſum producatur linea b a, in pun
              <lb/>
            ctum f:</s>
            <s xml:id="echoid-s20981" xml:space="preserve"> factiq́ue erunt duo ſectores b d e minor trigono b d c, &
              <lb/>
            b d f maior trigono b d a.</s>
            <s xml:id="echoid-s20982" xml:space="preserve"> Et quoniam eſt proportio ſectoris ad ſe-
              <lb/>
            ctorem, ſicut arcus f d ad arcum d e, ut patet per modum demon-
              <lb/>
            ſtrationis 1 p 6:</s>
            <s xml:id="echoid-s20983" xml:space="preserve"> quoniam omnes ſectores eiuſdem circuli, ſunt eiuſdẽ
              <lb/>
            altitudinis, & æquemultiplicia arcuum faciunt æquemultiplicia
              <lb/>
            ipſorum ſectorum:</s>
            <s xml:id="echoid-s20984" xml:space="preserve"> proportio uerò arcus d fad arcum d e eſt ſicut
              <lb/>
            anguli d b f ad angulum d b e per 33 p 6.</s>
            <s xml:id="echoid-s20985" xml:space="preserve"> Cum itaque trigonum c
              <lb/>
            d b ſit maius quàm ſector e d b, & ſector f d b ſit maior trigonoa
              <lb/>
            d b:</s>
            <s xml:id="echoid-s20986" xml:space="preserve"> erit per 9 huius trigoni c d b primi ad trigonum d b a ſecũdum
              <lb/>
            maior proportio, quàm ſectoris e b d tertij ad ſectorem d b f quar-
              <lb/>
            tum.</s>
            <s xml:id="echoid-s20987" xml:space="preserve"> Eſt autem per 1 p 6 trigoni c b d ad trigonum d b a, ſicut baſis
              <lb/>
            c d ad baſim d a:</s>
            <s xml:id="echoid-s20988" xml:space="preserve"> ſectoris uerò e d f ad ſectorem d b f, ut patet expræmiſsis, eſt proportio ſicut
              <lb/>
            anguli e b d ad angulũ d b f.</s>
            <s xml:id="echoid-s20989" xml:space="preserve"> Patet ergo, quòd maior eſt proportio lineæ c d ad lineam d a, quàm an-
              <lb/>
            guli c b d ad angulum d b a.</s>
            <s xml:id="echoid-s20990" xml:space="preserve"> Ergo minor eſt proportio anguli c b d ad angulum d b a, quàm lateris
              <lb/>
            c d ad latus d a:</s>
            <s xml:id="echoid-s20991" xml:space="preserve"> quod eſt propoſitum.</s>
            <s xml:id="echoid-s20992" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div719" type="section" level="0" n="0">
          <figure number="298">
            <variables xml:id="echoid-variables282" xml:space="preserve">e d b a c</variables>
          </figure>
          <head xml:id="echoid-head610" xml:space="preserve" style="it">36. Cuiuslibet trigoni duo latera producta, aliud trigonum
            <lb/>
          priori ſimile principiant, lateribus poſitione & ſitu tranſmutatis.</head>
          <p>
            <s xml:id="echoid-s20993" xml:space="preserve">Sit trigonum a b c, cuius latus a b ſit dextrum, & latus b c ſiniſtrũ,
              <lb/>
            quæ producantur ultra punctum b:</s>
            <s xml:id="echoid-s20994" xml:space="preserve"> & proportionaliter prioribus la-
              <lb/>
            teribus abſcindantur per 12 p 6, linea ſcilicet a b in puncto d, & linea
              <lb/>
            c b in puncto e:</s>
            <s xml:id="echoid-s20995" xml:space="preserve"> & coniungatur linea d e.</s>
            <s xml:id="echoid-s20996" xml:space="preserve"> Erit ita que trigonum d b e
              <lb/>
            ſimile trigono a b c:</s>
            <s xml:id="echoid-s20997" xml:space="preserve"> ſed & latus d b erit ſiniſtrum, & latus e b dextrũ.</s>
            <s xml:id="echoid-s20998" xml:space="preserve">
              <lb/>
            Sunt ita que latera iſtorum trigonorum poſitione, & ſitu tranſmuta-
              <lb/>
            ta:</s>
            <s xml:id="echoid-s20999" xml:space="preserve"> quod eſt propoſitum.</s>
            <s xml:id="echoid-s21000" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div720" type="section" level="0" n="0">
          <head xml:id="echoid-head611" xml:space="preserve" style="it">37. Omnium duorum trigonorum rectangulorum, quorum
            <lb/>
          unius unum laterum rectos angulos continentium fuerit maius
            <lb/>
          altero alterius, reliquum uerò minus reliquo: erit angulus acu-
            <lb/>
          tus unius maius latus reſpiciens, maior angulo alterius ſuum rela-
            <lb/>
          tiuum latus reſpiciente.</head>
          <p>
            <s xml:id="echoid-s21001" xml:space="preserve">Verbi gratia:</s>
            <s xml:id="echoid-s21002" xml:space="preserve"> ſint duo trianguli rectanguli a b c & a c d:</s>
            <s xml:id="echoid-s21003" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0317-03" xlink:href="fig-0317-03a" number="299">
                <variables xml:id="echoid-variables283" xml:space="preserve">a f h b e d c g</variables>
              </figure>
            ſintq́;</s>
            <s xml:id="echoid-s21004" xml:space="preserve"> anguli a b c & a d c recti:</s>
            <s xml:id="echoid-s21005" xml:space="preserve"> & ſit latus b c trianguli a b c
              <lb/>
            maius latere c d trianguli a c d, & reliquum laterum rectos
              <lb/>
            angulos continentium a b unius ſit minus reliquo latere al-
              <lb/>
            terius, quod eſt a d, ut patet in propoſita figuratione, ſi linea
              <lb/>
            a b intelligatur erecta ſuper lineam b c & ſuperficiem eius,
              <lb/>
            & linea b d intelligatur perpendicularis ſuper lineam d c in
              <lb/>
            eadem ſuperficie iacentem:</s>
            <s xml:id="echoid-s21006" xml:space="preserve"> tunc enim erit linea a d perpen-
              <lb/>
            dicularis ſuper lineam d c per 22 huius:</s>
            <s xml:id="echoid-s21007" xml:space="preserve"> quod etiam patet, ſi
              <lb/>
            in ſuperficie iacente ducatur linea b e æquidiſtanter lineæ
              <lb/>
            d c per 31 p 1.</s>
            <s xml:id="echoid-s21008" xml:space="preserve"> Et quoniam linea a b eſt perpendicularis ſuper
              <lb/>
            ſuperficiem iacentem, in qua ſunt lineæ b d, d c, b e, palàm
              <lb/>
            per definitionem lineæ erectæ, quoniam angulus a b e eſt
              <lb/>
            rectus:</s>
            <s xml:id="echoid-s21009" xml:space="preserve"> ſed & angulus e b d eſt rectus per 29 p 1, cum angu-
              <lb/>
            lus b d c ſit rectus per 22 huius, & lineæ b e & d c æquidiſtẽt:</s>
            <s xml:id="echoid-s21010" xml:space="preserve">
              <lb/>
            ergo per 4 p 11 linea b e eſt erecta ſuper ſuperficiem trigoni
              <lb/>
            a b d:</s>
            <s xml:id="echoid-s21011" xml:space="preserve"> ergo per 8 p 11 linea d c eſt perpen dicularis ſuper ean-
              <lb/>
            dem ſuperficiem trigoni a b d:</s>
            <s xml:id="echoid-s21012" xml:space="preserve"> angulus ergo a d c eſt rectus:</s>
            <s xml:id="echoid-s21013" xml:space="preserve">
              <lb/>
            ſed & latus a d maius eſt latere a b per 19 p 1:</s>
            <s xml:id="echoid-s21014" xml:space="preserve"> quoniam angulus a b d eſt rectus.</s>
            <s xml:id="echoid-s21015" xml:space="preserve"> Dico ergo, quòd
              <lb/>
            angulus a c d eſt maior angulo a c b.</s>
            <s xml:id="echoid-s21016" xml:space="preserve"> quoniam enim latus a d eſt maius latere b a per 19 p 1, cum an-
              <lb/>
            gulus a b d ſit rectus:</s>
            <s xml:id="echoid-s21017" xml:space="preserve"> patet, quòd præſens figuratio eſt cõformis hypotheſi.</s>
            <s xml:id="echoid-s21018" xml:space="preserve"> Reſecetur ergo per 3 p 1
              <lb/>
            </s>
          </p>
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