{"id":1207,"date":"2017-10-18T09:22:01","date_gmt":"2017-10-18T09:22:01","guid":{"rendered":"http:\/\/uni.hi.is\/einar\/?p=1207"},"modified":"2017-10-18T09:22:01","modified_gmt":"2017-10-18T09:22:01","slug":"aflfraedi-i-verkum-stefans-bjornssonar","status":"publish","type":"post","link":"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/?p=1207","title":{"rendered":"Aflfr\u00e6\u00f0i \u00ed verkum Stef\u00e1ns Bj\u00f6rnssonar"},"content":{"rendered":"

\u00cd f\u00e9lagaskr\u00e1 Hins (konunglega) \u00edslenska l\u00e6rd\u00f3mslistaf\u00e9lags<\/em> segir um Stef\u00e1n Bj\u00f6rnsson (1721-98) a\u00f0 hann s\u00e9\u00a0\u201eMatheseos et Antiqvitt patri\u00e6 Studiosus\u201c (l\u00e6r\u00f0ur \u00ed st\u00e6r\u00f0fr\u00e6\u00f0i og fornfr\u00e6\u00f0um f\u00f6\u00f0urlandsins). Hann s\u00e1 um fyrstu fr\u00e6\u00f0ilegu \u00fatg\u00e1funa \u00e1 R\u00edmbeglu<\/a> 1780 og sama \u00e1r kom \u00fat b\u00f3k hans, Ferhyrningafr\u00e6\u00f0i<\/a>. Hvatinn a\u00f0 seinna verkinu var sennilega margra \u00e1ra starf hans sem reiknimeistari (Kalkulator) vi\u00f0 \u00fer\u00edhyrningam\u00e6lingar og kortager\u00f0 Hins konunglega danska v\u00edsindaf\u00e9lags<\/a>. \u00c1 efri \u00e1rum var hann um t\u00edma styrk\u00feegi sj\u00f3\u00f0s \u00c1rna Magn\u00fassonar<\/a> og vann einnig fyrir hinn merka fr\u00e6\u00f0imann P. F. Suhm<\/a>, sem kosta\u00f0i \u00fatg\u00e1fu R\u00edmbeglu og eins latneska \u00fe\u00fd\u00f0ingu Stef\u00e1ns \u00e1 Hervarar s\u00f6gu og Hei\u00f0reks<\/a>.<\/p>\n

\u00de\u00f3tt Stef\u00e1n hafi dvalist mestan hluta starfs\u00e6vinnar \u00ed Danm\u00f6rku, voru tengsl hans vi\u00f0 \u00cdsland og \u00cdslendinga alla t\u00ed\u00f0 mj\u00f6g sterk. \u00dev\u00ed er r\u00e9tt a\u00f0 l\u00edta \u00e1 hann og verk hans sem hluta af \u00edslenskri v\u00edsindas\u00f6gu, \u00e1 svipa\u00f0an h\u00e1tt og vi\u00f0 gerum me\u00f0 samt\u00edmamann okkar, st\u00e6r\u00f0fr\u00e6\u00f0inginn Sigur\u00f0 Helgason, og fleiri. N\u00e1nar m\u00e1 lesa um Stef\u00e1n, \u00e6vi hans og st\u00f6rf, h\u00e9r<\/a> og h\u00e9r<\/a> (bls. 8-27). \u00cd \u00feessari f\u00e6rslu ver\u00f0ur hins vegar fjalla\u00f0 um aflfr\u00e6\u00f0ina \u00ed verkum hans, a\u00f0 loknum stuttum inngangi um st\u00e6r\u00f0fr\u00e6\u00f0ilegar l\u00e6rd\u00f3mslistir \u00e1 \u00e1tj\u00e1ndu \u00f6ld.<\/p>\n

St\u00e6r\u00f0fr\u00e6\u00f0ilegar l\u00e6rd\u00f3mslistir<\/em><\/span><\/p>\n

\u00c1 uppl\u00fdsingart\u00edmanum (og fyrr) voru hugt\u00f6kin st\u00e6r\u00f0fr\u00e6\u00f0i (mathematica) og st\u00e6r\u00f0fr\u00e6\u00f0ingur (mathematicus) notu\u00f0 \u00ed mun v\u00ed\u00f0ari merkingu en \u00ed dag.\u00a0 \u00c1 \u00edslensku hefur \u00fev\u00ed skapast s\u00fa hef\u00f0 a\u00f0 tala um st\u00e6r\u00f0fr\u00e6\u00f0ilegar l\u00e6rd\u00f3mslistir<\/em>, \u00feegar st\u00e6r\u00f0fr\u00e6\u00f0i \u00feess t\u00edma er til umr\u00e6\u00f0u. \u00dev\u00ed v\u00e6ri n\u00e6r a\u00f0 kalla Stef\u00e1n st\u00e6r\u00f0fr\u00e6\u00f0ilegan l\u00e6rd\u00f3ms(lista)mann en st\u00e6r\u00f0fr\u00e6\u00f0ing. <\/span><\/p>\n

Allt fram \u00e1 s\u00ed\u00f0asta fj\u00f3r\u00f0ung \u00e1tj\u00e1ndu aldar var hinn fr\u00e6gi Christian Wolff<\/a> mesti \u00e1hrifavaldur \u00fe\u00fdsk-d\u00f6nsku uppl\u00fdsingarinnar. Hann <\/span>haf\u00f0i til d\u00e6mis umtalsver\u00f0 \u00e1hrif \u00e1 Stef\u00e1n, eins og svo marga a\u00f0ra \u00edslenska og danska uppl\u00fdsingarmenn.
\n<\/span><\/p>\n

\"\"
Christian Wolff (1679 -1754)<\/figcaption><\/figure>\n

\u00c1 \u00feessum t\u00edma var hi\u00f0 mikla verk Wollfs um frumatri\u00f0i st\u00e6r\u00f0fr\u00e6\u00f0ilegra l\u00e6rd\u00f3mslista miki\u00f0 nota\u00f0 \u00ed h\u00e1sk\u00f3lum Nor\u00f0ur-Evr\u00f3pu, \u00fear \u00e1 me\u00f0al \u00ed Danm\u00f6rku. \u00dea\u00f0 var\u00f0 einnig fyrirmynd margra kennslub\u00f3ka fram eftir \u00e1tj\u00e1ndu \u00f6ldinni. Verki\u00f0 kom \u00ed m\u00f6rgum bindum og \u00ed m\u00f6rgum \u00fatg\u00e1fum, fyrst \u00e1 \u00fe\u00fdsku undir heitinu Die Anfangs-Gr\u00fcnde aller mathematischen Wissenschaften<\/em><\/span> og s\u00ed\u00f0an \u00e1 lat\u00ednu sem Elementa Matheseos Universae<\/em><\/span>. Einnig kom \u00fat einfaldara yfirlit \u00e1 \u00fe\u00fdsku, oftast kalla\u00f0 Auszug<\/a>, sem stundum var nota\u00f0 til kennslu. \u00dear eru eftirfarandi greinar settar undir hatt st\u00e6r\u00f0fr\u00e6\u00f0ilegra l\u00e6rd\u00f3mslista:<\/p>\n

\n
    \n
  1. Die Arithmetick.<\/a><\/li>\n
  2. Die Geometrie.<\/a><\/li>\n
  3. Die Trigonometrie.<\/a><\/li>\n
  4. Die Mechanick.<\/a><\/li>\n
  5. Die Hydrostatick.<\/a><\/li>\n
  6. Die Aerometrie.<\/a><\/li>\n
  7. Die Hydraulick.<\/a><\/li>\n
  8. Die Optick.<\/a><\/li>\n
  9. Die Catoptrick.<\/a><\/li>\n
  10. Die Dioptrick.<\/a><\/li>\n
  11. Die Perspectiv.<\/a><\/li>\n
  12. Die Astronomie.<\/a><\/li>\n
  13. Die Geographie.<\/a><\/li>\n
  14. Die Chronologie.<\/a><\/li>\n
  15. Die Gnomonick.<\/a><\/li>\n
  16. Die Artillerie.<\/a><\/li>\n
  17. Die Fortification.<\/a><\/li>\n
  18. Die Baukunst.<\/a><\/li>\n
  19. Die Algebra.<\/a><\/li>\n<\/ol>\n

    Flestar undirgreinarnar \u00ed \u00feessari upptalningu falla undir blanda\u00f0a st\u00e6r\u00f0fr\u00e6\u00f0i (mathesis mixta), hugtak sem talsvert var nota\u00f0 \u00e1 sautj\u00e1ndu og \u00e1tj\u00e1ndu \u00f6ld. \u00cd dag eru margar \u00feeirra sj\u00e1lfst\u00e6\u00f0ar fr\u00e6\u00f0igreinar e\u00f0a hluti af e\u00f0lisfr\u00e6\u00f0i (\u00e1\u00f0ur n\u00e1tt\u00faruspeki), fr\u00e6\u00f0igrein sem var\u00f0 ekki til \u00ed n\u00fat\u00edmaskilningi fyrr en vel var li\u00f0i\u00f0 \u00e1 n\u00edtj\u00e1ndu \u00f6ldina. Seint \u00e1 \u00e1tj\u00e1ndu \u00f6ld var hins vegar fari\u00f0 a\u00f0 tala um hagn\u00fdtta st\u00e6r\u00f0fr\u00e6\u00f0i (mathesis applicata) \u00ed sta\u00f0 blanda\u00f0rar (sj\u00e1 \u00ed \u00feessu sambandi fr\u00e1b\u00e6rt erindi Bj\u00f6rns Gunnlaugssonar um nytsemi m\u00e6lifr\u00e6\u00f0innar<\/a> (bls. 54-66)). Hagn\u00fdtt e\u00f0a heimf\u00e6r\u00f0 st\u00e6r\u00f0fr\u00e6\u00f0i t\u00f3k svo sm\u00e1m saman verulegum breytingum, einkum \u00fe\u00f3 \u00e1 tuttugustu \u00f6ld.\u00a0 <\/span><\/p>\n

    Stef\u00e1n Bj\u00f6rnsson og aflfr\u00e6\u00f0in<\/em><\/span><\/p>\n

    S\u00fa n\u00e1tt\u00faruspeki, sem Stef\u00e1n l\u00e6r\u00f0i \u00e1 s\u00ednum t\u00edma, var fyrst og fremst bygg\u00f0 \u00e1 hugmyndafr\u00e6\u00f0i Wolffs. Af tilv\u00edsunum \u00ed verkum hans m\u00e1 \u00fe\u00f3 r\u00e1\u00f0a, a\u00f0 hann hefur til vi\u00f0b\u00f3tar kynnt s\u00e9r \u00fdmis \u00feekkt fr\u00e6\u00f0irit s\u00edns t\u00edma, til d\u00e6mis verk Newtons<\/a> og n\u00e1tt\u00faruspeki-kennslub\u00f3k Willems ‘s Gravesande<\/a>, fyrsta l\u00e6risveins Newtons \u00e1 meginlandi Evr\u00f3pu. \u00de\u00e1 \u00feekkti Stef\u00e1n til sumra verka Eulers<\/a> (a.m.k. Introductio in analysin infinitorum<\/a> fr\u00e1 1748) og haf\u00f0i bla\u00f0a\u00f0 \u00ed v\u00f6kvaaflfr\u00e6\u00f0i Dan\u00edels Bernoulli<\/a>. <\/span><\/p>\n

    Helsta vi\u00f0fangsefni flestra st\u00e6r\u00f0fr\u00e6\u00f0ilegra l\u00e6rd\u00f3msmanna \u00e1 \u00e1tj\u00e1ndu \u00f6ld var aflfr\u00e6\u00f0i<\/a> og m\u00e1 fyrst og fremst rekja \u00feann \u00e1huga til hins st\u00f3rbrotna rits Newtons, St\u00e6r\u00f0fr\u00e6\u00f0il\u00f6gm\u00e1l n\u00e1tt\u00faruspekinnar<\/a>. \u00der\u00e1tt fyrir a\u00f0 vera stundum forn \u00ed skapi, var Stef\u00e1n einnig barn s\u00edns t\u00edma og hreifst \u00fev\u00ed e\u00f0lilega me\u00f0, \u00feegar n\u00fdlegar hugmyndir b\u00e1rust til Kaupmannahafnar. H\u00e9r ver\u00f0ur n\u00fa sagt fr\u00e1 verkum hans \u00e1 svi\u00f0i aflfr\u00e6\u00f0innar.<\/span>
    \n<\/span><\/p>\n<\/div>\n

    Disp\u00fatat\u00eda um \u00feyngdarl\u00f6gm\u00e1l og halastj\u00f6rnur<\/em><\/span><\/p>\n

    Stef\u00e1n Bj\u00f6rnson lauk pr\u00f3fi (baccalaureus philosophiae) fr\u00e1 heimspekideild Hafnarh\u00e1sk\u00f3la \u00e1ri\u00f0 1757, \u00fe\u00e1 36 \u00e1ra (n\u00e1tt\u00faruv\u00edsindadeild var ekki sett \u00e1 laggirnar vi\u00f0 sk\u00f3lann fyrr en 1850). \u00c1 \u00e1runum 1757 til 1760 disp\u00fatera\u00f0i hann fj\u00f3rum sinnum og eru fyrirlestrarnir til \u00e1 prenti. \u00de\u00f3tt allir s\u00e9u \u00feeir \u00e1hugaver\u00f0ir, ver\u00f0ur a\u00f0eins einn \u00feeirra, fr\u00e1 1758, til umr\u00e6\u00f0u h\u00e9r.<\/span><\/p>\n

    \"\"
    Fors\u00ed\u00f0an \u00e1 disp\u00fatat\u00edu Stef\u00e1ns fr\u00e1 1758. Tengill \u00e1 verki\u00f0 allt er h\u00e9r<\/a>.<\/figcaption><\/figure>\n

    \u00c1 \u00ed<\/span>slensku er titill disp\u00fatat\u00edunnar Um verkan halastjarna sem ganga ni\u00f0ur \u00ed reikistj\u00f6rnukerfi vort<\/em>. Framsetningin er \u00ed anda n\u00e1tt\u00faruspeki frekar en st\u00e6r\u00f0fr\u00e6\u00f0i, en <\/span>greinilega kemur fram, a\u00f0 Stef\u00e1n hefur veri\u00f0 vel a\u00f0 s\u00e9r \u00ed aflfr\u00e6\u00f0i Newtons og vitnar me\u00f0al annars \u00ed verk hans. Fjalla\u00f0 er \u00edtarlega um \u00feyngdarl\u00f6gm\u00e1li\u00f0 og \u00fev\u00ed l\u00fdst, hvernig halastj\u00f6rnur hreyfast vegna \u00feyngdarhrifa fr\u00e1 s\u00f3linni. Jafnframt r\u00e6\u00f0ir Stef\u00e1n \u00e1hrif halastjarna \u00e1 hreyfingu s\u00f3lar og reikistjarna og einnig um sj\u00e1varf\u00f6ll af \u00feeirra v\u00f6ldum. \u00d6ll umfj\u00f6llunin er bygg\u00f0 \u00e1 n\u00e1tt\u00faruspeki og heimsmynd Newtons.<\/p>\n

    Stef\u00e1n Bj\u00f6rnsson var fyrsti \u00cdslendingurinn sem kynnti s\u00e9r verk Newtons til nokkurrar hl\u00edtar. Ekki er lj\u00f3st hvort hann hefur or\u00f0i\u00f0 fyrir \u00e1hrifum fr\u00e1 hinum merka st\u00e6r\u00f0fr\u00e6\u00f0ilega l\u00e6rd\u00f3msmanni, Jens Kraft<\/a> vi\u00f0\u00a0 akadem\u00eduna \u00ed S\u00f3rey<\/a>, sem fyrstur Dana lag\u00f0i sig eftir verkum Newtons.\u00a0 Aflfr\u00e6\u00f0i Newtons var hins vegar ekki kennd opinberlega vi\u00f0 Hafnarh\u00e1sk\u00f3la fyrr en l\u00f6ngu s\u00ed\u00f0ar, \u00feegar Thomas Bugge<\/a>\u00a0 kom til starfa vi\u00f0 sk\u00f3lann \u00e1ri\u00f0 1777. \u00dev\u00ed fer <\/span>ekki \u00e1 milli m\u00e1la, a\u00f0 me\u00f0 disp\u00fatat\u00edum s\u00ednum var Stef\u00e1n \u00ed h\u00f3pi \u00feeirra, sem fyrstir r\u00e6ddu n\u00e1tt\u00faruspeki Newtons opinberlega vi\u00f0 H\u00e1sk\u00f3lann.
    \n<\/span><\/p>\n

    Aflfr\u00e6\u00f0i fyrir \u00edslenska b\u00e6ndur
    \n<\/em><\/span><\/h1>\n

    Sama \u00e1r og Stef\u00e1n B\u00f6rnsson var\u00f0 sextugur kom \u00fat eftir hann fyrsta greinin af \u00e1tta um aflfr\u00e6\u00f0i \u00e1 \u00edslensku. Greinarnar voru \u00e6tla\u00f0ar \u00edslenskri al\u00fe\u00fd\u00f0u, einkum \u00fe\u00f3 b\u00e6ndum, og birtust \u00fe\u00e6r allar \u00ed Riti \u00feess (konunglega) \u00edslenska l\u00e6rd\u00f3mslistaf\u00e9lags<\/em> \u00e1 \u00e1runum 1781 til 1789. Stef\u00e1n valdi a\u00f0 taka fyrir svokalla\u00f0ar einfaldar v\u00e9lar<\/a> (m<\/span>achinis simplicibus<\/span>) sem hann kaus a\u00f0 kalla grunnmask\u00ednur<\/em> \u00e1 \u00edslensku. \u00cd vissum skilningi m\u00e1 segja, a\u00f0 h\u00e9r s\u00e9 um a\u00f0 r\u00e6\u00f0a fyrstu \u00edslensku kennslub\u00f3kina \u00ed e\u00f0lisfr\u00e6\u00f0i.<\/span><\/p>\n

    \u00cd form\u00e1la a\u00f0 ritinu, \u00fear sem fyrsta greinin birtist, segir ritstj\u00f3rnin me\u00f0al annars (bls. iv-vi):
    \n<\/span><\/p>\n

    Um \u00fe\u00e6r einf\u00f6ldustu grunnmask\u00ednur, og s\u00e9r\u00edlagi um vegst\u00f6ngina hefur Steph\u00e1n Bi\u00f6rnsson \u00fearme\u00f0 byrja\u00f0 \u00e1, a\u00f0 f\u00e6ra sinn \u00e1setning \u00ed verk, (nefnilega:) a\u00f0 \u00fatlista sm\u00e1msaman \u00fe\u00e1 parta af hinni gj\u00f6ranlegu m\u00e6lingarfr\u00e6\u00f0i, sem eina mestu nytsemi veita \u00ed hvers manns daglegum ath\u00f6fnum, en menn hafa \u00fe\u00f3 eigi neitt haft prenta\u00f0 um hinga\u00f0 til \u00e1 \u00edslenska tungu. \u00deessu m\u00e1 \u00fe\u00e1 v\u00e6nta a\u00f0 framhaldi\u00f0 ver\u00f0i me\u00f0 t\u00ed\u00f0inni. A\u00f0 nokkrum m\u00e1ske mun erfitt veita kunna, a\u00f0 skilja hitt og \u00feetta til fulls \u00ed riti \u00feessu, \u00fea\u00f0 m\u00e1 helst umkenna n\u00e1tt\u00farulegu efnisins \u00e1sigkomulagi; \u00fe\u00f3 \u00e6tla menn, a\u00f0 sl\u00edkt muni eigi ver\u00f0a neinum til hindrunar, sem skilur nokku\u00f0 \u00ed matemat\u00edskum reikningsh\u00e6tti, og veit s\u00e9r til lei\u00f0arv\u00edsis a\u00f0 vi\u00f0neyta \u00feeirra \u00fatreikninga, auk f\u00edg\u00faranna, sem leturgj\u00f6r\u00f0in sj\u00e1lf \u00ed s\u00e9r hefur.<\/p><\/blockquote>\n

    \"\"
    Fors\u00ed\u00f0an a\u00f0 fyrstu grein Stef\u00e1ns um grunnmask\u00ednur fr\u00e1 1781.<\/figcaption><\/figure>\n

    Sj\u00e1lfur kemst Stef\u00e1n svo a\u00f0 or\u00f0i \u00ed inngangi greinarinnar:<\/p>\n

    En \u00fe\u00f3 a\u00f0 \u00f3l\u00e6r\u00f0ir menn hafi af n\u00e1tt\u00farunni nokkura \u00feekking af \u00feessum hr\u00e6ringar verkf\u00e6rum, \u00fe\u00e1 er h\u00fan eigi a\u00f0 s\u00ed\u00f0ur mj\u00f6g \u00f3fullkomin, og kann h\u00fan eigi alt\u00ed\u00f0 a\u00f0 f\u00e6rast \u00ed nyt; \u00fev\u00ed menn kunna eigi a\u00f0 lagf\u00e6ra \u00feau, n\u00e9 gj\u00f6ra nokkurn \u00fatreikning, og \u00ed einu or\u00f0i a\u00f0 segja: hafa mj\u00f6g \u00f3greinilegt skyn \u00e1 \u00feeim. Vir\u00f0ist \u00fev\u00ed b\u00e6\u00f0i nau\u00f0synlegt og nytsamlegt, a\u00f0 gefa b\u00e6ndum sk\u00edrari \u00e1v\u00edsun um \u00feessar fyrsu og einf\u00f6ldustu grunnmask\u00ednur, svo a\u00f0 \u00feeir hvarvetna kunni \u00fev\u00ed betur a\u00f0 n\u00fdta \u00feeirra br\u00fakun.\u00a0 [<\/em>\u2026]<\/em><\/p>\n

    En ver\u00f0a kann, a\u00f0 b\u00e6\u00f0i leikum og l\u00e6r\u00f0um \u00e1 \u00cdslandi \u00feyki h\u00fan\u00a0[\u00fe.e. greinin]<\/em> eigi allau\u00f0skilin, hverju \u00e9g a\u00f0 s\u00f6nnu eigi neita; en \u00fea\u00f0 veldur, a\u00f0 til a\u00f0 skilja hana fullkomnlega, \u00fatheimtast nokkrar grunnst\u00e6\u00f0ur \u00far geometria og \u00fe\u00e6r fyrstu og einf\u00f6ldustu reglur \u00far algebra (e\u00f0a stafareikningi) og trigonometria (e\u00f0a \u00fer\u00edhyrnings-reikningi), hvar um \u00e9g e\u00f0a einhver annar kannski nokku\u00f0 skrifa mun framvegis. \u00dev\u00ed mundi best, a\u00f0 menn fyrst kynni s\u00e9r \u00feessar ge\u00f3metr\u00edsku, algebra\u00edsku og tr\u00edg\u00f3n\u00f3metr\u00edsku grunn-reglur, og lesi s\u00ed\u00f0an me\u00f0 athygli \u00feessa hugvekju um vegst\u00f6ngina og hinar, sem sm\u00e1msaman fylgja munu um \u00fe\u00e6r a\u00f0rar fyrstu og einf\u00f6ldu grunnmask\u00ednur, ver\u00f0ur \u00fe\u00e1 allt vel skili\u00f0.<\/p><\/blockquote>\n

    \u00cd \u00feessari fyrstu grein Stef\u00e1ns um aflfr\u00e6\u00f0i eru l\u00f6g\u00f0 dr\u00f6g a\u00f0 jafnv\u00e6gis-kunn\u00e1ttunni<\/em> (Statica; sem hann kallar einnig jafnvigtar-kunn\u00e1ttu<\/em>) og hr\u00e6ringar-kunn\u00e1ttunni<\/em> (Mechanica). Einnig er fjalla\u00f0 um vegst\u00f6ngina<\/em> (\u00fea\u00f0 er vogarst\u00f6ngina) og notkun hennar. \u00cd seinni greinum er svo r\u00e6tt um hallanda<\/em> (sk\u00e1bor\u00f0 e\u00f0a brekku), hj\u00f3l, trissur, fleyga, skr\u00fafur, sk\u00e1lavogir og rei\u00f0slur. Fyrir \u00fe\u00e1, sem \u00e1huga hafa, m\u00e1 h\u00e9r n\u00e1lgast greinarnar sj\u00e1lfar, \u00e1samt tilheyrandi myndum:<\/p>\n

    (1) Um \u00fe\u00e6r einf\u00f6ldustu grunnmask\u00ednur, og fyrst um vegst\u00f6ngina<\/em> (1781): Texti.<\/a> Myndir.<\/a><\/span><\/p>\n

    (2) Um jafnvigtina \u00e1 hallandanum<\/em> (Plano inclinato) (1784): Fyrri hluti.<\/a> Myndir.<\/a> Seinni hluti.<\/a> <\/span><\/p>\n

    (3) Um jafnvigtina \u00e1 vinduhj\u00f3linu<\/em> (Rota v. axi in peritrochio);\u00a0 Um Jafnvigtina \u00e1 dr\u00e1ttarhj\u00f3linu<\/em> (Trochlea, Tridsen);\u00a0 Um Fleyginn<\/em> (Cuneum, Kilen). (1785): Fyrri hluti.<\/a> Myndir.<\/a> Seinni hluti.<\/a>
    \n<\/span><\/p>\n

    (4) Um Jafnvigtina \u00e1 skr\u00fafunni<\/em> (Cochlea) (1987): Texti.<\/a> Myndir.<\/a>
    \n<\/span><\/p>\n

    (5) Um sk\u00e1lavigt, sem ogsvo kallast metask\u00e1lar, og met \u00e1 \u00fe\u00e1 g\u00f6mlu \u00edslensku<\/em>. (1788): Texti.<\/a> Myndir.<\/a>
    \n<\/span><\/p>\n

    (6) Um rei\u00f0slur og pundara. (1789): Texti.<\/a> Myndir.<\/a> <\/span><\/p>\n

    Ef menn vilja kafa enn d\u00fdpra, m\u00e1 til samanbur\u00f0ar kanna umfj\u00f6llun um einfaldar v\u00e9lar \u00ed tveimur b\u00f3kum, sem Stef\u00e1n Bj\u00f6rnsson \u00feekkti vel. S\u00fa fyrri er anna\u00f0 bindi\u00f0 af verki Christians Wolff, Elementa Matheseos Universae<\/a> (h\u00e9r \u00fatg\u00e1fa fr\u00e1 1746), sj\u00e1 bls. 204-226. Hin s\u00ed\u00f0ari er fyrsta bindi\u00f0 af hinni vins\u00e6lu kennslub\u00f3k Willems ‘s Gravesande, Physices elementa mathematica, experimentis confirmata: sive Introductio ad philosophiam Newtonianam<\/a> (h\u00e9r \u00fatg\u00e1fa fr\u00e1 1725), sj\u00e1 bls. 36-57. <\/span><\/p>\n

    Hvort er mikilv\u00e6gara, skri\u00f0\u00feungi e\u00f0a hreyfiorka?
    \n<\/em><\/span><\/p>\n

    Me\u00f0 St\u00e6r\u00f0fr\u00e6\u00f0il\u00f6gm\u00e1lum n\u00e1tt\u00faruspekinnar<\/em> fr\u00e1 1687 haf\u00f0i Newton lagt st\u00e6r\u00f0fr\u00e6\u00f0ilegan grunn a\u00f0 \u00feeirri fr\u00e6\u00f0igrein, sem vi\u00f0 n\u00fa k\u00f6llum s\u00edgilda aflfr\u00e6\u00f0i og kennum \u00ed framhaldssk\u00f3lum og h\u00e1sk\u00f3lum. \u00dea\u00f0 t\u00f3k n\u00e1tt\u00faruspekinga og a\u00f0ra heimspekinga \u00e1tj\u00e1ndu aldar hins vegar talsver\u00f0an t\u00edma a\u00f0 melta a\u00f0fer\u00f0afr\u00e6\u00f0i meistarans og leggja dr\u00f6g a\u00f0 \u00feeirri hugmyndafr\u00e6\u00f0ilegu t\u00falkun \u00e1 aflfr\u00e6\u00f0inni, sem n\u00fa er talin sj\u00e1lfs\u00f6g\u00f0. Langt fram eftir \u00f6ldinni var \u00fev\u00ed deilt um notkun or\u00f0a og hugtaka og merkingu \u00feeirra, nokku\u00f0 sem vi\u00f0 eigum erfitt me\u00f0 a\u00f0 skilja \u00ed dag.<\/p>\n

    Fr\u00e6gasta deilan snerist um \u00fea\u00f0, hvernig best v\u00e6ri a\u00f0 l\u00fdsa \u201emagninu\u201c, \u201eaflinu\u201c e\u00f0a \u201ekraftinum\u201c sem f\u00f3lgin v\u00e6ri \u00ed hreyfingu hluta. Newton og fylgismenn hans fylgdu \u00ed f\u00f3tspor Descartes<\/a> og v\u00f6ldu \u00fea\u00f0 hugtak, sem vi\u00f0 \u00ed dag k\u00f6llum skri\u00f0\u00feunga. Heimspekingurinn Leibniz<\/a> og hans menn voru \u00fev\u00ed ekki samm\u00e1la. \u00deeir t\u00f6ldu a\u00f0 hugtak, sem Leibniz kalla\u00f0i \u201evis viva\u201c (l\u00edfskraft e\u00f0a l\u00edfsafl) v\u00e6ri mun e\u00f0lilegra \u00ed \u00feessu sambandi, en samkv\u00e6mt n\u00fat\u00edmaskilningi er \u00fea\u00f0 ekkert anna\u00f0 en tv\u00f6f\u00f6ld hreyfiorka. Um \u00feetta efni var \u00ferasa\u00f0 \u00e1ratugum saman, e\u00f0a \u00feanga\u00f0 til \u00fea\u00f0 rann upp fyrir m\u00f6nnum, a\u00f0 \u00fer\u00e1tt fyrir \u00f3l\u00edka merkingu v\u00e6ru b\u00e6\u00f0i hugt\u00f6kin gagnleg.<\/p>\n

    \"\"
    G. W. Leibniz (1646-1716) \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0 \u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 \u00a0 I. Newton (1642-1727)<\/figcaption><\/figure>\n

    \u00c1ri\u00f0 1793 hlaut Stef\u00e1n Bj\u00f6rnsson gullver\u00f0laun Kaupmannahafnarh\u00e1sk\u00f3la \u00ed st\u00e6r\u00f0fr\u00e6\u00f0i (\u00fe.e. st\u00e6r\u00f0fr\u00e6\u00f0ilegum l\u00e6rd\u00f3mslistum) fyrir ritger\u00f0 um \u00e1\u00f0urnefnda deilu \u00feeirra Newtons og Leibniz. Ritger\u00f0in mun l\u00f6ngu t\u00fdnd, en verkefni\u00f0 var \u00feannig or\u00f0a\u00f0:<\/p>\n

    Explicare virum mensuram Neutonianam & Leibnitzianam, & de celebri hac controversia verram dicere sententiam [\u00datsk\u00fdri\u00f0 kraftm\u00e6lingu \u00feeirra Newtons og Leibniz og felli\u00f0 sannan d\u00f3m um hina v\u00ed\u00f0fr\u00e6gu \u00fer\u00e6tu].<\/em><\/p><\/blockquote>\n

    Ums\u00f6gn d\u00f3mnefndar hlj\u00f3\u00f0a\u00f0i svo:<\/p>\n

    Den f\u00f6rste [Afhandling]<\/em> me\u00f0 Devise: Honos alit artes [Vir\u00f0ing elur listir]<\/em>, har meget omst\u00e6ndeligen giennemgaaet Sp\u00f6rgsmaalet og grundigen besvaret samme, saa at denne Afhandling b\u00f6r have Pr\u00e6mien; vi maatte allene anm\u00e6rke, at om den skulle trykkest, da maatte nogle faa tilbageblevne Skriverfeil rettes, og det latinske Sprog paa nogle Steder forbedres. Priisafhandlingens Forfatter er Hr. Steffen Bi\u00f6rnsen, som i forrige Aar erholdt Accessit [hlaut vi\u00f0urkenningu]<\/em>: en Veteraner, som denne Kampplads vel egentligen ikke er bestemt for.<\/p><\/blockquote>\n

    S\u00ed\u00f0asta setningin v\u00edsar til \u00feess, a\u00f0 \u00e1 \u00feessum t\u00edma var Stef\u00e1n or\u00f0inn r\u00famlega sj\u00f6tugur , en ver\u00f0launasamkeppnin var fyrst og fremst\u00a0 hugsu\u00f0 fyrir unga st\u00fadenta vi\u00f0 H\u00e1sk\u00f3lann. \u00dea\u00f0 ver\u00f0ur \u00fe\u00f3 ekki fr\u00e1 Stef\u00e1ni teki\u00f0, a\u00f0 hann var fyrsti \u00cdslendingurinn, sem hlaut \u00feessi ver\u00f0laun (hinir eru Bj\u00f6rn Gunnlaugsson 1818 og 1819, \u00d3lafur Dan Dan\u00edelsson 1901 og Sigur\u00f0ur Helgason 1951).<\/p>\n

    Ritger\u00f0ir um \u00f6lduhreyfingu
    \n<\/em><\/span><\/p>\n

    Fyrstu \u00feekktu tilraunina til a\u00f0 \u00fatsk\u00fdra eiginleika bylgna er a\u00f0 finna hj\u00e1 Newton \u00ed St\u00e6r\u00f0fr\u00e6\u00f0il\u00f6gm\u00e1lum n\u00e1tt\u00faruspekinnar<\/em> (8. kafli \u00ed b\u00f3k 2). L\u00e6risveinar hans, \u00fear \u00e1 me\u00f0al ‘s Gravesande, fj\u00f6llu\u00f0u um \u00feessar vangaveltur \u00ed kennslub\u00f3kum \u00e1 fyrstu \u00e1ratugum \u00e1tj\u00e1ndu aldar, \u00e1n \u00feess \u00fe\u00f3 a\u00f0 b\u00e6ta neinu vi\u00f0. Dan\u00edel Bernoulli n\u00e1lga\u00f0ist vi\u00f0fangsefni\u00f0 fr\u00e1 \u00f6rl\u00edti\u00f0 \u00f6\u00f0ru sj\u00f3narhorni \u00ed b\u00f3k sinni um v\u00f6kvaaflfr\u00e6\u00f0i, Hydrodynamica<\/a>, \u00e1ri\u00f0 1738 (kaflar 6 og 7), en \u00fea\u00f0 var ekki fyrr en Euler haf\u00f0i lagt h\u00f6nd \u00e1 pl\u00f3g \u00ed kringum 1760, sem Laplace<\/a> (1776) og Lagrange<\/a> (\u00e1 n\u00edunda \u00e1ratugnum) leiddu fyrstir \u00fat l\u00ednulegu bylgjuj\u00f6fnuna fyrir litlar sveiflur. Eftir \u00fea\u00f0 fengu fleiri \u00e1huga \u00e1 efninu og enn \u00ed dag er \u00fea\u00f0 tali\u00f0 ver\u00f0ugt vi\u00f0fangsefni fr\u00e6\u00f0imanna.<\/p>\n

    \u00cd byrjun \u00e1rs, 1768, efndi V\u00edsindaf\u00e9lagi<\/em>\u00f0 danska \u00ed fyrsta sinn til ver\u00f0launasamkeppni, \u00fear sem l\u00e6rd\u00f3msm\u00f6nnum var bo\u00f0i\u00f0 a\u00f0 svara spurningum um \u00e1kve\u00f0in verkefni \u00ed st\u00e6r\u00f0fr\u00e6\u00f0ilegum l\u00e6rd\u00f3mslistum.\u00a0 Ef besta ritger\u00f0in var talin n\u00f3gu g\u00f3\u00f0, hlaut h\u00fan ver\u00f0launapening f\u00e9lagsins \u00far gulli. \u00c1ri\u00f0 1791 fjalla\u00f0i verkefni\u00f0 um \u00fea\u00f0 \u201ehvernig st\u00e6r\u00f0 og hra\u00f0i hafaldnanna og breyting \u00e1 \u00f6lduh\u00e6\u00f0 \u00feeirra er h\u00e1\u00f0 v\u00ed\u00f0\u00e1ttu og d\u00fdpi hafsins<\/em>\u201c. Ein ritger\u00f0 barst fr\u00e1 fr\u00f6nskum stj\u00f6rnufr\u00e6\u00f0ingi, en h\u00fan \u00fe\u00f3tti ekki n\u00f3gu g\u00f3\u00f0. \u00dev\u00ed var verkefni\u00f0 lagt fyrir aftur \u00e1ri\u00f0 1793 og \u00fe\u00e1 var Stef\u00e1n Bj\u00f6rnsson eini \u00fe\u00e1tttakandinn. Hann hlaut ver\u00f0launin ekki heldur. \u00c1ri\u00f0 1794 var reynt \u00ed \u00feri\u00f0ja sinn. N\u00fa b\u00e1rust \u00ferj\u00e1r ritger\u00f0ir til f\u00e9lagsins, \u00fear \u00e1 me\u00f0al ein fr\u00e1 Stef\u00e1ni, en h\u00fan var \u00ed raun a\u00f0eins endurb\u00e6tt \u00fatg\u00e1fa fyrri ritger\u00f0arinnar. \u00cd \u00feetta sinn gekk gullpeningurinn \u00fat og hann hlaut franski a\u00f0alsma\u00f0urinn og l\u00e6rd\u00f3msma\u00f0urinn Fran\u00e7ois de la Coudraye<\/a>, sem um \u00fe\u00e6r mundir var landfl\u00f3tta \u00ed Kaupmannah\u00f6fn.<\/p>\n

    Ritger\u00f0ir Stef\u00e1ns eru var\u00f0veittar \u00e1 b\u00f3kasafni V\u00edsindaf\u00e9lagsin<\/em>s \u00ed Kaupmannah\u00f6fn. \u00de\u00e6r eru b\u00e1\u00f0ar handskrifa\u00f0ar \u00e1 lat\u00ednu og innbundnar. S\u00fa fyrri, fr\u00e1 1793, er \u00ed 54 k\u00f6flum og myndskreytt. Hin, fr\u00e1 1795, er \u00ed 84 k\u00f6flum og einnig fallega myndskreytt. Efnislega eru ritger\u00f0irnar eins, en s\u00fa s\u00ed\u00f0ari er heldur \u00edtarlegri og betur uppsett. \u00c9g hef haft t\u00e6kif\u00e6ri til a\u00f0 renna augunum yfir \u00fe\u00e6r b\u00e1\u00f0ar og m\u00e9r s\u00fdnist a\u00f0 Stef\u00e1n sty\u00f0jist fyrst og fremst vi\u00f0 hinar g\u00f6mlu hugmyndir \u00feeirra Newtons og Bernoulli, sem \u00e1\u00f0ur var minnst \u00e1. Til d\u00e6mis kemur \u00e1 \u00f3vart a\u00f0 Euler er fjarverandi.\u00a0 F\u00e1tt n\u00fdtt vir\u00f0ist \u00fev\u00ed koma fram \u00ed ritger\u00f0unum, enda var Stef\u00e1n kominn \u00e1 \u00e1ttr\u00e6\u00f0isaldur, \u00feegar hann samdi \u00fe\u00e6r. Hins vegar er \u00e1st\u00e6\u00f0a til a\u00f0 benda s\u00e9rstaklega \u00e1, a\u00f0 hann var eini Nor\u00f0urlandab\u00fainn sem reyndi vi\u00f0 verkefni\u00f0, sem \u00e1 \u00feessum t\u00edma taldist til \u00f3leystra grundvallarvandam\u00e1la \u00ed aflfr\u00e6\u00f0i v\u00f6kva.<\/p>\n

    \"\"
    Fors\u00ed\u00f0an \u00e1 handskrifa\u00f0ri ritger\u00f0 Stef\u00e1ns, sem hann sendi Hinu konunglega danska v\u00edsindaf\u00e9lagi<\/em> sumari\u00f0 1795. \u00c1 \u00edslensku hlj\u00f3\u00f0ar titillinn svo: Ritger\u00f0, \u00fear sem \u00fatsk\u00fdrt er og s\u00fdnt, hvernig \u00f6lduh\u00e6\u00f0 og \u00f6ldubreidd veltur \u00e1 v\u00edddum vatna, sem vindur hr\u00e6rir<\/em>.<\/figcaption><\/figure>\n
    \"\"
    Myndirnar \u00ed handriti Stef\u00e1ns fr\u00e1 1795.<\/figcaption><\/figure>\n","protected":false},"excerpt":{"rendered":"

    \u00cd f\u00e9lagaskr\u00e1 Hins (konunglega) \u00edslenska l\u00e6rd\u00f3mslistaf\u00e9lags segir um Stef\u00e1n Bj\u00f6rnsson (1721-98) a\u00f0 hann s\u00e9\u00a0\u201eMatheseos et Antiqvitt patri\u00e6 Studiosus\u201c (l\u00e6r\u00f0ur \u00ed st\u00e6r\u00f0fr\u00e6\u00f0i og fornfr\u00e6\u00f0um f\u00f6\u00f0urlandsins). Hann s\u00e1 um fyrstu fr\u00e6\u00f0ilegu \u00fatg\u00e1funa \u00e1 R\u00edmbeglu 1780 og sama \u00e1r kom \u00fat b\u00f3k hans, Ferhyrningafr\u00e6\u00f0i. Hvatinn a\u00f0 seinna verkinu var sennilega margra \u00e1ra starf hans sem reiknimeistari (Kalkulator) vi\u00f0 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,4,14],"tags":[],"_links":{"self":[{"href":"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/index.php?rest_route=\/wp\/v2\/posts\/1207"}],"collection":[{"href":"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1207"}],"version-history":[{"count":0,"href":"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/index.php?rest_route=\/wp\/v2\/posts\/1207\/revisions"}],"wp:attachment":[{"href":"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1207"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1207"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wizardly-antonelli.176-10-35-210.plesk.page\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1207"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}