When were vectors invented?












1












$begingroup$


Encyclopedia Britannica says,




In their modern form, vectors appeared late in the 19th century when Josiah Willard Gibbs and Oliver Heaviside (...) independently developed vector analysis to express the new laws of electromagnetism discovered by ... James Clerk Maxwell.




The phrase "in their modern form" suggests vectors were perhaps
used earlier in other forms. There seems to be no deep mathematical
idea needed for vectors to be "invented" and used much earlier.
Can anyone suggest some earlier uses of what we now call vectors?
E.g., did Newton use vectors?






mathematics mathematical-physics







share|improve this question









$endgroup$












  • $begingroup$
    Hermann Grassmann is credited with the first known use of what we know call a vector space in his foundational papers on linear algebra written in 1840 but not published until his Collected Works 1894-1911.
    $endgroup$
    – Nick R
    1 hour ago
















1












$begingroup$


Encyclopedia Britannica says,




In their modern form, vectors appeared late in the 19th century when Josiah Willard Gibbs and Oliver Heaviside (...) independently developed vector analysis to express the new laws of electromagnetism discovered by ... James Clerk Maxwell.




The phrase "in their modern form" suggests vectors were perhaps
used earlier in other forms. There seems to be no deep mathematical
idea needed for vectors to be "invented" and used much earlier.
Can anyone suggest some earlier uses of what we now call vectors?
E.g., did Newton use vectors?






mathematics mathematical-physics







share|improve this question









$endgroup$












  • $begingroup$
    Hermann Grassmann is credited with the first known use of what we know call a vector space in his foundational papers on linear algebra written in 1840 but not published until his Collected Works 1894-1911.
    $endgroup$
    – Nick R
    1 hour ago














1












1








1





$begingroup$


Encyclopedia Britannica says,




In their modern form, vectors appeared late in the 19th century when Josiah Willard Gibbs and Oliver Heaviside (...) independently developed vector analysis to express the new laws of electromagnetism discovered by ... James Clerk Maxwell.




The phrase "in their modern form" suggests vectors were perhaps
used earlier in other forms. There seems to be no deep mathematical
idea needed for vectors to be "invented" and used much earlier.
Can anyone suggest some earlier uses of what we now call vectors?
E.g., did Newton use vectors?






mathematics mathematical-physics







share|improve this question









$endgroup$




Encyclopedia Britannica says,




In their modern form, vectors appeared late in the 19th century when Josiah Willard Gibbs and Oliver Heaviside (...) independently developed vector analysis to express the new laws of electromagnetism discovered by ... James Clerk Maxwell.




The phrase "in their modern form" suggests vectors were perhaps
used earlier in other forms. There seems to be no deep mathematical
idea needed for vectors to be "invented" and used much earlier.
Can anyone suggest some earlier uses of what we now call vectors?
E.g., did Newton use vectors?






mathematics mathematical-physics




mathematics mathematical-physics






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked 4 hours ago









Joseph O'RourkeJoseph O'Rourke

563213




563213












  • $begingroup$
    Hermann Grassmann is credited with the first known use of what we know call a vector space in his foundational papers on linear algebra written in 1840 but not published until his Collected Works 1894-1911.
    $endgroup$
    – Nick R
    1 hour ago


















  • $begingroup$
    Hermann Grassmann is credited with the first known use of what we know call a vector space in his foundational papers on linear algebra written in 1840 but not published until his Collected Works 1894-1911.
    $endgroup$
    – Nick R
    1 hour ago
















$begingroup$
Hermann Grassmann is credited with the first known use of what we know call a vector space in his foundational papers on linear algebra written in 1840 but not published until his Collected Works 1894-1911.
$endgroup$
– Nick R
1 hour ago




$begingroup$
Hermann Grassmann is credited with the first known use of what we know call a vector space in his foundational papers on linear algebra written in 1840 but not published until his Collected Works 1894-1911.
$endgroup$
– Nick R
1 hour ago










1 Answer
1






active

oldest

votes


















3












$begingroup$

This question was actually discussed on this site several times, for example here:
When was the vector notation in physics and other sciences first introduced?
It indeed looks strange to modern people but this simple idea came so late late.
Maxwell never uses vectors in his Treatise on electricity and magnetism,
which makes his notation somewhat clumsy.



In fact the idea had a predecessor: quaternions. Yes, quaternions were invented before vectors:-) And Newton did not use vectors in the explicit form.



Instead people thought in very "roundabout", complicated ways about subjects which we routinely treat with vectors nowadays. A striking example is the famous theorem of Apollonius, about "equivalence of excentric and epicycle". Motion on epicycle means that a point moves on a circle around the center (E), while the planet moves on another circle (of smaller radius) around this point. Excentric means that the planet moves on a circle of large radius whose center is different from E, and this center rotates about E (on a circle of small radius).



To us it seems completely evident that these two things are the same. If you look into
Apollonius proof of this, you see that he really proves commutativity of vector addition. And Ptolemy prises Apollonius for this.






share|improve this answer









$endgroup$














    Your Answer








    StackExchange.ready(function() {
    var channelOptions = {
    tags: "".split(" "),
    id: "587"
    };
    initTagRenderer("".split(" "), "".split(" "), channelOptions);

    StackExchange.using("externalEditor", function() {
    // Have to fire editor after snippets, if snippets enabled
    if (StackExchange.settings.snippets.snippetsEnabled) {
    StackExchange.using("snippets", function() {
    createEditor();
    });
    }
    else {
    createEditor();
    }
    });

    function createEditor() {
    StackExchange.prepareEditor({
    heartbeatType: 'answer',
    autoActivateHeartbeat: false,
    convertImagesToLinks: false,
    noModals: true,
    showLowRepImageUploadWarning: true,
    reputationToPostImages: null,
    bindNavPrevention: true,
    postfix: "",
    imageUploader: {
    brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
    contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
    allowUrls: true
    },
    noCode: true, onDemand: true,
    discardSelector: ".discard-answer"
    ,immediatelyShowMarkdownHelp:true
    });


    }
    });














    draft saved

    draft discarded


















    StackExchange.ready(
    function () {
    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fhsm.stackexchange.com%2fquestions%2f8488%2fwhen-were-vectors-invented%23new-answer', 'question_page');
    }
    );

    Post as a guest















    Required, but never shown

























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    3












    $begingroup$

    This question was actually discussed on this site several times, for example here:
    When was the vector notation in physics and other sciences first introduced?
    It indeed looks strange to modern people but this simple idea came so late late.
    Maxwell never uses vectors in his Treatise on electricity and magnetism,
    which makes his notation somewhat clumsy.



    In fact the idea had a predecessor: quaternions. Yes, quaternions were invented before vectors:-) And Newton did not use vectors in the explicit form.



    Instead people thought in very "roundabout", complicated ways about subjects which we routinely treat with vectors nowadays. A striking example is the famous theorem of Apollonius, about "equivalence of excentric and epicycle". Motion on epicycle means that a point moves on a circle around the center (E), while the planet moves on another circle (of smaller radius) around this point. Excentric means that the planet moves on a circle of large radius whose center is different from E, and this center rotates about E (on a circle of small radius).



    To us it seems completely evident that these two things are the same. If you look into
    Apollonius proof of this, you see that he really proves commutativity of vector addition. And Ptolemy prises Apollonius for this.






    share|improve this answer









    $endgroup$


















      3












      $begingroup$

      This question was actually discussed on this site several times, for example here:
      When was the vector notation in physics and other sciences first introduced?
      It indeed looks strange to modern people but this simple idea came so late late.
      Maxwell never uses vectors in his Treatise on electricity and magnetism,
      which makes his notation somewhat clumsy.



      In fact the idea had a predecessor: quaternions. Yes, quaternions were invented before vectors:-) And Newton did not use vectors in the explicit form.



      Instead people thought in very "roundabout", complicated ways about subjects which we routinely treat with vectors nowadays. A striking example is the famous theorem of Apollonius, about "equivalence of excentric and epicycle". Motion on epicycle means that a point moves on a circle around the center (E), while the planet moves on another circle (of smaller radius) around this point. Excentric means that the planet moves on a circle of large radius whose center is different from E, and this center rotates about E (on a circle of small radius).



      To us it seems completely evident that these two things are the same. If you look into
      Apollonius proof of this, you see that he really proves commutativity of vector addition. And Ptolemy prises Apollonius for this.






      share|improve this answer









      $endgroup$
















        3












        3








        3





        $begingroup$

        This question was actually discussed on this site several times, for example here:
        When was the vector notation in physics and other sciences first introduced?
        It indeed looks strange to modern people but this simple idea came so late late.
        Maxwell never uses vectors in his Treatise on electricity and magnetism,
        which makes his notation somewhat clumsy.



        In fact the idea had a predecessor: quaternions. Yes, quaternions were invented before vectors:-) And Newton did not use vectors in the explicit form.



        Instead people thought in very "roundabout", complicated ways about subjects which we routinely treat with vectors nowadays. A striking example is the famous theorem of Apollonius, about "equivalence of excentric and epicycle". Motion on epicycle means that a point moves on a circle around the center (E), while the planet moves on another circle (of smaller radius) around this point. Excentric means that the planet moves on a circle of large radius whose center is different from E, and this center rotates about E (on a circle of small radius).



        To us it seems completely evident that these two things are the same. If you look into
        Apollonius proof of this, you see that he really proves commutativity of vector addition. And Ptolemy prises Apollonius for this.






        share|improve this answer









        $endgroup$



        This question was actually discussed on this site several times, for example here:
        When was the vector notation in physics and other sciences first introduced?
        It indeed looks strange to modern people but this simple idea came so late late.
        Maxwell never uses vectors in his Treatise on electricity and magnetism,
        which makes his notation somewhat clumsy.



        In fact the idea had a predecessor: quaternions. Yes, quaternions were invented before vectors:-) And Newton did not use vectors in the explicit form.



        Instead people thought in very "roundabout", complicated ways about subjects which we routinely treat with vectors nowadays. A striking example is the famous theorem of Apollonius, about "equivalence of excentric and epicycle". Motion on epicycle means that a point moves on a circle around the center (E), while the planet moves on another circle (of smaller radius) around this point. Excentric means that the planet moves on a circle of large radius whose center is different from E, and this center rotates about E (on a circle of small radius).



        To us it seems completely evident that these two things are the same. If you look into
        Apollonius proof of this, you see that he really proves commutativity of vector addition. And Ptolemy prises Apollonius for this.







        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered 3 hours ago









        Alexandre EremenkoAlexandre Eremenko

        25.4k13593




        25.4k13593






























            draft saved

            draft discarded




















































            Thanks for contributing an answer to History of Science and Mathematics Stack Exchange!


            • Please be sure to answer the question. Provide details and share your research!

            But avoid …



            • Asking for help, clarification, or responding to other answers.

            • Making statements based on opinion; back them up with references or personal experience.


            Use MathJax to format equations. MathJax reference.


            To learn more, see our tips on writing great answers.




            draft saved


            draft discarded














            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fhsm.stackexchange.com%2fquestions%2f8488%2fwhen-were-vectors-invented%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown





















































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown

































            Required, but never shown














            Required, but never shown












            Required, but never shown







            Required, but never shown







            -

            Popular posts from this blog

            Knooppunt Holsloot

            Image
            Knooppunt Holsloot Kenmerken Wegen A37 × N34 Type knooppunt klaverblad Portaal     Verkeer & Vervoer Knooppunt Holsloot is een verkeersknooppunt op de kruising van de autosnelweg A37 en de N34 in Drenthe, tussen Emmen en Coevorden. Oorspronkelijk was deze aansluiting een afritconstructie van het type Haarlemmermeeraansluiting, zoals bij Knooppunt Hooipolder. Sinds 2002 is het knooppunt omgebouwd tot een volledig klaverblad. Als noviteit werd hier voor het eerst gebruikgemaakt van dimbare verlichting in plaats van de normale vaste tijden waarop de verlichting aan en uit gaat, wat een grote kostenbesparing opleverde. [1] Dat Holsloot als volwaardig knooppunt is uitgevoerd, waarbij alle verkeersstromen en afbuigingen ononderbroken kunnen doorgaan, is uitzonderlijk. Het betreft hier namelijk een aansluiting tussen een autosnelweg en niet-snelweg. Een vergelijkbare situatie treft men nabij Hoensbroek bij het knooppunt Ten Esschen.     Aa
            Read more

            Altaar (religie)

            Image
            Deel van de serie over kerkelijk gerei waaronder paramenten en liturgisch vaatwerk gebruikt in de liturgie Liturgisch vaatwerk Vasa sacra Miskelk · Pateen Kelklepeltje Ciborie · Monstrans Pyxis · Custodiale Vasa non sacra Ampullen · Wijwatervat Olievaatje Wierookvat · Ablutievat Paramenten Amict · Albe · Baarkleed · Cingel Tuniek · Dalmatiek · Fanon Kazuifel · Manipel · Stola Gremiale · Benedictievelum Mijter Koorkledij Rochet · Superplie Koorkap · Cappa magna Kovel Kelkgerei Bursa · Kelkvelum Ciborievelum Kerklinnen Corporale · Kelkdoekje Lavabodoekje · Palla Altaardwaal Kerkinterieur Altaar · Ambo Biechtstoel · Communiebank Doksaal · Doopvont Faldistorium Godslamp · Hoogaltaar Heilig Kruisaltaar Katheder · Preekstoel Sedilia Tabernakel · Volksaltaar Liturgische boeken Altaarmissaal Benedictionale · Brevier Evangeliarium · Evangelistarium Graduale · Kyriale Lectionarium Psalter · Rituaal Sacramentarium · Volksmissaal Overige Flambou
            Read more

            Gregoriusmis

            Image
            Een afbeelding van de Gregoriusmis uit een getijdenboek gemaakt in de zuidelijke Nederlanden tussen 1500 en 1525 Gregoriusmis, Meester van het Akense Altaar, ca. 1500-1525. Collectie Museum Catharijneconvent De Gregoriusmis of de Mis van Sint Gregorius is een motief in katholieke kunst, dat het eerst verscheen in de late Middeleeuwen en dat nog steeds werd gebruikt tijdens de contrareformatie. Paus Gregorius I (ca. 540-604) is afgebeeld, de H. Mis opdragend, terwijl Christus als de Man van Smarten verschijnt op het altaar dat voor Sint Gregorius staat. Volgens de legende had St. Gregorius gebeden om een teken voor een betwijfelaar van de transsubstantiatieleer, waarop de lijdende Christus tijdens het opdragen van de Mis verscheen om hem te overtuigen en waarbij zijn bloed in de altaarkelk liep. Vaak zijn ook de passiewerktuigen afgebeeld. Zie de categorie Mass of Saint Gregory van Wikimedia Commons voor mediabestanden over dit onderwerp. This page is onl
            Read more