When were vectors invented? Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern) Announcing the arrival of Valued Associate #679: Cesar Manara Unicorn Meta Zoo #1: Why another podcast?When was the vector notation in physics and other sciences first introduced?Who invented the integers?When were numbers first used for anything other than counting?When was the cogwheel gear invented?When/How were the product and chain rules first proved?How were vector calculus nabla ∇ identities first derived?Electromagnetics and vector calculusWhen was (and in what paper) Paley-Wiener integral invented?Was mathematics invented or discovered?When were polynomial equations first factored?Earliest Instances of a Slope/Direction Field for a First-Order ODE

Do I really need recursive chmod to restrict access to a folder?

Denied boarding although I have proper visa and documentation. To whom should I make a complaint?

When a candle burns, why does the top of wick glow if bottom of flame is hottest?

What's the meaning of 間時肆拾貳 at a car parking sign

Can I cast Passwall to drop an enemy into a 20-foot pit?

Identify plant with long narrow paired leaves and reddish stems

What causes the vertical darker bands in my photo?

Why is my conclusion inconsistent with the van't Hoff equation?

How widely used is the term Treppenwitz? Is it something that most Germans know?

How can I make names more distinctive without making them longer?

3 doors, three guards, one stone

Why aren't air breathing engines used as small first stages

Dating a Former Employee

What is Wonderstone and are there any references to it pre-1982?

What would be the ideal power source for a cybernetic eye?

What is the logic behind the Maharil's explanation of why we don't say שעשה ניסים on Pesach?

What is Arya's weapon design?

When do you get frequent flier miles - when you buy, or when you fly?

Can an alien society believe that their star system is the universe?

Extract all GPU name, model and GPU ram

Single word antonym of "flightless"

Should I discuss the type of campaign with my players?

How to answer "Have you ever been terminated?"

Error "illegal generic type for instanceof" when using local classes



When were vectors invented?



Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)
Announcing the arrival of Valued Associate #679: Cesar Manara
Unicorn Meta Zoo #1: Why another podcast?When was the vector notation in physics and other sciences first introduced?Who invented the integers?When were numbers first used for anything other than counting?When was the cogwheel gear invented?When/How were the product and chain rules first proved?How were vector calculus nabla ∇ identities first derived?Electromagnetics and vector calculusWhen was (and in what paper) Paley-Wiener integral invented?Was mathematics invented or discovered?When were polynomial equations first factored?Earliest Instances of a Slope/Direction Field for a First-Order ODE










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?










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?










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?










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






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

            Era Viking Índice Início da Era Viquingue | Cotidiano | Sociedade | Língua | Religião | A arte | As primeiras cidades | As viagens dos viquingues | Viquingues do Oeste e Leste | Fim da Era Viquingue | Fontes históricas | Referências Bibliografia | Ligações externas | Menu de navegação«Sverige då!»«Handel I vikingetid»«O que é Nórdico Antigo»Mito, magia e religião na volsunga saga Um olhar sobre a trajetória mítica do herói sigurd«Bonden var den verklige vikingen»«Vikingatiden»«Vikingatiden»«Vinland»«Guerreiras de Óðinn: As Valkyrjor na Mitologia Viking»1519-9053«Esculpindo símbolos e seres: A arte viking em pedras rúnicas»1679-9313Historia - Tema: VikingarnaAventura e Magia no Mundo das Sagas IslandesasEra Vikinge

            What's the metal clinking sound at the end of credits in Avengers: Endgame?What makes Thanos so strong in Avengers: Endgame?Who is the character that appears at the end of Endgame?What happens to Mjolnir (Thor's hammer) at the end of Endgame?The People's Ages in Avengers: EndgameWhat did Nebula do in Avengers: Endgame?Messing with time in the Avengers: Endgame climaxAvengers: Endgame timelineWhat are the time-travel rules in Avengers Endgame?Why use this song in Avengers: Endgame Opening Logo Sequence?Peggy's age in Avengers Endgame

            Mortes em março de 2019 Referências Menu de navegação«Zhores Alferov, Nobel de Física bielorrusso, morre aos 88 anos - Ciência»«Fallece Rafael Torija, o bispo emérito de Ciudad Real»«Peter Hurford dies at 88»«Keith Flint, vocalista do The Prodigy, morre aos 49 anos»«Luke Perry, ator de 'Barrados no baile' e 'Riverdale', morre aos 52 anos»«Former Rangers and Scotland captain Eric Caldow dies, aged 84»«Morreu, aos 61 anos, a antiga lenda do wrestling King Kong Bundy»«Fallece el actor y director teatral Abraham Stavans»«In Memoriam Guillaume Faye»«Sidney Sheinberg, a Force Behind Universal and Spielberg, Is Dead at 84»«Carmine Persico, Colombo Crime Family Boss, Is Dead at 85»«Dirigent Michael Gielen gestorben»«Ciclista tricampeã mundial e prata na Rio 2016 é encontrada morta em casa aos 23 anos»«Pagan Community Notes: Raven Grimassi dies, Indianapolis pop-up event cancelled, Circle Sanctuary announces new podcast, and more!»«Hal Blaine, Wrecking Crew Drummer, Dies at 90»«Morre Coutinho, que editou dupla lendária com Pelé no Santos»«Cantor Demétrius, ídolo da Jovem Guarda, morre em SP»«Ex-presidente do Vasco, Eurico Miranda morre no Rio de Janeiro»«Bronze no Mundial de basquete de 1971, Laís Elena morre aos 76 anos»«Diretor de Corridas da F1, Charlie Whiting morre aos 66 anos às vésperas do GP da Austrália»«Morreu o cardeal Danneels, da Bélgica»«Morreu o cartoonista Augusto Cid»«Morreu a atriz Maria Isabel de Lizandra, de "Vale Tudo" e novelas da Tupi»«WS Merwin, prize-winning poet of nature, dies at 91»«Atriz Márcia Real morre em São Paulo aos 88 anos»«Mauritanie: décès de l'ancien président Mohamed Mahmoud ould Louly»«Morreu Dick Dale, o rei da surf guitar e de "Pulp Fiction"»«Falleció Víctor Genes»«João Carlos Marinho, autor de 'O Gênio do Crime', morre em SP»«Legendary Horror Director and SFX Artist John Carl Buechler Dies at 66»«Morre em Salvador a religiosa Makota Valdina»«مرگ بازیکن‌ سابق نساجی بر اثر سقوط سنگ در مازندران»«Domingos Oliveira morre no Rio»«Morre Airton Ravagniani, ex-São Paulo, Fla, Vasco, Grêmio e Sport - Notícias»«Morre o escritor Flavio Moreira da Costa»«Larry Cohen, Writer-Director of 'It's Alive' and 'Hell Up in Harlem,' Dies at 77»«Scott Walker, experimental singer-songwriter, dead at 76»«Joseph Pilato, Day of the Dead Star and Horror Favorite, Dies at 70»«Sheffield United set to pay tribute to legendary goalkeeper Ted Burgin who has died at 91»«Morre Rafael Henzel, sobrevivente de acidente aéreo da Chapecoense»«Morre Valery Bykovsky, um dos primeiros cosmonautas da União Soviética»«Agnès Varda, cineasta da Nouvelle Vague, morre aos 90 anos»«Agnès Varda, cineasta francesa, morre aos 90 anos»«Tania Mallet, James Bond Actress and Helen Mirren's Cousin, Dies at 77»e