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











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asked 3 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


















2












$begingroup$

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









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    1 Answer
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    1 Answer
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    $begingroup$

    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









    $endgroup$


















      2












      $begingroup$

      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









      $endgroup$
















        2












        2








        2





        $begingroup$

        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






























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