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Intersecting with the x-axis / intersecting the x-axis


“proficient <in/at/with>” What is the correct usage?Can any transitive verb be accompanied by a preposition?Using prepositions with timeUsing a verb +prep in a sentence with prepositions at the frontIs “augmented with” or “augmented by” preferable?Verb “escape”: with or without preposition?What is the difference between “rotation around / along” an axis?Single preposition to choose with several verbsUsing “to” with “listen”Fascinated by or with?






.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;








1















Which is correct?:
"The function intersects with the x-axis" or "The function intersects the x-axis"



Is the verb 'to intersect' in the mathematical sense accompanied by the preposition 'with'?










share|improve this question




























    1















    Which is correct?:
    "The function intersects with the x-axis" or "The function intersects the x-axis"



    Is the verb 'to intersect' in the mathematical sense accompanied by the preposition 'with'?










    share|improve this question
























      1












      1








      1








      Which is correct?:
      "The function intersects with the x-axis" or "The function intersects the x-axis"



      Is the verb 'to intersect' in the mathematical sense accompanied by the preposition 'with'?










      share|improve this question














      Which is correct?:
      "The function intersects with the x-axis" or "The function intersects the x-axis"



      Is the verb 'to intersect' in the mathematical sense accompanied by the preposition 'with'?







      prepositions






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked 2 hours ago









      StallmpStallmp

      1085




      1085




















          2 Answers
          2






          active

          oldest

          votes


















          4














          The second is correct. Geometrically, lines "intersect one another". It is incorrect to include "with", which would render the verb "intersect" intransitive. The geometrical meaning is OED - sense 1b in the OED:




          1b. Geometry. Of a line or surface: To pass through or across (a line
          or surface), so as to lie on both sides of it with one point (or line)
          in common: = cut v. 15b. 1646 Sir T. Browne Pseudodoxia Epidemica
          vi. v. 292 Being in the Æquator it would intersect their Horizon,
          and be halfe above and halfe beneath it. 1700 Moxon's Mech.
          Exercises: Bricklayers-wks. 30 Where these two Arches Intersect, or
          cut each other, there is the Center. 1840 D. Lardner Treat. Geom. x.
          125 If two chords intersect each other in a circle, the rectangle
          under the segments of the one will be equal to the rectangle under the
          segments of the other. 1858 O. W. Holmes Autocrat of Breakfast-table
          xii. 330 Keep any line of knowledge ten years and some other line
          will intersect it. 1873 B. Williamson Elem. Treat. Differential
          Calculus (ed. 2) xiii. §190 Every [straight] line must intersect a
          curve of an odd degree in at least one real point.




          There is an intransitive form of "intersect", but it does not involve the use of "with". It is used where the intersecting parties are collectively the subject of the verb. It is sense 2a.




          2a. intransitive (for reflexive). To cross or cut each another:
          chiefly Geometry of lines or surfaces. 1755 in Johnson: quoting
          Wiseman in error: see quot. 1676 at interject v. 2a. 1849 G. Grote
          Hist. Greece VI. ii. xlvii. 27 Straight streets intersecting at
          right angles. 1869 J. Tyndall Notes 9 Lect. on Light 24 The rays
          from a luminous point placed beyond the focus intersect at the
          opposite side of the lens. 1873 B. Williamson Elem. Treat.
          Differential Calculus (ed. 2) xiv. §204 The Lemniscate whose
          equation is (x2 + y2)2 = a (x2 − y2)..[has] two branches intersecting
          at the origin.




          It would seem that the use of "intersect with" is an incorrect form.






          share|improve this answer






























            3














            While one might interact with something, one intersects something. From Merriam-Webster:




            intersect verb



            in·​ter·​sect | ˌin-tər-ˈsekt



            intersected; intersecting; intersects



            Definition of intersect



            transitive verb



            : to pierce or divide by passing through or across : CROSS



            // a comet intersecting earth's orbit



            // one line intersects another



            intransitive verb



            1 : to meet and cross at a point



            // lines intersecting at right angles



            2 : to share a common area : OVERLAP



            //where morality and self-interest intersect







            share|improve this answer























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              2 Answers
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              2 Answers
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              active

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              active

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              4














              The second is correct. Geometrically, lines "intersect one another". It is incorrect to include "with", which would render the verb "intersect" intransitive. The geometrical meaning is OED - sense 1b in the OED:




              1b. Geometry. Of a line or surface: To pass through or across (a line
              or surface), so as to lie on both sides of it with one point (or line)
              in common: = cut v. 15b. 1646 Sir T. Browne Pseudodoxia Epidemica
              vi. v. 292 Being in the Æquator it would intersect their Horizon,
              and be halfe above and halfe beneath it. 1700 Moxon's Mech.
              Exercises: Bricklayers-wks. 30 Where these two Arches Intersect, or
              cut each other, there is the Center. 1840 D. Lardner Treat. Geom. x.
              125 If two chords intersect each other in a circle, the rectangle
              under the segments of the one will be equal to the rectangle under the
              segments of the other. 1858 O. W. Holmes Autocrat of Breakfast-table
              xii. 330 Keep any line of knowledge ten years and some other line
              will intersect it. 1873 B. Williamson Elem. Treat. Differential
              Calculus (ed. 2) xiii. §190 Every [straight] line must intersect a
              curve of an odd degree in at least one real point.




              There is an intransitive form of "intersect", but it does not involve the use of "with". It is used where the intersecting parties are collectively the subject of the verb. It is sense 2a.




              2a. intransitive (for reflexive). To cross or cut each another:
              chiefly Geometry of lines or surfaces. 1755 in Johnson: quoting
              Wiseman in error: see quot. 1676 at interject v. 2a. 1849 G. Grote
              Hist. Greece VI. ii. xlvii. 27 Straight streets intersecting at
              right angles. 1869 J. Tyndall Notes 9 Lect. on Light 24 The rays
              from a luminous point placed beyond the focus intersect at the
              opposite side of the lens. 1873 B. Williamson Elem. Treat.
              Differential Calculus (ed. 2) xiv. §204 The Lemniscate whose
              equation is (x2 + y2)2 = a (x2 − y2)..[has] two branches intersecting
              at the origin.




              It would seem that the use of "intersect with" is an incorrect form.






              share|improve this answer



























                4














                The second is correct. Geometrically, lines "intersect one another". It is incorrect to include "with", which would render the verb "intersect" intransitive. The geometrical meaning is OED - sense 1b in the OED:




                1b. Geometry. Of a line or surface: To pass through or across (a line
                or surface), so as to lie on both sides of it with one point (or line)
                in common: = cut v. 15b. 1646 Sir T. Browne Pseudodoxia Epidemica
                vi. v. 292 Being in the Æquator it would intersect their Horizon,
                and be halfe above and halfe beneath it. 1700 Moxon's Mech.
                Exercises: Bricklayers-wks. 30 Where these two Arches Intersect, or
                cut each other, there is the Center. 1840 D. Lardner Treat. Geom. x.
                125 If two chords intersect each other in a circle, the rectangle
                under the segments of the one will be equal to the rectangle under the
                segments of the other. 1858 O. W. Holmes Autocrat of Breakfast-table
                xii. 330 Keep any line of knowledge ten years and some other line
                will intersect it. 1873 B. Williamson Elem. Treat. Differential
                Calculus (ed. 2) xiii. §190 Every [straight] line must intersect a
                curve of an odd degree in at least one real point.




                There is an intransitive form of "intersect", but it does not involve the use of "with". It is used where the intersecting parties are collectively the subject of the verb. It is sense 2a.




                2a. intransitive (for reflexive). To cross or cut each another:
                chiefly Geometry of lines or surfaces. 1755 in Johnson: quoting
                Wiseman in error: see quot. 1676 at interject v. 2a. 1849 G. Grote
                Hist. Greece VI. ii. xlvii. 27 Straight streets intersecting at
                right angles. 1869 J. Tyndall Notes 9 Lect. on Light 24 The rays
                from a luminous point placed beyond the focus intersect at the
                opposite side of the lens. 1873 B. Williamson Elem. Treat.
                Differential Calculus (ed. 2) xiv. §204 The Lemniscate whose
                equation is (x2 + y2)2 = a (x2 − y2)..[has] two branches intersecting
                at the origin.




                It would seem that the use of "intersect with" is an incorrect form.






                share|improve this answer

























                  4












                  4








                  4







                  The second is correct. Geometrically, lines "intersect one another". It is incorrect to include "with", which would render the verb "intersect" intransitive. The geometrical meaning is OED - sense 1b in the OED:




                  1b. Geometry. Of a line or surface: To pass through or across (a line
                  or surface), so as to lie on both sides of it with one point (or line)
                  in common: = cut v. 15b. 1646 Sir T. Browne Pseudodoxia Epidemica
                  vi. v. 292 Being in the Æquator it would intersect their Horizon,
                  and be halfe above and halfe beneath it. 1700 Moxon's Mech.
                  Exercises: Bricklayers-wks. 30 Where these two Arches Intersect, or
                  cut each other, there is the Center. 1840 D. Lardner Treat. Geom. x.
                  125 If two chords intersect each other in a circle, the rectangle
                  under the segments of the one will be equal to the rectangle under the
                  segments of the other. 1858 O. W. Holmes Autocrat of Breakfast-table
                  xii. 330 Keep any line of knowledge ten years and some other line
                  will intersect it. 1873 B. Williamson Elem. Treat. Differential
                  Calculus (ed. 2) xiii. §190 Every [straight] line must intersect a
                  curve of an odd degree in at least one real point.




                  There is an intransitive form of "intersect", but it does not involve the use of "with". It is used where the intersecting parties are collectively the subject of the verb. It is sense 2a.




                  2a. intransitive (for reflexive). To cross or cut each another:
                  chiefly Geometry of lines or surfaces. 1755 in Johnson: quoting
                  Wiseman in error: see quot. 1676 at interject v. 2a. 1849 G. Grote
                  Hist. Greece VI. ii. xlvii. 27 Straight streets intersecting at
                  right angles. 1869 J. Tyndall Notes 9 Lect. on Light 24 The rays
                  from a luminous point placed beyond the focus intersect at the
                  opposite side of the lens. 1873 B. Williamson Elem. Treat.
                  Differential Calculus (ed. 2) xiv. §204 The Lemniscate whose
                  equation is (x2 + y2)2 = a (x2 − y2)..[has] two branches intersecting
                  at the origin.




                  It would seem that the use of "intersect with" is an incorrect form.






                  share|improve this answer













                  The second is correct. Geometrically, lines "intersect one another". It is incorrect to include "with", which would render the verb "intersect" intransitive. The geometrical meaning is OED - sense 1b in the OED:




                  1b. Geometry. Of a line or surface: To pass through or across (a line
                  or surface), so as to lie on both sides of it with one point (or line)
                  in common: = cut v. 15b. 1646 Sir T. Browne Pseudodoxia Epidemica
                  vi. v. 292 Being in the Æquator it would intersect their Horizon,
                  and be halfe above and halfe beneath it. 1700 Moxon's Mech.
                  Exercises: Bricklayers-wks. 30 Where these two Arches Intersect, or
                  cut each other, there is the Center. 1840 D. Lardner Treat. Geom. x.
                  125 If two chords intersect each other in a circle, the rectangle
                  under the segments of the one will be equal to the rectangle under the
                  segments of the other. 1858 O. W. Holmes Autocrat of Breakfast-table
                  xii. 330 Keep any line of knowledge ten years and some other line
                  will intersect it. 1873 B. Williamson Elem. Treat. Differential
                  Calculus (ed. 2) xiii. §190 Every [straight] line must intersect a
                  curve of an odd degree in at least one real point.




                  There is an intransitive form of "intersect", but it does not involve the use of "with". It is used where the intersecting parties are collectively the subject of the verb. It is sense 2a.




                  2a. intransitive (for reflexive). To cross or cut each another:
                  chiefly Geometry of lines or surfaces. 1755 in Johnson: quoting
                  Wiseman in error: see quot. 1676 at interject v. 2a. 1849 G. Grote
                  Hist. Greece VI. ii. xlvii. 27 Straight streets intersecting at
                  right angles. 1869 J. Tyndall Notes 9 Lect. on Light 24 The rays
                  from a luminous point placed beyond the focus intersect at the
                  opposite side of the lens. 1873 B. Williamson Elem. Treat.
                  Differential Calculus (ed. 2) xiv. §204 The Lemniscate whose
                  equation is (x2 + y2)2 = a (x2 − y2)..[has] two branches intersecting
                  at the origin.




                  It would seem that the use of "intersect with" is an incorrect form.







                  share|improve this answer












                  share|improve this answer



                  share|improve this answer










                  answered 2 hours ago









                  WS2WS2

                  52.6k28117253




                  52.6k28117253























                      3














                      While one might interact with something, one intersects something. From Merriam-Webster:




                      intersect verb



                      in·​ter·​sect | ˌin-tər-ˈsekt



                      intersected; intersecting; intersects



                      Definition of intersect



                      transitive verb



                      : to pierce or divide by passing through or across : CROSS



                      // a comet intersecting earth's orbit



                      // one line intersects another



                      intransitive verb



                      1 : to meet and cross at a point



                      // lines intersecting at right angles



                      2 : to share a common area : OVERLAP



                      //where morality and self-interest intersect







                      share|improve this answer



























                        3














                        While one might interact with something, one intersects something. From Merriam-Webster:




                        intersect verb



                        in·​ter·​sect | ˌin-tər-ˈsekt



                        intersected; intersecting; intersects



                        Definition of intersect



                        transitive verb



                        : to pierce or divide by passing through or across : CROSS



                        // a comet intersecting earth's orbit



                        // one line intersects another



                        intransitive verb



                        1 : to meet and cross at a point



                        // lines intersecting at right angles



                        2 : to share a common area : OVERLAP



                        //where morality and self-interest intersect







                        share|improve this answer

























                          3












                          3








                          3







                          While one might interact with something, one intersects something. From Merriam-Webster:




                          intersect verb



                          in·​ter·​sect | ˌin-tər-ˈsekt



                          intersected; intersecting; intersects



                          Definition of intersect



                          transitive verb



                          : to pierce or divide by passing through or across : CROSS



                          // a comet intersecting earth's orbit



                          // one line intersects another



                          intransitive verb



                          1 : to meet and cross at a point



                          // lines intersecting at right angles



                          2 : to share a common area : OVERLAP



                          //where morality and self-interest intersect







                          share|improve this answer













                          While one might interact with something, one intersects something. From Merriam-Webster:




                          intersect verb



                          in·​ter·​sect | ˌin-tər-ˈsekt



                          intersected; intersecting; intersects



                          Definition of intersect



                          transitive verb



                          : to pierce or divide by passing through or across : CROSS



                          // a comet intersecting earth's orbit



                          // one line intersects another



                          intransitive verb



                          1 : to meet and cross at a point



                          // lines intersecting at right angles



                          2 : to share a common area : OVERLAP



                          //where morality and self-interest intersect








                          share|improve this answer












                          share|improve this answer



                          share|improve this answer










                          answered 2 hours ago









                          wonkypianowonkypiano

                          1022




                          1022



























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