principal axisn.

Brit.

/ˌprɪnsᵻpl ˈaksɪs/, U.S.

/ˌprɪnsəp(ə)l ˈæksəs/

Origin: Formed within English, by compounding. Etymons: principal adj., axis n.¹

Etymology: < principal adj. + axis n.¹ Compare French axe principal (1797 or earlier in sense 1a; 1811 or earlier in sense 1c, in a mechanics context; 1857 or earlier in sense 1c, in a mineralogy context; 1858 or earlier in sense 1b).

a. Mathematics. The axis of symmetry of a conic which passes through the foci; the transverse axis. Contrasted with conjugate axis.

ΘΚΠ

the world > relative properties > number > geometry > geometric space > [noun] > division or marking of > axis > passing through foci

principal axis1704

transverse axis1704

transverse1743

longitudinal axis1744

focal axis1794

major axis1840

1704 C. Hayes Treat. Fluxions p. vii All those Lines which intersect the Parabola in one point only are parallel to the Principal Axis.

1842 Penny Cycl. XXIII. 304/2 For the elliptic paraboloid, let a parabola revolve about its principal axis, and let the circular sections become ellipses.

1951 W. W. Elliott & E. R. C. Miles College Math. (ed. 2) xx. 284 The hyperbola is symmetric with respect to a line through its center and perpendicular to its principal axis, although it does not cut this line.

b. Optics. The optical axis of a lens.

ΘΚΠ

the world > matter > physics > electromagnetic radiation > light > emission of light, radiation > [noun] > line of vision

axle-tree1624

axis1701

principal axisa1764

a1764 J. Harris Treat. Optics (1775) ii. 196 If the object is a strait line or a plane, placed at right angles to the principal axis AO, its geometrical image will always be concave.

1889 E. J. Wall Dict. Photogr. 151 Principal axis is the right line which joins the centres of curvature of the spherical surfaces of a lens.

1962 M. L. Haselgrove Photographers' Dict. 141 (caption) A beam parallel to the principal axis will not be brought to a focus at the principal focus; marginal rays will converge to M while axial rays converge to A.

c. Chiefly Mathematics and Crystallography. Each of three chief lines of reference in a body or system (often mutually perpendicular), such as those used in relation to forces, moments of inertia, etc. Also: each of the axes of a conic or quadric surface with respect to which the figure's equation has the simplest possible form.

ΚΠ

1854 Philos. Trans. (Royal Soc.) 144 100 Let the fixed point be taken for the origin, and the principal axes of the body through that point for the axes of x, y, z.

1879 W. Thomson & P. G. Tait Treat. Nat. Philos. (new ed.) I: Pt. i. 262 Any axis is called a principal axis of a body's inertia, or simply a principal axis of the body, if when the body rotates round it the centrifugal forces either balance or are reducible to a single force.

1940 Proc. Royal Soc. A. 174 59 With rotation axis parallel to principal axis a₁, sharp reflexions due to potash-felspar lie on straight layer-lines.

1992 S. P. Maran Astron. & Astrophysics Encycl. 225/2 The principal axes of the velocity ellipsoid are oriented along the cardinal directions of the galactic coordinate frame, except for the youngest stars.

1999 I. Kostov & R. I. Kostov Crystal Habits Minerals iv. 66 The transition of the crystal habits along the principal axis runs in an analogous manner as with the axial minerals.

2. A main line of extension or growth.

ΘΚΠ

the world > space > direction > [noun] > main line of direction

principal axis1793

axis1818

1793 Philos. Trans. (Royal Soc.) 83 76 These several parts constitute the principal axis of the instrument [sc. an equatorial telescope], the lower end of which terminates in a steel point or cone.

1867 A. Barry Life & Wks. Sir C. Barry vii. 240 The principal axis of the building.

1947 T. J. Reynolds & E. Kent Struct. Steelwork (ed. 8) xi. 212 A load..eccentric with respect to both principal axes of a column section.

1998 L. Margulis & K. V. Schwartz Five Kingdoms (ed. 3) v. 400/1 In Cycas and Dioon , the petioles (leaf stalks) of shed leaves cover the trunk (the principal axis of the cycad, also called the stem).

This entry has been updated (OED Third Edition, June 2007; most recently modified version published online March 2022).

7. Geometry. Any line in a regular figure which divides it into two symmetrical parts, e.g., which joins opposite angles or the centres of opposite sides; in a conic section, the line from the principal vertex or vertices, perpendicular to the tangent at that point; in a curve, a straight line which bisects a system of parallel chords (called principal axis when it cuts them at right angles). transverse axis (in the ellipse and hyperbola): that which passes through the two foci; conjugate axis, that which bisects the transverse one at right angles. The axes of an ellipse are also called major and minor.

ΘΚΠ

the world > relative properties > number > geometry > line > [noun] > other

medial line1570

radius1590

lineature1630

foot line1658

rectification1685

axis1734

slant side1824

radiant1842

transverse1867

median1883

bilinear1923

1734 Builder's Dict. Axis of a Conic Section, is a quiescent Right Line passing through the Middle of the Figure, and cutting all the Ordinates at Right Angles.

1796 C. Hutton Math. & Philos. Dict. (new ed.) I. 177 Axis..more generally..a right line conceived to be drawn from the vertex of a figure to the middle of the base.

1796 C. Hutton Math. & Philos. Dict. (new ed.) I. 177 The ellipse and hyperbola have each two axes; but the parabola has only one, and that infinite in length.

1796 in C. Hutton Math. & Philos. Dict. I. 177 In curves of the second order, that diameter whose parallel ordinates are at right angles to it, when possible, is an Axis.

1849 M. Somerville On Connexion Physical Sci. (ed. 8) xxi. 201 Cut longitudinally, that is, parallel to the axis of the prism.

1853 J. F. W. Herschel Pop. Lect. Sci. (1873) vi. §23. 106 The longer axes or longest dimensions of their orbits.

1879 W. Thomson & P. G. Tait Treat. Nat. Philos. (new ed.) I: Pt. i. §120.

单词	principal axis
释义	principal axisn. Brit. /ˌprɪnsᵻpl ˈaksɪs/, U.S. /ˌprɪnsəp(ə)l ˈæksəs/ Origin: Formed within English, by compounding. Etymons: principal adj., axis n.¹ Etymology: < principal adj. + axis n.¹ Compare French axe principal (1797 or earlier in sense 1a; 1811 or earlier in sense 1c, in a mechanics context; 1857 or earlier in sense 1c, in a mineralogy context; 1858 or earlier in sense 1b). 1. a. Mathematics. The axis of symmetry of a conic which passes through the foci; the transverse axis. Contrasted with conjugate axis. ΘΚΠ the world > relative properties > number > geometry > geometric space > [noun] > division or marking of > axis > passing through foci principal axis1704 transverse axis1704 transverse1743 longitudinal axis1744 focal axis1794 major axis1840 1704 C. Hayes Treat. Fluxions p. vii All those Lines which intersect the Parabola in one point only are parallel to the Principal Axis. 1842 Penny Cycl. XXIII. 304/2 For the elliptic paraboloid, let a parabola revolve about its principal axis, and let the circular sections become ellipses. 1951 W. W. Elliott & E. R. C. Miles College Math. (ed. 2) xx. 284 The hyperbola is symmetric with respect to a line through its center and perpendicular to its principal axis, although it does not cut this line. b. Optics. The optical axis of a lens. ΘΚΠ the world > matter > physics > electromagnetic radiation > light > emission of light, radiation > [noun] > line of vision axle-tree1624 axis1701 principal axisa1764 a1764 J. Harris Treat. Optics (1775) ii. 196 If the object is a strait line or a plane, placed at right angles to the principal axis AO, its geometrical image will always be concave. 1889 E. J. Wall Dict. Photogr. 151 Principal axis is the right line which joins the centres of curvature of the spherical surfaces of a lens. 1962 M. L. Haselgrove Photographers' Dict. 141 (caption) A beam parallel to the principal axis will not be brought to a focus at the principal focus; marginal rays will converge to M while axial rays converge to A. c. Chiefly Mathematics and Crystallography. Each of three chief lines of reference in a body or system (often mutually perpendicular), such as those used in relation to forces, moments of inertia, etc. Also: each of the axes of a conic or quadric surface with respect to which the figure's equation has the simplest possible form. ΚΠ 1854 Philos. Trans. (Royal Soc.) 144 100 Let the fixed point be taken for the origin, and the principal axes of the body through that point for the axes of x, y, z. 1879 W. Thomson & P. G. Tait Treat. Nat. Philos. (new ed.) I: Pt. i. 262 Any axis is called a principal axis of a body's inertia, or simply a principal axis of the body, if when the body rotates round it the centrifugal forces either balance or are reducible to a single force. 1940 Proc. Royal Soc. A. 174 59 With rotation axis parallel to principal axis a₁, sharp reflexions due to potash-felspar lie on straight layer-lines. 1992 S. P. Maran Astron. & Astrophysics Encycl. 225/2 The principal axes of the velocity ellipsoid are oriented along the cardinal directions of the galactic coordinate frame, except for the youngest stars. 1999 I. Kostov & R. I. Kostov Crystal Habits Minerals iv. 66 The transition of the crystal habits along the principal axis runs in an analogous manner as with the axial minerals. 2. A main line of extension or growth. ΘΚΠ the world > space > direction > [noun] > main line of direction principal axis1793 axis1818 1793 Philos. Trans. (Royal Soc.) 83 76 These several parts constitute the principal axis of the instrument [sc. an equatorial telescope], the lower end of which terminates in a steel point or cone. 1867 A. Barry Life & Wks. Sir C. Barry vii. 240 The principal axis of the building. 1947 T. J. Reynolds & E. Kent Struct. Steelwork (ed. 8) xi. 212 A load..eccentric with respect to both principal axes of a column section. 1998 L. Margulis & K. V. Schwartz Five Kingdoms (ed. 3) v. 400/1 In Cycas and Dioon , the petioles (leaf stalks) of shed leaves cover the trunk (the principal axis of the cycad, also called the stem). This entry has been updated (OED Third Edition, June 2007; most recently modified version published online March 2022). > as lemmas principal axis 7. Geometry. Any line in a regular figure which divides it into two symmetrical parts, e.g., which joins opposite angles or the centres of opposite sides; in a conic section, the line from the principal vertex or vertices, perpendicular to the tangent at that point; in a curve, a straight line which bisects a system of parallel chords (called principal axis when it cuts them at right angles). transverse axis (in the ellipse and hyperbola): that which passes through the two foci; conjugate axis, that which bisects the transverse one at right angles. The axes of an ellipse are also called major and minor. ΘΚΠ the world > relative properties > number > geometry > line > [noun] > other medial line1570 radius1590 lineature1630 foot line1658 rectification1685 axis1734 slant side1824 radiant1842 transverse1867 median1883 bilinear1923 1734 Builder's Dict. Axis of a Conic Section, is a quiescent Right Line passing through the Middle of the Figure, and cutting all the Ordinates at Right Angles. 1796 C. Hutton Math. & Philos. Dict. (new ed.) I. 177 Axis..more generally..a right line conceived to be drawn from the vertex of a figure to the middle of the base. 1796 C. Hutton Math. & Philos. Dict. (new ed.) I. 177 The ellipse and hyperbola have each two axes; but the parabola has only one, and that infinite in length. 1796 in C. Hutton Math. & Philos. Dict. I. 177 In curves of the second order, that diameter whose parallel ordinates are at right angles to it, when possible, is an Axis. 1849 M. Somerville On Connexion Physical Sci. (ed. 8) xxi. 201 Cut longitudinally, that is, parallel to the axis of the prism. 1853 J. F. W. Herschel Pop. Lect. Sci. (1873) vi. §23. 106 The longer axes or longest dimensions of their orbits. 1879 W. Thomson & P. G. Tait Treat. Nat. Philos. (new ed.) I: Pt. i. §120. extracted from axisn.¹ < n.1704 as lemmas
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principal axisn.

> as lemmas