Axes showing trigonometric angles, and quadrants.

Trigonometric Angles and Quadrants

Axes showing trigonometric angles, and quadrants.

An ax, from Prehistoric man.

Ax

An ax, from Prehistoric man.

An iron tool with a steel edge, for hewing and chopping.

Ax

An iron tool with a steel edge, for hewing and chopping.

An ax of flint.

Ax

An ax of flint.

Diagram showing all of the different axes of symmetry of a cube.

Axes of Symmetry of a Cube

Diagram showing all of the different axes of symmetry of a cube.

An illustration of four various axes: "1, Horseman's hammer of about the time of Edward IV; 2, Martel-de-fer, time of Henry VIII; 3, Martel-de-fer, time of Edward VI; 4, Martel-de-fer with hand-gun, time of Queen Elizabeth." -Century, 1889

Four Axes

An illustration of four various axes: "1, Horseman's hammer of about the time of Edward IV; 2, Martel-de-fer,…

Three bronze celts (axes). Not drawn to scale.

Bronze Age Bronze Celts

Three bronze celts (axes). Not drawn to scale.

Conjugate diameters perpendicular to each other are called, axes, and the points where they cut the curve vertices of the conic.

Conic Axes

Conjugate diameters perpendicular to each other are called, axes, and the points where they cut the…

Copper axes from the Bronze age. Not drawn to scale.

Bronze Age Copper Axes

Copper axes from the Bronze age. Not drawn to scale.

"...take any three edges formed by the intersection of three faces of a crystal. These axes are called the crystallographic axes, and the planes in which they lie are the axial planes. A fourth face on the crystal intersecting these three axes in the points A, B, C is taken as the parametral plan, and the lengths OA:OB:OC are the parameters of the crystal." -The Encyclopedia Britannica 1910

Crystallographic Axes of Reference

"...take any three edges formed by the intersection of three faces of a crystal. These axes are called…

"Science has succeeded in classifying the thousands of known crystals in six systems, to each of which belongs a number of forms having some property in common. In order to classify these different crystals, the existence of certain lines within the crystal, called axes, is assumed, around which the form can be symmetrically build up. These axes are assumed to intersect in the center of the crystal, and to pass through from one side to the other." — Hallock, 1905

Cube

"Science has succeeded in classifying the thousands of known crystals in six systems, to each of which…

Illustration of an ellipse with major and minor axes.

Ellipse With Axes

Illustration of an ellipse with major and minor axes.

Illustration used to show how to draw an ellipse when given the diameters.

Construction Of Ellipse

Illustration used to show how to draw an ellipse when given the diameters.

Illustration used to show how to draw an ellipse by circular arcs.

Construction Of Ellipse

Illustration used to show how to draw an ellipse by circular arcs.

Diagram showing how to construct an ellipse when given the two foci and the length of the major axis (2a).

Construction of an Ellipse

Diagram showing how to construct an ellipse when given the two foci and the length of the major axis…

An illustration of 2 ellipses that have the equal vertical axes, but different horizontal axes. The ellipse on the left has a larger horizontal axis than the ellipse on the right.

2 Ellipses With Equal Vertical Axes

An illustration of 2 ellipses that have the equal vertical axes, but different horizontal axes. The…

An illustration of 2 ellipses that have the equal vertical axes, but different horizontal axes. The ellipse on the left has a larger horizontal axis than the ellipse on the right. The ellipse on the left has equal horizontal and vertical axes, making it a circle.

2 Ellipses With Equal Vertical Axes

An illustration of 2 ellipses that have the equal vertical axes, but different horizontal axes. The…

An illustration of 3 concentric ellipses that are tangent at the end points of the vertical axes. The horizontal axes (the major axes of the ellipses) decreases in size in each successive ellipse. The major axis equals the minor axis in the smallest ellipse, thus forming a circle.

3 Concentric Ellipses

An illustration of 3 concentric ellipses that are tangent at the end points of the vertical axes. The…

An illustration of 3 concentric ellipses that are tangent at the end points of the vertical axes, which is drawn in the illustration. The horizontal axes decreases in size in each successive ellipse. The major axis is horizontal for the outmost ellipse and vertical for the innermost ellipse. When the major and minor axes are equal, the result is a circle (as in the second/middle ellipse).

3 Concentric Ellipses

An illustration of 3 concentric ellipses that are tangent at the end points of the vertical axes, which…

An illustration of 3 concentric ellipses that are tangent at the end points of the vertical axes. The horizontal axes decreases in size in each successive ellipse. The major axis is horizontal for the outmost ellipse and vertical for the innermost ellipse. When the major and minor axes are equal, the result is a circle (as in the second/middle ellipse).

3 Concentric Ellipses

An illustration of 3 concentric ellipses that are tangent at the end points of the vertical axes. The…

An illustration of 4 concentric ellipses that are tangent at the end points of the vertical axes. The horizontal axes (the major axes of the ellipses) decreases in size in each successive ellipse.

4 Concentric Ellipses

An illustration of 4 concentric ellipses that are tangent at the end points of the vertical axes. The…

An illustration of 4 concentric ellipses that are tangent at the end points of the vertical axes. The horizontal axes decreases in size in each successive ellipse. The major axis is horizontal for the outer two ellipses and vertical for the innermost ellipse. When the major and minor axes are equal, the result is a circle (as in the third ellipse).

4 Concentric Ellipses

An illustration of 4 concentric ellipses that are tangent at the end points of the vertical axes. The…

An illustration of 4 concentric ellipses that are tangent at the end points of the vertical axes, which is drawn in the illustration. The horizontal axes decreases in size in each successive ellipse. The major axis is horizontal for the outer two ellipses and vertical for the innermost ellipse. When the major and minor axes are equal, the result is a circle (as in the third ellipse).

4 Concentric Ellipses

An illustration of 4 concentric ellipses that are tangent at the end points of the vertical axes, which…

An illustration of 5 concentric ellipses that are tangent at the end points of the vertical axes. The horizontal axes decreases in size in each successive ellipse. The major axis is horizontal for the outer three ellipses and vertical for the innermost ellipse. When the major and minor axes are equal, the result is a circle (as in the fourth ellipse).

5 Concentric Ellipses

An illustration of 5 concentric ellipses that are tangent at the end points of the vertical axes. The…

An illustration of 5 concentric ellipses that are tangent at the end points of the vertical axes, which is drawn in the illustration. The horizontal axes decreases in size in each successive ellipse. The major axis is horizontal for the outer three ellipses and vertical for the innermost ellipse. When the major and minor axes are equal, the result is a circle (as in the fourth ellipse).

5 Concentric Ellipses

An illustration of 5 concentric ellipses that are tangent at the end points of the vertical axes, which…

An illustration of 6 concentric ellipses that are tangent at the end points of the vertical axes. The horizontal axes decreases in size in each successive ellipse. The major axis is horizontal for the outer four ellipses and vertical for the innermost ellipse. When the major and minor axes are equal, the result is a circle (as in the fifth ellipse).

6 Concentric Ellipses

An illustration of 6 concentric ellipses that are tangent at the end points of the vertical axes. The…

An illustration of 6 concentric ellipses that are tangent at the end points of the vertical axes, which is drawn in the illustration. The horizontal axes decreases in size in each successive ellipse. The major axis is horizontal for the outer four ellipses and vertical for the innermost ellipse. When the major and minor axes are equal, the result is a circle (as in the fifth ellipse).

6 Concentric Ellipses

An illustration of 6 concentric ellipses that are tangent at the end points of the vertical axes, which…

"Science has succeeded in classifying the thousands of known crystals in six systems, to each of which belongs a number of forms having some property in common. In order to classify these different crystals, the existence of certain lines within the crystal, called axes, is assumed, around which the form can be symmetrically build up. These axes are assumed to intersect in the center of the crystal, and to pass through from one side to the other." — Hallock, 1905

First Right Square Octahedron

"Science has succeeded in classifying the thousands of known crystals in six systems, to each of which…

"Science has succeeded in classifying the thousands of known crystals in six systems, to each of which belongs a number of forms having some property in common. In order to classify these different crystals, the existence of certain lines within the crystal, called axes, is assumed, around which the form can be symmetrically build up. These axes are assumed to intersect in the center of the crystal, and to pass through from one side to the other." — Hallock, 1905

First Right Square Prism

"Science has succeeded in classifying the thousands of known crystals in six systems, to each of which…

A small axe with a short handle, to be used with one hand.

Hatchet

A small axe with a short handle, to be used with one hand.

Diagram showing how to construct a hyperbola when given the two foci and the length of the major axis (2a).

Construction of a Hyperbola

Diagram showing how to construct a hyperbola when given the two foci and the length of the major axis…

Lictors were guards of magistrates who carried fasces to show power to execute.

Lictors with Fasces

Lictors were guards of magistrates who carried fasces to show power to execute.

A kind of pick-axe, having the iron ends broad, instead of pointed.

Mattock

A kind of pick-axe, having the iron ends broad, instead of pointed.

"Prisims with edges parallel to neither of the axes OX and OY...are usually called hemi-pyramids." -The Encyclopedia Britannica

Monoclinic Axes and Hemi-pyramid

"Prisims with edges parallel to neither of the axes OX and OY...are usually called hemi-pyramids." -The…

Illustration used to show how to draw an egg-shaped oval when given the diameters.

Construction Of Oval

Illustration used to show how to draw an egg-shaped oval when given the diameters.

"Crystal faces are described according to their relations to the crystallographic axes. A series of numbers which indicate the relative distances by which a face intersects the different axes are called its parameters." — Ford, 1912

Orthohombie prism

"Crystal faces are described according to their relations to the crystallographic axes. A series of…

"Crystal faces are described according to their relations to the crystallographic axes. A series of numbers which indicate the relative distances by which a face intersects the different axes are called its parameters." — Ford, 1912

Orthorhombie pyramid

"Crystal faces are described according to their relations to the crystallographic axes. A series of…

"The symmetry of the Pyritohedral class is as follows: The three crystal axes of binary symmetry; the four diagonal axes, each of which emerges in the middle of the octant, are axes of trigonal symmetry." — Ford, 1912

Symmetry of pyritohedral class

"The symmetry of the Pyritohedral class is as follows: The three crystal axes of binary symmetry; the…

"Science has succeeded in classifying the thousands of known crystals in six systems, to each of which belongs a number of forms having some property in common. In order to classify these different crystals, the existence of certain lines within the crystal, called axes, is assumed, around which the form can be symmetrically build up. These axes are assumed to intersect in the center of the crystal, and to pass through from one side to the other." — Hallock, 1905

Regular Octahedron

"Science has succeeded in classifying the thousands of known crystals in six systems, to each of which…

"Science has succeeded in classifying the thousands of known crystals in six systems, to each of which belongs a number of forms having some property in common. In order to classify these different crystals, the existence of certain lines within the crystal, called axes, is assumed, around which the form can be symmetrically build up. These axes are assumed to intersect in the center of the crystal, and to pass through from one side to the other." — Hallock, 1905

Regular Tetrahedron

"Science has succeeded in classifying the thousands of known crystals in six systems, to each of which…

"Science has succeeded in classifying the thousands of known crystals in six systems, to each of which belongs a number of forms having some property in common. In order to classify these different crystals, the existence of certain lines within the crystal, called axes, is assumed, around which the form can be symmetrically build up. These axes are assumed to intersect in the center of the crystal, and to pass through from one side to the other." — Hallock, 1905

Rhombic Dodecahedron

"Science has succeeded in classifying the thousands of known crystals in six systems, to each of which…

"Science has succeeded in classifying the thousands of known crystals in six systems, to each of which belongs a number of forms having some property in common. In order to classify these different crystals, the existence of certain lines within the crystal, called axes, is assumed, around which the form can be symmetrically build up. These axes are assumed to intersect in the center of the crystal, and to pass through from one side to the other." — Hallock, 1905

Second Right Square Octahedron

"Science has succeeded in classifying the thousands of known crystals in six systems, to each of which…

"Science has succeeded in classifying the thousands of known crystals in six systems, to each of which belongs a number of forms having some property in common. In order to classify these different crystals, the existence of certain lines within the crystal, called axes, is assumed, around which the form can be symmetrically build up. These axes are assumed to intersect in the center of the crystal, and to pass through from one side to the other." — Hallock, 1905

Second Right Square Prism

"Science has succeeded in classifying the thousands of known crystals in six systems, to each of which…

Stone and horn ax and hammer. A Neolithic age implement. Not drawn to scale.

Neolithic Implements Stone and Horn Ax and Hammer

Stone and horn ax and hammer. A Neolithic age implement. Not drawn to scale.

"The symmetry of this class is as follows: The three crystallographic axes are axes of binary symmetry; the four diagonal axes are axes of trigonal symmetry; there are six diagonal planes of symmetry." — Ford, 1912

Symmetry of tetrahedral class

"The symmetry of this class is as follows: The three crystallographic axes are axes of binary symmetry;…

Transformation of coordinates to new axes.

Transform Coordinates

Transformation of coordinates to new axes.

"Umbel is formed when the secondary axes originate from the same point on the stem, and rise to nearly the same height. The whole is called a universal umbel. If the secondary axes develop tertiary ones in the same manner, each is called a partial umbel."—Darby, 1855

Umbels

"Umbel is formed when the secondary axes originate from the same point on the stem, and rise to nearly…