Axes showing trigonometric angles, and quadrants.

Trigonometric Angles and Quadrants

Axes showing trigonometric angles, and quadrants.

"A, portion of a colony of Antipathes dichotoma. B, single zooid and axis of the same magnified. m, mouth; mf, mesenterial filament; ax, axis. C, transverse section through the oral cone of Antipathella minor; st, stomodaeum; ov, ovary." — The Encyclopedia Britannica, 1910

Antipathes Dichotoma

"A, portion of a colony of Antipathes dichotoma. B, single zooid and axis of the same magnified. m,…

This illustration shows the Appalachian Mountains, a region of numerous flexures on a grand scale, as well as many faults; some flexures having a span of several miles, and others only a few feet or inches.

Appalachian Mountains

This illustration shows the Appalachian Mountains, a region of numerous flexures on a grand scale, as…

The axis, which is the second cervical vertebra. Labels: D, odontoid process of axis; Fas, facet on upper side of atlas with which the skull articulates; Frt, vertebral foramen.

The Axis (2nd Cervical Vertebra)

The axis, which is the second cervical vertebra. Labels: D, odontoid process of axis; Fas, facet on…

Second cervical vertebra, or axis.

Axis

Second cervical vertebra, or axis.

The axis from behind and above.

Axis from Above

The axis from behind and above.

The axis from left side.

Axis from Side

The axis from left side.

The axis from the side.

Axis from the Side

The axis from the side.

The axis from in front.

Front View of Axis

The axis from in front.

"A crystal has a center of symmetry if an imaginary line is passed from some point on its surface through its center, and a similar point is found on the line at an equal distance beyond the center." — Ford, 1912

Symmetry axis

"A crystal has a center of symmetry if an imaginary line is passed from some point on its surface through…

B, the first cervical vertebra, the atlas. A, the atlas, and the second cervical vertebra, the axis; e, the odontoid process; c. the foramen.

The First and Second Cervical Vertebrae

B, the first cervical vertebra, the atlas. A, the atlas, and the second cervical vertebra, the axis;…

"Orthorhombic. Usually in small tabular crystals with hexagonal outline. Striated parallel to the brachy-axis." — Ford, 1912

Chalcocite

"Orthorhombic. Usually in small tabular crystals with hexagonal outline. Striated parallel to the brachy-axis."…

Possible forms of the invariable cone by means of the intersections with a concentric spherical surface.

Invariable Cone

Possible forms of the invariable cone by means of the intersections with a concentric spherical surface.

Two dimensional view of the cuts required to create the conic sections hyperbola, parabola, ellipse, and circle.

Conic Sections 2D

Two dimensional view of the cuts required to create the conic sections hyperbola, parabola, ellipse,…

Three dimensional representation of the intersecting planes required to create the conic sections hyperbola, parabola, ellipse, and circle.

Conic Sections 3D

Three dimensional representation of the intersecting planes required to create the conic sections hyperbola,…

"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…

"Now it is the inclination of the Earth's axis, as above described, which causes the lengths of the days and nights to differ at the same place at different seasons of the year, for on reviewing the positions of the globe at A, it will be observed that the line formed by the enlightened and dark hemispheres, does not coincide with the line of the axis and the pole, but that the line formed by the darkness and the light, extends obliquely across the line of the Earth's axis, so that the north pole is in the light while the south is in the dark. In the position A, therefore, an observer at the north pole would see the sun constantly, while another at the south pole would not see it at all. Hence those living in the north temperate zone, at the season of the year when the earth is at A, or in the Summer, would have long days and short nights, in proportion as they approached the polar circle; while those who live in the south temperate zone, at the same time, and when it would be Winter there, would have long nights and short days in the same proportion." —Comstock, 1850

Earth Axis

"Now it is the inclination of the Earth's axis, as above described, which causes the lengths of the…

"Now it is the inclination of the Earth's axis, as above described, which causes the lengths of the days and nights to differ at the same place at different seasons of the year, for on reviewing the positions of the globe at A, it will be observed that the line formed by the enlightened and dark hemispheres, does not coincide with the line of the axis and the pole, but that the line formed by the darkness and the light, extends obliquely across the line of the Earth's axis, so that the north pole is in the light while the south is in the dark. In the position A, therefore, an observer at the north pole would see the sun constantly, while another at the south pole would not see it at all. Hence those living in the north temperate zone, at the season of the year when the earth is at A, or in the Summer, would have long days and short nights, in proportion as they approached the polar circle; while those who live in the south temperate zone, at the same time, and when it would be Winter there, would have long nights and short days in the same proportion." —Comstock, 1850

Earth Axis

"Now it is the inclination of the Earth's axis, as above described, which causes the lengths of the…

"The earth shown as it would be if its axis were perpendicular to the plane of the orbit." -Wiswell, 1913

Earth's Axis Perpendicular to Plane of Orbit

"The earth shown as it would be if its axis were perpendicular to the plane of the orbit." -Wiswell,…

"A quadrant, or one fourth of a circle. The oblique lines indicate various angles with the base. The heavy line indicates the inclination of the earth's axis as compared with the plane of its orbit, which is represented by the base." -Wiswell, 1913

Inclination of Earth's Axis

"A quadrant, or one fourth of a circle. The oblique lines indicate various angles with the base. The…

"In geometry, an angle connected with an ellipse and defined as ... angle BCL, reckoned from one determinate end, B, of the transverse axis, called the eccentric angle of the point H." -Whitney, 1911

Eccentric Angle

"In geometry, an angle connected with an ellipse and defined as ... angle BCL, reckoned from one determinate…

"The electrical machine most usually employed consists of a large circular plate of glass, mounted upon a metallic axis, and supported upon pillars fixed to a secure base, so that the plate can, by means of a handle, w, be turned with ease. Upon the supports of the glass, and fixed so as to press easily but uniformly on the plate, are four rubbers, marked r r r r in the figure; and flaps of silk, s s, oiled on one side, are attached to these, and secured to fixed supports by several silk cords. When the machine is put in motion, these flaps of silk are drawn tightly against the glass, and thus the friction is increased, and electricity excited. The points p p collect the electricity from the glass, and convey it to the conductor, c, which is supported by the glass rod g." —Wells, 1857

Electrical Machine

"The electrical machine most usually employed consists of a large circular plate of glass, mounted upon…

"A form of an electrical machine. S being the glass cylinder turning on an axis, Y the conductor, F the rubber, A A supports." —Wells, 1857

Electrical Machine

"A form of an electrical machine. S being the glass cylinder turning on an axis, Y the conductor, F…

Draftsman's second method for drawing an ellipse

Ellipse Second Method

Draftsman's second method for drawing an ellipse

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.

"Relative positions of the earth and the sun on March 21 (spring equinox) and September 21 (autumn equinox) as seen from the position occupied by the earth on June 21 (summer solstice). Rays of light and heat meet the earth vertically on the Equator, and the days and nights are everywhere of equal length." -Wiswell, 1913

Spring Equinox and Autumn Equinox

"Relative positions of the earth and the sun on March 21 (spring equinox) and September 21 (autumn equinox)…

"This form consists of twelve isoceles triangular faces, each of which intersects two of the horizontal crystallographic axes equally, is parallel to the third horizontal axis and intersects the vertical axis." — Ford, 1912

Pyramid of the first order

"This form consists of twelve isoceles triangular faces, each of which intersects two of the horizontal…

"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…

This illustration shows a rock formation with folds or flexures in strata. a x represents the axis or axial plane of the fold.

Flexures

This illustration shows a rock formation with folds or flexures in strata. a x represents the axis or…

"The type of instrument which resulted from Russian labors. The brass tube, strengthened at the bearing points by a strong truly-turned collars, rotates in the cast-iron cradle g attached to the declination axis. a is the eye-piece fixed in that axis, b the micrometer for reading both scales." —The Encyclopedia Britannica, 1903

Heliometer

"The type of instrument which resulted from Russian labors. The brass tube, strengthened at the bearing…

An illustration of magnetic curves, "the name given to those curves in which an infinite number of very needles would arrange themselves when placed round a magnet and at liberty to move round an axis." -Century, 1886

Magnetic Curves

An illustration of magnetic curves, "the name given to those curves in which an infinite number of very…

"The horizontal section in the direction of the axis of the telescope. The eye-piece ab consists of two planoconvex lenses a, b, of nearly the same focal length, and with the two convex sides facing each other. They are placed at a distance apart less than the focal length of a, so that the wires of the micrometer, which must be distinctly seen are beyond b. The eye-piece slides into the tube cd, which screws into the brass ring ef, through two openings in which the oblong frame, containing the micrometer slides, passes." —The Encyclopedia Britannica, 1903

Micrometer

"The horizontal section in the direction of the axis of the telescope. The eye-piece ab consists of…

"The vertical section in the direction of the axis of the telescope. The eye-piece ab consists of two planoconvex lenses a, b, of nearly the same focal length, and with the two convex sides facing each other. They are placed at a distance apart less than the focal length of a, so that the wires of the micrometer, which must be distinctly seen are beyond b. The eye-piece slides into the tube cd, which screws into the brass ring ef, through two openings in which the oblong frame, containing the micrometer slides, passes." —The Encyclopedia Britannica, 1903

Micrometer

"The vertical section in the direction of the axis of the telescope. The eye-piece ab consists of two…

"a is the sphere, placed in half-holes on the axis bb, so that when its principal axis is parallel to the axis the telescope it gives only one image of the object. In a direction perpendicular to that axis it must be so placed that when it is moved by rotation of the axis bb the separation of the images shall be parallel to that motion. The angle of rotation is measured on the grduated circle C. The angle between the objects measured is = r sin 20, where r is a constant to be determined for each magnifying power employed." —The Encyclopedia Britannica, 1903

Micrometer

"a is the sphere, placed in half-holes on the axis bb, so that when its principal axis is parallel to…

"a is the sphere, placed in half-holes on the axis bb, so that when its principal axis is parallel to the axis the telescope it gives only one image of the object. In a direction perpendicular to that axis it must be so placed that when it is moved by rotation of the axis bb the separation of the images shall be parallel to that motion. The angle of rotation is measured on the grduated circle C. The angle between the objects measured is = r sin 20, where r is a constant to be determined for each magnifying power employed." —The Encyclopedia Britannica, 1903

Micrometer

"a is the sphere, placed in half-holes on the axis bb, so that when its principal axis is parallel to…

"a, axis cylinder; b, inner border of white substance; c, c, outer border of same; d, d, tubular membrane; B, tubular fibres; e, in natural state; f, under pressure; g, varicose fibres." — Richardson, 1906

Nerves

"a, axis cylinder; b, inner border of white substance; c, c, outer border of same; d, d, tubular membrane;…

Dissection from behind the ligaments connecting the occipital bone, the atlas, and the axis with each other.

Ligaments of the Occipital Bone

Dissection from behind the ligaments connecting the occipital bone, the atlas, and the axis with each…

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.

"Two hoops of thin iron are placed upon an axis which passes through their poles. The two ends of each hoop cross each other at right angles, and are fastened together, and to the axis at the bottom. At the upper end they slide up and down on the axis, which is turned rapidly by wheel-work as represented. These hoops, before the motion begins, have an oval form, but when turned rapidly, the centrifugal force causes them to expand, or swell at the equator, while they are depressed at the poles, the two polar regions becoming no more distant than a and b." —Comstock, 1850

Pole Depression

"Two hoops of thin iron are placed upon an axis which passes through their poles. The two ends of each…

"[The pulley] consists of a wheel with a grooved circumference, over which a rope passes, and an axis or pin, round which the wheel may be made to turn. A represents the block, B the axis, C the wheel." —Quackenbos 1859

Pulley

"[The pulley] consists of a wheel with a grooved circumference, over which a rope passes, and an axis…

A point lies in the first quadrant if the plan lies below, the elevation above the axis; in the second if plan and elevation both lie above; in the third if the plan lies above, the elevation below; in the the fourth if plan and elevation both lie below the axis.

Quadrants

A point lies in the first quadrant if the plan lies below, the elevation above the axis; in the second…

"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…

"Diagram illustrating the points at which incident rays meet the retina. xx, optic axis; k, first nodal point; k', second nodal point; b, point where the image of B would be formed, were the eye properly accommodated for it; a, the retinal point where the image of A would be formed." —Martin, 1917

Retina

"Diagram illustrating the points at which incident rays meet the retina. xx, optic axis; k, first nodal…

"Diagrammatic section through the eyeball. xx, optic axis; k, nodal point." —Martin, 1917

Retina

"Diagrammatic section through the eyeball. xx, optic axis; k, nodal point." —Martin, 1917

"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…

"Proliferous or monstrous Rose, showing the prolongation of the axis beyond the flower. C, calyx transformed into leaves; P. petals multiplied at the expense of the stamens, which are reduced in number; F, colored leaves representing abortive carpels; A, axis prolonged, bearing an imperfect flower at its apex." — Encyclopedia Britanica, 1893

Rose

"Proliferous or monstrous Rose, showing the prolongation of the axis beyond the flower. C, calyx transformed…

"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…

"Fig 56 - Axial skeleton, minus the skull, of an owl, Asio wilsonianus, life size; from nature by Dr. R.W. Shufeldt, USA.at, atlas; ax,axis; cv, cervical vertebrae; c, c', cervical ribs, or free pleurapophyses; dv, dorsal vertebrae, excepting the last one, which joins the sacrum; R, two of the six true ribs (pleurapophyses), whereof sr is sacral; u, one of the five uncinate processes or epipleura; cr, two of the six sternal ribs(haemapophyses), whereof the sixth floats; p, pelvic or sacral region of the spine, comprehending one dorsal, and several lumbar, sacral proper, and urosacral vertebrae; I ilium; Is, ischium; P pubis; a, acetabulum; in, ischio-iliac foremen; o, obturator foramen; clv, caudal or coccygeal vertebrae, whereof py is the pygostyle; s, scapula; ohs, os humero-scapulare; cl, clavicle; C, coracoid; S, sternum." Elliot Coues, 1884

Axial Skeleton

"Fig 56 - Axial skeleton, minus the skull, of an owl, Asio wilsonianus, life size; from nature by Dr.…

These are skew bevel wheels, made of a hyperboloid of revolution around an axis.

Sliding Contact

These are skew bevel wheels, made of a hyperboloid of revolution around an axis.

The lines of contact are equal, but the axes are neither parallel to each other, or the line of contact.

Lateral Sliding Contact

The lines of contact are equal, but the axes are neither parallel to each other, or the line of contact.

"Coil some No. 12 copper wire throuh holes in a board, as shown, and pass a strong current through it. Sprinkle iron filling as before and note the effect. Such a coil of conducting wire, wound so as to afford a number of equal and parallel circular electric circuits arranged upon a common axis, is called a solenoid." -Avery 1895

Solenoid

"Coil some No. 12 copper wire throuh holes in a board, as shown, and pass a strong current through it.…

"Relative positions of the earth and the sun on June 21, the summer solstice. Summer and long days north of the Equator; winter and short days south of it." -Wiswell, 1913

Summer Solstice

"Relative positions of the earth and the sun on June 21, the summer solstice. Summer and long days north…

"Relative positions of the earth and the sun on December 21, the winter solstice. Winter and short days north of the Equator; summer and long days south of it. 1, North Frigid Zone; 2, North Temperate Zone; 3, Torrid Zone; 4, South Temperate Zone; 5, South Frigid Zone." -Wiswell, 1913

Winter Solstice

"Relative positions of the earth and the sun on December 21, the winter solstice. Winter and short days…

Illustration of a sphere generated by the revolution of a semicircle ACB about its diameter AB as an axis.

Sphere Made by Revolution of Semicircle

Illustration of a sphere generated by the revolution of a semicircle ACB about its diameter AB as an…

Transformation of coordinates to new axes.

Transform Coordinates

Transformation of coordinates to new axes.

"One of the most important of astronomical instruments, consists of a telescope fixed to a horizontal axis, so as to revolve in the plane of the meridian, and is employed, as its name denotes, in the observation of the meridian transits of the heavenly bodies. The axis, which is the most important part of the instrument, and thus demands the utmost care in its construction, consists of a hollow sphere or cube, to opposite sides of which are tightly fastened the bases of two cones in whose apices the pivots are screwed; the sphere or cube is pierced for the admission of the telescope, which is firmly soldered at right angles to the axis." — Chambers, 1881

Transit Instrument

"One of the most important of astronomical instruments, consists of a telescope fixed to a horizontal…