ClipArt ETC
"Two cylinders, one horizontal, the other perpendicular. The base of the horizontal cylinder is at one angle of 40° with the PP. The sun's inclination 50°m elevation 28°." (Britannica, 1891)

Shadows of Two Cylinders

"Two cylinders, one horizontal, the other perpendicular. The base of the horizontal cylinder is at one…

"Endless screw, a mechanical arrangement consisting of a screw the thread of which gears into a wheel with skew teeth, the obliquity corresponding to the angle of pitch of the screw." -Whitney, 1911

Endless Screw and Wheel

"Endless screw, a mechanical arrangement consisting of a screw the thread of which gears into a wheel…

Illustration of two triangles, showing the sine of the sum of two acute angles expressed in terms of the sines and cosines of the angles.

Sum of 2 Acute Angles

Illustration of two triangles, showing the sine of the sum of two acute angles expressed in terms of…

Illustration of an angle with the terminal side used to draw a triangle in quadrant II.

Triangle in Quadrant II

Illustration of an angle with the terminal side used to draw a triangle in quadrant II.

Illustration that can be used to show that when given an angle, expressed as an inverse function of u, it can be used to find the value of any function of the angle in terms of u.

Angle Expressed As An Inverse Function

Illustration that can be used to show that when given an angle, expressed as an inverse function of…

Illustration that can be used to show that if the cotangent of an angle is negative the angle must terminate in either the second or fourth quadrant.

Negative Cotangent Angles

Illustration that can be used to show that if the cotangent of an angle is negative the angle must terminate…

Illustration two types of triangles that can be used to model the law of sines. "In a plane triangle any two sides are to each other as the sines of the opposite angles."

Law of Sines

Illustration two types of triangles that can be used to model the law of sines. "In a plane triangle…

Illustration of one possible outcome (no triangle occurs) when discussing the ambiguous case using the Law of Sines. In this case, side a is less than the height (bsinα).

Ambiguous Case

Illustration of one possible outcome (no triangle occurs) when discussing the ambiguous case using the…

Illustration of one possible outcome (1 triangle occurs) when discussing the ambiguous case using the Law of Sines. In this case, side a is equal to the height (bsinα).

Ambiguous Case

Illustration of one possible outcome (1 triangle occurs) when discussing the ambiguous case using the…

Illustration of one possible outcome (2 triangles occur) when discussing the ambiguous case using the Law of Sines. In this case, side a is greater than the height (bsinα).

Ambiguous Case

Illustration of one possible outcome (2 triangles occur) when discussing the ambiguous case using the…

Illustration of an angle &alpha with the terminal side used to draw a triangle in quadrant I.

Triangle in Quadrant I

Illustration of an angle &alpha with the terminal side used to draw a triangle in quadrant I.

Illustration of an angle &alpha with the vertex at the center, O, of a circle with radius OB. AC and BD are perpendicular to OB and join B with C. The are of the triangle OBC is less than the are of the sector OBC, and the sector OBC is less than the triangle OBD.

Triangles and Sectors in Quadrant I

Illustration of an angle &alpha with the vertex at the center, O, of a circle with radius OB. AC and…

Illustration used, with the law of sines, to find the relation between two sides of a spherical triangle and the angles opposite.

Relationships In A Spherical Triangle

Illustration used, with the law of sines, to find the relation between two sides of a spherical triangle…

Illustration used, with the law of cosines, to find the relation between the three sides and an angle of a spherical triangle.

Relationships In A Spherical Triangle

Illustration used, with the law of cosines, to find the relation between the three sides and an angle…

Illustration used to extend the law of cosines when finding the relation between the three sides and an angle of a spherical triangle. In this case both angles b and c are greater than 90°.

Relationships In A Spherical Triangle

Illustration used to extend the law of cosines when finding the relation between the three sides and…

Illustration used to extend the law of cosines when finding the relation between the three sides and an angle of a spherical triangle. In this case angle b<90&deg; and angle c>90&deg;.

Relationships In A Spherical Triangle

Illustration used to extend the law of cosines when finding the relation between the three sides and…

Illustration of a right spherical triangle with a and b the sides, and &alpha; and &beta; the angles opposite them. Side c is the hypotenuse.

Right Spherical Triangle

Illustration of a right spherical triangle with a and b the sides, and α and β the angles…

Illustration of a right spherical triangle and the five circular parts placed in the sectors of a circle in the order in which they occur in the triangle. "The ten formulas used in the solution of spherical right triangles can be expressed by means of two rules, known as Napier's rules of circular parts."

Napier's Right Spherical Triangle

Illustration of a right spherical triangle and the five circular parts placed in the sectors of a circle…

This Antique simpula is a right angled spoon.

Antique Simpula

This Antique simpula is a right angled spoon.

This Antique simpula is a right angled spoon.

Antique Simpula

This Antique simpula is a right angled spoon.

Illustration used to show how to construct a bisector of an angle when the sides intersect within the limits of the drawing.

Bisect An Angle

Illustration used to show how to construct a bisector of an angle when the sides intersect within the…

Illustration used to show how to construct a bisector of an angle when the sides no not intersect within the limits of the drawing.

Bisect An Angle

Illustration used to show how to construct a bisector of an angle when the sides no not intersect within…

Illustration used to show how to "draw a straight line through any given point on a given straight line to make any required angle with that line."

Construction Of Angle On Straight Line

Illustration used to show how to "draw a straight line through any given point on a given straight line…

Illustration used to show how to draw a triangle when given two sides and the included angle of the triangle.

Construction Of Triangle

Illustration used to show how to draw a triangle when given two sides and the included angle of the…

Illustration of the projection of a rectangular prism whose broad side makes an angle of 30&deg; with the horizontal.

Projection Of Rectangular Prism

Illustration of the projection of a rectangular prism whose broad side makes an angle of 30° with…

Illustration of the projection of a rectangular prism whose base makes an angle of 160&deg; with the horizontal.

Projection Of Rectangular Prism

Illustration of the projection of a rectangular prism whose base makes an angle of 160° with the…

Illustration of the projection of a rectangular prism whose base makes an angle of 17.5&deg; with the horizontal.

Projection Of Rectangular Prism

Illustration of the projection of a rectangular prism whose base makes an angle of 17.5° with the…

Illustration of the projection of a hexagonal prism having two of its parallel sides parallel to the plane of the paper, and its axis vertical. instead of a side elevation at right angles to the horizontal, the angle is 30&deg; with the horizontal.

Projection Of Hexagonal Prism

Illustration of the projection of a hexagonal prism having two of its parallel sides parallel to the…

Illustration of the projection of a hexagonal prism whose axis is parallel to the plane of the paper and whose base makes and angle of 30&deg; with the horizontal.

Projection Of Hexagonal Prism

Illustration of the projection of a hexagonal prism whose axis is parallel to the plane of the paper…

Illustration of the projection of a cylinder whose axis is parallel to the plane of the paper and makes an angle of 77&deg; with the horizontal.

Projection Of Cylinder

Illustration of the projection of a cylinder whose axis is parallel to the plane of the paper and makes…

Illustration of a cylinder cut by a plane making an angle of 57&deg; with the base.

Plane Intersecting A Cylinder

Illustration of a cylinder cut by a plane making an angle of 57° with the base.

From this angle it is easy to see the bay window at the front of the house. A large fireplace is situated along the right wall of the parlor. The kitchen has a walk-in pantry. The sitting room is large and extends the wall of the house, giving it character. The master bedroom on the second floor has a large walk-in closet. In 1917, this medium-sized house cost between $2,600 and $2,800 to build depending on the locality.

"The Baldwin" Floor Plans

From this angle it is easy to see the bay window at the front of the house. A large fireplace is situated…

Illustration of the intersection of a quadrangular prism and an octagonal prism. The figures intersect at a right angle.

Intersecting Prisms

Illustration of the intersection of a quadrangular prism and an octagonal prism. The figures intersect…

Illustration of the intersection of an octagonal prism and a cylinder. The figures intersect at an oblique angle.

Intersecting Prism and Cylinder

Illustration of the intersection of an octagonal prism and a cylinder. The figures intersect at an oblique…

"If two angles not in the same plane have their sides respectively parallel and lying in the same direction, they are equal and their planes are parallel."

Angles In Parallel Planes

"If two angles not in the same plane have their sides respectively parallel and lying in the same direction,…

A dihedral angle is the opening between two intersecting planes.

Dihedral Angle

A dihedral angle is the opening between two intersecting planes.

"Skull of Cat (Felis catus), showing the following bones, viz. : na, nasal; pm, premaxillary; m, maxillary; l, lacrymal; f, frontal; j, jugal; pa, palatine; p, parietal; sq, squamosal; ip, interparietal; so, supra-occipital; eo, exoccipital (the line leads to the occipital condyle); t, tympanic bulla; smf, stylomastoid foramen; mf, mental foramen; c, coronoid process of mandible; ar, ascending ramus of mandible; hr, horizontal ramus of mandible; an, angle of jaw." -Whitney, 1911

Domestic Cat Skull

"Skull of Cat (Felis catus), showing the following bones, viz. : na, nasal; pm, premaxillary; m, maxillary;…

"In heraldry, broken asunder. This condition is depicted in different ways: thus, a fesse fracted may be represented as two demi-bars touching at one angle, or as a bar with a piece broken out of the middle and moved away." -Whitney, 1911

Chevron Fracted

"In heraldry, broken asunder. This condition is depicted in different ways: thus, a fesse fracted may…

"A battle-ax used by the Franks, of which the typical form is a head long in proportion to its width, and expanding toward a convex curved edge, the general direction of which forms a considerable angle with the handle." -Whitney, 1911

Francisca, Throwing Axe

"A battle-ax used by the Franks, of which the typical form is a head long in proportion to its width,…

"The Dodo, ...was an immense Pigeon-like bird bigger than a Turkey, with an aborted keel to the sternum and the wings also aborted. The coracoid and scapula met at an obtuse angle, as in many other flightless species. The huge blackish bill terminated in a large horny hook, the cheeks were partly bare, the short yellow legs were stout, scaly, and feathered on the upper portion; the plumage was dark ash- coloured, with whitish breast and tail, yellowish-white wings, and black tips to their coverts. The short rectrices formed a curled tuft, and the first four primaries were directed backwards." A. H. Evans, 1900

Dodo

"The Dodo, ...was an immense Pigeon-like bird bigger than a Turkey, with an aborted keel to the sternum…

Diagram used to prove the theorem: "Every point in a plane which bisects a dihedral angle is equidistant from the faces of the angle"

Plane Bisecting Dihedral Angle

Diagram used to prove the theorem: "Every point in a plane which bisects a dihedral angle is equidistant…

Diagram used to prove the theorem: "The sum of two face angles of a trihedral angle is greater than the third."

Face Angles of Trihedral Angle

Diagram used to prove the theorem: "The sum of two face angles of a trihedral angle is greater than…

Diagram used to prove the theorem: "The sum of the face angles of any convex polyhedral angle is less than four right angles."

Face Angles of Convex Polyhedral Angle

Diagram used to prove the theorem: "The sum of the face angles of any convex polyhedral angle is less…

Diagram used to prove the theorem: "Two trihedral angles, which have three face angles of the one equal respectively to three face angles of the other , are either equal or symmetrical."

Symmetrical or Equal Trihedral Angles

Diagram used to prove the theorem: "Two trihedral angles, which have three face angles of the one equal…

Diagram used to prove the theorem: "Two prisms are equal when the three faces about a trihedral of one are equal respectively to the three faces about a trihedral of the other, and similarly arranged."

Two Equal Prisms

Diagram used to prove the theorem: "Two prisms are equal when the three faces about a trihedral of one…

Diagram used to prove the theorem: "Two tetrahedrons having a trihedral angle in each equal, are to each other as the products of the including edges."

Two Proportional Tetrahedrons

Diagram used to prove the theorem: "Two tetrahedrons having a trihedral angle in each equal, are to…

Diagram used to prove the theorem: "A spherical angle is measured by the arc of a great circle described from its vertex as a ole and included between its sides (produced if necessary)."

Measure of a Spherical Angle

Diagram used to prove the theorem: "A spherical angle is measured by the arc of a great circle described…

Diagram used to prove the theorem: "In a spherical triangle, the greater side is opposite the greater angle, and conversely."

Side Comparison of Spherical Triangle

Diagram used to prove the theorem: "In a spherical triangle, the greater side is opposite the greater…

Diagram an ellipse with a tangent line that illustrates "A line through a point on the ellipse and bisecting the external angle between the focal radii is a tangent."

Tangent to an Ellipse

Diagram an ellipse with a tangent line that illustrates "A line through a point on the ellipse and bisecting…

Diagram part of a hyperbola with a tangent line that illustrates "A line through a point on the hyperbola and bisecting the internal angle between the focal radii is a tangent."

Tangent to a Hyperbola

Diagram part of a hyperbola with a tangent line that illustrates "A line through a point on the hyperbola…

Consonants have a closed or narrowly expanded adjustment of the vocal organs, so that in their production some part of the throat or mouth obstructs, squeezes, or divides the breath. &hellip;in representing consonants the hand suggests a narrow adjustment of the organs, by having the prominent or accented fingers straightened and the second phalanx of the thumb close to the plane of the palm. <p>Non-Vocal Consonant positions have the voice phalanx of the thumb bent at right angles to the breath phalanx, or unaccented. Primary Consonant positions have only the first finger accented. Back Consonant positions, being posterior, have the palm held laterally at an angle to the arm.

Non-Vocal Primary Back Consonant

Consonants have a closed or narrowly expanded adjustment of the vocal organs, so that in their production…

Consonants have a closed or narrowly expanded adjustment of the vocal organs, so that in their production some part of the throat or mouth obstructs, squeezes, or divides the breath. &hellip;in representing consonants the hand suggests a narrow adjustment of the organs, by having the prominent or accented fingers straightened and the second phalanx of the thumb close to the plane of the palm. <P>Non-Vocal Consonant positions have the voice phalanx of the thumb bent at right angles to the breath phalanx, or unaccented. Mixed Consonant positions have the second, third, and fourth fingers accented. Back Consonant positions, being posterior, have the palm held laterally at an angle to the arm.

Non-Vocal Mixed Back Consonant

Consonants have a closed or narrowly expanded adjustment of the vocal organs, so that in their production…

Consonants have a closed or narrowly expanded adjustment of the vocal organs, so that in their production some part of the throat or mouth obstructs, squeezes, or divides the breath. &hellip;in representing consonants the hand suggests a narrow adjustment of the organs, by having the prominent or accented fingers straightened and the second phalanx of the thumb close to the plane of the palm. <p> Non-Vocal Consonant positions have the voice phalanx of the thumb bent at right angles to the breath phalanx, or unaccented. Divided Consonant positions have the first and second fingers accented. Back Consonant positions, being posterior, have the palm held laterally at an angle to the arm.

Non-Vocal Divided Back Consonant

Consonants have a closed or narrowly expanded adjustment of the vocal organs, so that in their production…

Consonants have a closed or narrowly expanded adjustment of the vocal organs, so that in their production some part of the throat or mouth obstructs, squeezes, or divides the breath. &hellip;in representing consonants the hand suggests a narrow adjustment of the organs, by having the prominent or accented fingers straightened and the second phalanx of the thumb close to the plane of the palm. <p> Non-Vocal Consonant positions have the voice phalanx of the thumb bent at right angles to the breath phalanx, or unaccented. Mixed-Divided Consonant positions have all of the fingers accented. Back Consonant positions, being posterior, have the palm held laterally at an angle to the arm.

Non-Vocal Mixed-Divided Back Consonant

Consonants have a closed or narrowly expanded adjustment of the vocal organs, so that in their production…

Consonants have a closed or narrowly expanded adjustment of the vocal organs, so that in their production some part of the throat or mouth obstructs, squeezes, or divides the breath. &hellip;in representing consonants the hand suggests a narrow adjustment of the organs, by having the prominent or accented fingers straightened and the second phalanx of the thumb close to the plane of the palm. <p> Non-Vocal Consonant positions have the voice phalanx of the thumb bent at right angles to the breath phalanx, or unaccented. Shut Consonant positions do not have any of the fingers accented. Back Consonant positions, being posterior, have the palm held laterally at an angle to the arm.

Non-Vocal Shut Back Consonant

Consonants have a closed or narrowly expanded adjustment of the vocal organs, so that in their production…

Consonants have a closed or narrowly expanded adjustment of the vocal organs, so that in their production some part of the throat or mouth obstructs, squeezes, or divides the breath. &hellip;in representing consonants the hand suggests a narrow adjustment of the organs, by having the prominent or accented fingers straightened and the second phalanx of the thumb close to the plane of the palm. <p> Non-Vocal Consonant positions have the voice phalanx of the thumb bent at right angles to the breath phalanx, or unaccented. Nasal Consonant positions have the breath phalanx of the thumb in the position to indicate Nasality. None of the fingers are accented. Back Consonant positions, being posterior, have the palm held laterally at an angle to the arm.

Non-Vocal Nasal Back Consonant

Consonants have a closed or narrowly expanded adjustment of the vocal organs, so that in their production…

Consonants have a closed or narrowly expanded adjustment of the vocal organs, so that in their production some part of the throat or mouth obstructs, squeezes, or divides the breath. &hellip;in representing consonants the hand suggests a narrow adjustment of the organs, by having the prominent or accented fingers straightened and the second phalanx of the thumb close to the plane of the palm. <p> Vocalized Consonant positions have the voice phalanx of the thumb accented; that is, brought in line with the breath phalanx; this constitutes the only difference between the Vocalized and analogous Non-Vocal Consonant positions. Primary Consonant positions have only the first finger accented. Back Consonant positions, being posterior, have the palm held laterally at an angle to the arm.

Vocalized Primary Back Consonant

Consonants have a closed or narrowly expanded adjustment of the vocal organs, so that in their production…

Consonants have a closed or narrowly expanded adjustment of the vocal organs, so that in their production some part of the throat or mouth obstructs, squeezes, or divides the breath. &hellip;in representing consonants the hand suggests a narrow adjustment of the organs, by having the prominent or accented fingers straightened and the second phalanx of the thumb close to the plane of the palm. <p> Vocalized Consonant positions have the voice phalanx of the thumb accented; that is, brought in line with the breath phalanx; this constitutes the only difference between the Vocalized and analogous Non-Vocal Consonant positions. Mixed Consonant positions have the second, third, and fourth fingers accented. Back Consonant positions, being posterior, have the palm held laterally at an angle to the arm.

Vocalized Mixed Back Consonant

Consonants have a closed or narrowly expanded adjustment of the vocal organs, so that in their production…

Consonants have a closed or narrowly expanded adjustment of the vocal organs, so that in their production some part of the throat or mouth obstructs, squeezes, or divides the breath. &hellip;in representing consonants the hand suggests a narrow adjustment of the organs, by having the prominent or accented fingers straightened and the second phalanx of the thumb close to the plane of the palm. <p> Vocalized Consonant positions have the voice phalanx of the thumb accented; that is, brought in line with the breath phalanx; this constitutes the only difference between the Vocalized and analogous Non-Vocal Consonant positions. Divided Consonant positions have the first and second fingers accented. Back Consonant positions, being posterior, have the palm held laterally at an angle to the arm.

Vocalized Divided Back Consonant

Consonants have a closed or narrowly expanded adjustment of the vocal organs, so that in their production…

Consonants have a closed or narrowly expanded adjustment of the vocal organs, so that in their production some part of the throat or mouth obstructs, squeezes, or divides the breath. &hellip;in representing consonants the hand suggests a narrow adjustment of the organs, by having the prominent or accented fingers straightened and the second phalanx of the thumb close to the plane of the palm. <p> Vocalized Consonant positions have the voice phalanx of the thumb accented; that is, brought in line with the breath phalanx; this constitutes the only difference between the Vocalized and analogous Non-Vocal Consonant positions. Mixed-Divided Consonant positions have all of the fingers accented. Back Consonant positions, being posterior, have the palm held laterally at an angle to the arm.

Vocalized Mixed-Divided Back Consonant

Consonants have a closed or narrowly expanded adjustment of the vocal organs, so that in their production…