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"Lyle Life-saving Gun. LYLE GUN, a bronze life-saving gun, designed by Captain D. A. Lyle of the United States Ordnance Department for throwing elongated projectiles having lines attached to them, in order to establish communication between the shore and a stranded or wrecked vessel. The projectile has at the rear end a shank, to which the line is attached." -Whitney, 1911

Lyle Gun

"Lyle Life-saving Gun. LYLE GUN, a bronze life-saving gun, designed by Captain D. A. Lyle of the United…

Illustration used to prove "The line joining the mid-points of two sides of a triangle is parallel to the third side and equal to one half the third side."

Line Joining Midpoints on a Triangle

Illustration used to prove "The line joining the mid-points of two sides of a triangle is parallel to…

"Argent, a pale azure engrailed. ENGRAILED. Any object being edged with small semi-circles, the points turning outwards, is said to be engrailed." -Hall, 1862

Pale Engrailed

"Argent, a pale azure engrailed. ENGRAILED. Any object being edged with small semi-circles, the points…

"PARTED PER PALE AND PER BEND SINISTER Counterchanged, or and gules. PARTY or PARTED signifies divided, and applies to the several parts of an escutcheon parted by a line, which always runs in the direction of one or more of the honourable ordinaries." -Hall, 1862

Parted Per Pale and Per Bend Sinister

"PARTED PER PALE AND PER BEND SINISTER Counterchanged, or and gules. PARTY or PARTED signifies divided,…

"PARTED PER PALE AND PER CHEVRON Gules and or, counter changed. PARTY or PARTED signifies divided, and applies to the several parts of an escutcheon parted by a line, which always runs in the direction of one or more of the honourable ordinaries." -Hall, 1862

Parted Per Pale and Per Chevron

"PARTED PER PALE AND PER CHEVRON Gules and or, counter changed. PARTY or PARTED signifies divided, and…

"Party per fess, engrailed, argent and gules. PARTY PER FESS. A shield parted in the centre by an horizontal line through the fess point." -Hall, 1862

Party Per Fess Engrailed

"Party per fess, engrailed, argent and gules. PARTY PER FESS. A shield parted in the centre by an horizontal…

"Parted per pale, gules and argent. PARTY PER PALE. This signifies a shield parted by a perpendicular line down the centre, so that one shield may contain two coats of arms." -Hall, 1862

Party Per Pale

"Parted per pale, gules and argent. PARTY PER PALE. This signifies a shield parted by a perpendicular…

A perpendicular line drawn from point P to straight line RS.

Perpendicular Line Drawn From Point P to Line RS

A perpendicular line drawn from point P to straight line RS.

Two planes lie perpendicular to one another. A line perpendicular to plane 1 and a line perpendicular to plane 2 will meet at a point, A, and form a perpendicular intersection.

Perpendicular Planes

Two planes lie perpendicular to one another. A line perpendicular to plane 1 and a line perpendicular…

Illustration of a plane determined by 2 intersecting lines

Plane Determined by 2 Intersecting Lines

Illustration of a plane determined by 2 intersecting lines

Illustration of a straight line projected upon a plane.

Line Projected Upon Plane

Illustration of a straight line projected upon a plane.

"The locus of a point in space equidistant from the extremities of a straight line is the plane perpendicular to this line at its middle point."

Locus Point to a Plane

"The locus of a point in space equidistant from the extremities of a straight line is the plane perpendicular…

Oblique lines drawn from a point to a plane.

Oblique Lines Drawn to a Plane

Oblique lines drawn from a point to a plane.

Illustration of a plane determined by 2 parallel lines

Plane Determined by 2 Parallel Lines

Illustration of a plane determined by 2 parallel lines

If a straight line is perpendicular to each of two other straight lines in a plane at their point of intersection, it is perpendicular to the plane of the two lines.

Line Perpendicular to Plane

If a straight line is perpendicular to each of two other straight lines in a plane at their point of…

Straight line AB is perpendicular to the lines in plane MN at point B.

Line Perpendicular to Plane

Straight line AB is perpendicular to the lines in plane MN at point B.

Straight line AB is perpendicular to the lines in plane MN at point B. "If from the foot of a perpendicular to a plane a straight line is drawn at right angles to any line in the plane, the line drawn from its intersection with the line in the plane to any point of the perpendicular is perpendicular to the line of the plane."

Line Perpendicular to Plane

Straight line AB is perpendicular to the lines in plane MN at point B. "If from the foot of a perpendicular…

Two straight lines, AB and CD, perpendicular to the same plane (MN) are parallel.

Lines Perpendicular to Plane

Two straight lines, AB and CD, perpendicular to the same plane (MN) are parallel.

Illustration of a plane rotated about a straight line.

Plane Rotated About a Straight Line

Illustration of a plane rotated about a straight line.

"If two straight lines are cut by three parallel planes, the corresponding segments are proportional."

3 Parallel Planes

"If two straight lines are cut by three parallel planes, the corresponding segments are proportional."

The intersection of two planes is a straight line.

Intersecting Planes

The intersection of two planes is a straight line.

The intersection of two planes is a straight line.

Intersecting Planes

The intersection of two planes is a straight line.

The intersection of two planes is a straight line.

Intersecting Planes

The intersection of two planes is a straight line.

The intersection of two planes is a straight line.

Intersecting Planes

The intersection of two planes is a straight line.

Two intersecting planes on a third plane. "If two intersecting planes are each perpendicular to a third plane, their intersection is also perpendicular to that plane."

Intersecting Planes

Two intersecting planes on a third plane. "If two intersecting planes are each perpendicular to a third…

CD is the projection of AB upon OX. In each case AE=CD and AE=ABcos theta.

Projection of a Line Segment

CD is the projection of AB upon OX. In each case AE=CD and AE=ABcos theta.

Illustration of an axis of symmetry drawn with respect to a quadrilateral.

Axis of Symmetry Drawn on a Quadrilateral

Illustration of an axis of symmetry drawn with respect to a quadrilateral.

Illustration of a quadrilateral which has two adjacent sides equal and the other two sides equal. It is symmetrical with respect to the diagonal joining the vertices of the angles formed by the equal sides, and the diagonals are perpendicular to each other.

Quadrilateral with Symmetry

Illustration of a quadrilateral which has two adjacent sides equal and the other two sides equal. It…

"Quarterly per pale dove-tailed, or and gules. DOVETAILED. A term borrowed from carpentry to show tinctures joined together by reversed wedges, which, being shaped like doves' tails, are by joiners called dovetailing." -Hall, 1862

Quarterly Dove-Tailed

"Quarterly per pale dove-tailed, or and gules. DOVETAILED. A term borrowed from carpentry to show tinctures…

Illustrations to show that if two parallel lines are cut by a transversal, the bisectors of the interior angles form a rectangle.

Rectangle Formed When Two Parallel Lines are Cut by a Transversal

Illustrations to show that if two parallel lines are cut by a transversal, the bisectors of the interior…

A man wearing a life jacket with a line in his hand.

Sailor

A man wearing a life jacket with a line in his hand.

A secant is "a line which cuts a figure in any way. Specifically, in trigonometry, a line from the center of a circle through one extremity of an arc (whose secant it is said to be) to the tangent from the other extremity of the same arc; or the ratio of this line to the radius; the reciprocal of the cosine. The ratio of AB to AD is the secant of the angle A; and AB is the secant of the arc CD." —Whitney, 1889

Circle with Secant

A secant is "a line which cuts a figure in any way. Specifically, in trigonometry, a line from the center…

"A draftsman's instrument for ruling parallel lines. It consists of a triangle so attached to a straight-edge that it can be moved back and forth on it a distance predetermined by the adjustment of a set-screw. a, a straight-edge; b, triangle moving on <i>a</i> for a distance determined by the set of the micrometer scale <i>c</i>; d, spring for releasing triangle and keeping it in the end of its slot." -Whitney, 1889

Section Liner, A Draftsman's Tool

"A draftsman's instrument for ruling parallel lines. It consists of a triangle so attached to a straight-edge…

Illustrations of a segment, a ray, and a line that can be used when providing definitions.

Definitions, Segment, Ray, Line

Illustrations of a segment, a ray, and a line that can be used when providing definitions.

Semicircle with line drawn perpendicular to the diameter.

Semicircle

Semicircle with line drawn perpendicular to the diameter.

"A semicylindrical piece of wood, fitted with a handle...used for convenience in serving ropes...to prevent chafing. a, serving-mallet; b, 'wormed' rope 'parceled' with canvas; c, serving-yarn." -Whitney, 1911

Serving Mallet

"A semicylindrical piece of wood, fitted with a handle...used for convenience in serving ropes...to…

To form a sheet bend, pass the end of one rope through the bight of another, round both parts of the other, and under its own standing part.

Sheet Bend

To form a sheet bend, pass the end of one rope through the bight of another, round both parts of the…

Illustration used to prove "The line bisecting one side of a triangle and parallel to another side bisects the third side."

Line Bisecting Side of a Triangle

Illustration used to prove "The line bisecting one side of a triangle and parallel to another side bisects…

A line with arrows on both ends to show that it extends indefinitely. The line is slanting up when read from left to right.

Line, Slanted

A line with arrows on both ends to show that it extends indefinitely. The line is slanting up when read…

A line with arrows on both ends to show that it extends indefinitely. The line is slanting down when read from left to right.

Line, Slanted

A line with arrows on both ends to show that it extends indefinitely. The line is slanting down when…

A line with arrows on both ends to show that it extends indefinitely. The line is slanting up when read from left to right.

Line, Slanted

A line with arrows on both ends to show that it extends indefinitely. The line is slanting up when read…

A line with arrows on both ends to show that it extends indefinitely. The line is slanting down when read from left to right.

Line, Slanted

A line with arrows on both ends to show that it extends indefinitely. The line is slanting down when…

Spiral with lines AB and CD drawn on piece of paper shown flat.

Spiral Drawn on Piece of Paper Shown Flat

Spiral with lines AB and CD drawn on piece of paper shown flat.

Spiral with lines AB and CD drawn on piece of paper and rolled into a cylinder to form spiral running from A to D.

Spiral Drawn on Piece of Paper and Rolled

Spiral with lines AB and CD drawn on piece of paper and rolled into a cylinder to form spiral running…

"The warmer current ascends, as indicated by the small arrows, and curls at the black wreath (u) of cloud, and then the commingling of the two currents forms an imposing dark dome (v) of cloud, from which heavy rain (r) or hail descends. The light grayish cloud which is seen behind the black wreath is the rain descending from the dark dome. The heavy raindrops bring down a large quantity of cold air, which flies straight out in advance of the storm, and produces the squall (q) indicated by the long arrow."&mdash;Finley, 1917

Line squall

"The warmer current ascends, as indicated by the small arrows, and curls at the black wreath (u) of…

Illustration showing a square with diagonals, lines, and parallel lines

Square With Diagonals and Lines Drawn

Illustration showing a square with diagonals, lines, and parallel lines

The straight line is the simplest type of locus and the simplest first degree equation.

Straight Line

The straight line is the simplest type of locus and the simplest first degree equation.

Illustration showing a survey on the lake front in Chicago with distances and angle measures shown.

Survey of Lake Front in Chicago

Illustration showing a survey on the lake front in Chicago with distances and angle measures shown.

Illustration of an axis of symmetry drawn with respect to a straight line.

Axis of Symmetry

Illustration of an axis of symmetry drawn with respect to a straight line.

Illustration of point of tangency (line and circle).

Point of Tangency

Illustration of point of tangency (line and circle).

Illustration of radius drawn to point of contact of a tangent.

Point of Tangency

Illustration of radius drawn to point of contact of a tangent.

"With a long main-line and many instruments in circuit, the resistance may be so great as to render the main-battery current so feeble that it cannot operate the sounder with sufficient energy to render the signals distinctly audible. This difficulty is met by introducing a 'local battery,' and a 'relay' at each station on the line." -Avery 1895

Telegraph Relay

"With a long main-line and many instruments in circuit, the resistance may be so great as to render…

Illustration used to prove the theorem, "Two angles whose sides are parallel, each to each, are either equal or supplementary."

2 Angles With Parallel Sides Theorem

Illustration used to prove the theorem, "Two angles whose sides are parallel, each to each, are either…

Illustration used to prove the theorem, "Two angles whose sides are perpendicular, each to each, are either equal or supplementary."

2 Angles With Perpendicular Sides Theorem

Illustration used to prove the theorem, "Two angles whose sides are perpendicular, each to each, are…

Illustration used to prove that "If two straight lines are parallel to a third straight line, they are parallel to each other."

Parallel Lines Theorem

Illustration used to prove that "If two straight lines are parallel to a third straight line, they are…

Illustration used to prove the theorem, "The sum of the angles of any triangle is two right angles."

Sum Of Angles In Triangle Theorem

Illustration used to prove the theorem, "The sum of the angles of any triangle is two right angles."

To tie a timber hitch, take the end 'a' of a rope round a spar, then round the standing part 'b', then several times round its own part 'c'.

Timber Hitch

To tie a timber hitch, take the end 'a' of a rope round a spar, then round the standing part 'b', then…

Illustration used to prove the theorem, "If two straight lines are cut by a transversal making a pair of alternate interior angles equal, the lines are parallel."

Parallel Lines Cut By A Transversal Theorem

Illustration used to prove the theorem, "If two straight lines are cut by a transversal making a pair…

Illustration used to prove the theorem, "If two parallel lines are cut by a transversal, the alternate interior angles are equal."

Parallel Lines Cut By A Transversal Theorem

Illustration used to prove the theorem, "If two parallel lines are cut by a transversal, the alternate…

Illustration of two straight lines cut by a transversal. The 8 angles formed are labeled.

2 Lines Cut By A Transversal

Illustration of two straight lines cut by a transversal. The 8 angles formed are labeled.