Projections of a line inclined to both the horizontal and vertical planes will not show its true length,…

Illustration showing how a rolling logarithmic spiral can be constructed by taking successive values…

Illustration showing the rolling of two logarithmic spirals of equal obliquity.

"Orthorhombic. Crystals commonly tabular parallel to basal plane, showing also short prisms and low…

"Suppose the mirror, a b, to be placed on the side of a room, and a lamp to be set in antoher room,…

"Suppose the arrow a to be the object reflected b the mirror d c; the incident rays a, flowing from…

"If an object is placed before a plane mirror, a virtual image appears behind the mirror. Each point…

"A plane mirror reflects from a flat surface, like a common looking glass." —Quackenbos 1859

"By placing two plane mirrors facing each other, we may produce an indefinite series of images of an…

"The construction for the image produced by a plane mirror depends upon the fact that the image of the…

"The incident rays, a and b, being parallel before they reach the reflectors, are thrown off at unequal…

Illustration showing that the rolling of non-cylindrical surfaces. "If the angular velocity ratio of…

Illustration of a hollow nonagonal pyramid that has been cut by a plane parallel to the base. The top…

"Two stars in the Big Dipper opposite the handle indicate the direction toward the North Star, which,…

Illustration of a right octagonal pyramid, with hidden edges shown, that has been cut by a plane parallel…

Illustration of a right octagonal pyramid that has been cut by a plane parallel to the base. The lower…

Illustration of a hollow octagonal pyramid that has been cut by a plane parallel to the base. The top…

"A contact twin, since the two individuals lie simply in contact with each other upon a certain plane."…

An orthographic projection of a pyramid from three dimensional space into two dimensional space

Diagram of a cone intersected by plane J to form a parabola. Also pictured is a circle formed by the…

Diagram showing how to construct a parabola when given the directrix (d), the focus (F) and the eccentricity…

Illustration of a right pentagonal pyramid that has been cut by a plane parallel to the base. The top…

Illustration of a hollow pentagonal pyramid that has been cut by a plane parallel to the base. The top…

Illustration of a right pentagonal pyramid, with a height much larger than the edge lengths of the base,…

Illustration of a right pentagonal pyramid, with a height smaller than the edge lengths of the base,…

Illustration of a hollow pentagonal pyramid that has been cut by a plane parallel to the base. The top…

Illustration of a skewed pentagonal pyramid that has been cut by a plane parallel to the base. The top…

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

A pusher aeroplane plan illustrating the proper ribbing and wiring for the plane. The wires are used…

A propeller airplane plan illustrating the proper location of the skeleton and placement of the wires…

A top view plan of a propeller aeroplane, or airplane. The plan shows the proper ribs and skeleton for…

A side view plan of a propeller aeroplane for two people. The plan illustrates the the proper location…

A plan for pusher aeroplane, or airplanes. The propeller of the pusher plane is located behind the cockpit…

Illustration showing a how in "analytic geometry it is customary to specify the position of a plane…

A plane is a tool for shaping wood. Planes are used to flatten, reduce the thickness of, and impart…

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

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. "If from the foot of a perpendicular…

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

Diagram used to prove the theorem: "If a pyramid is cut by a plane parallel to the base, the edges are…

Diagram used to prove the theorem: "Every section of a sphere by a lane is a circle."

Diagram used to prove the theorem: "A plane perpendicular to a radius at its extremity is tangent to…

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

Illustration of three intersecting planes. "The intersections of two parallel planes by a third plane…

Illustration of three intersecting planes. "The straight line perpendicular to one of two parallel lanes…

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

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