ClipArt ETC
An illustration showing the construction used to divide a line AB into two equal parts; and to erect a perpendicular through the middle. "With the end A and B as centers, draw the dotted circle arcs with a radius greater than half the line. Through the crossings of the arcs draw the perpendicular CD, which divides the line into two equal parts."

Construction Of A Line Divided In Equal Parts

An illustration showing the construction used to divide a line AB into two equal parts; and to erect…

Illustration used to show how to find a straight line of the same length as a given arc of a circle.

Construction Of Line Equal To Arc

Illustration used to show how to find a straight line of the same length as a given arc of a circle.

Illustration showing how a rolling logarithmic spiral can be constructed by taking successive values of theta, starting from oc. The values of r can be calculated and then the curve can be plotted.

Construction of Logarithmic Spiral

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

An illustration showing how to construct a regular octagon from a square by cutting off the corners of the square. "With the corners as centers, draw circle arcs through the center of the square to the side, which determine the cut-off."

Construction Of An Octagon From a Square

An illustration showing how to construct a regular octagon from a square by cutting off the corners…

Illustration used to show how to inscribe a regular octagon in a given circle.

Construction Of Octagon Inscribed In Circle

Illustration used to show how to inscribe a regular octagon in a given circle.

An illustration showing how to construct an octagon on a given line. "Prolong AB to C. With B as center and AB as radius, draw the circle AFDEC; from B, draw BI at right angles to AB; divide the angles ABC and DBC each into two equal parts; then BD is one side of the octagon. With A and E as centers, draw the arcs HKE and AKI, which determine the points H and I, and thus complete the octagon as shown in the illustration."

Construction Of An Octagon

An illustration showing how to construct an octagon on a given line. "Prolong AB to C. With B as center…

Pattern that can be cut out and folded to construct a regular octahedron. Fold on the dotted lines, and keep the edges in contact by the glued strips of paper.

Pattern for Octahedron

Pattern that can be cut out and folded to construct a regular octahedron. Fold on the dotted lines,…

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.

Illustration used to construct and oval when given the width.

Construction of Oval

Illustration used to construct and oval when given the width.

Illustration used to draw a parabola when given the base and height.

Construction of Parabola Given Base and Height

Illustration used to draw a parabola when given the base and height.

An illustration showing how to construct a parabola by plotting. "Having given the axis, vertex, and focus of the parabola. Divide the transverse axis into any desired number of parts 1, 2, 3, etc., and draw ordinates through the divisions; take the distance A1, and set it off on the 1st ordinate from the focus f to a, so that A1 = fa. Repeat the same operation with the other ordinates - that is, set off the distance A5 from f to e, so that A5 = fe; and so the parabola is constructed."

Construction Of A Parabola

An illustration showing how to construct a parabola by plotting. "Having given the axis, vertex, and…

An illustration showing how to construct a parabola using a pencil and a string. "Having given the two axes, vertex, and focus of the parabola. Take a square cde, and fix to it a string at c; fix the other end of the string at the focus f. The length of the sting should be such that when the square is in the position of the axis Af, the string should reach to the vertex A. Move the square along BB, and the pencil P will describe the parabola."

Construction Of A Parabola

An illustration showing how to construct a parabola using a pencil and a string. "Having given the two…

An illustration showing how to construct a parabola. "Given the vertex A, axis x, and a point P. Draw AB at right angle to x, and BP parallel to x, divide AB and BP into an equal number of equal parts. From the vertex A draw lines to the divisions on BP, from the divisions on AB draw the ordinates parallel to x, the corresponding intersections are points in the parabola."

Construction Of A Parabola

An illustration showing how to construct a parabola. "Given the vertex A, axis x, and a point P. Draw…

An illustration showing how to construct a parabola. "Given the axis of ordinate B, and vertex A. Take A as a center and describe a semicircle from B which gives the focus of the parabola at f. Draw any ordinate y at right angle to the abscissa Ax, take a as radius and the focus f as a center, then intersect the ordinate y, by a circle-arc in P which will be a point in the parabola. In the same manner the whole Parabola is constructed."

Construction Of A Parabola

An illustration showing how to construct a parabola. "Given the axis of ordinate B, and vertex A. Take…

Illustration used to show how to draw a parabola when the axis and longest double ordinate is given.

Construction Of Parabola

Illustration used to show how to draw a parabola when the axis and longest double ordinate is given.

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

Construction of a Parabola

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

Illustration of the construction used to create a line parallel to a given line.

Construction Of A Parallel Line

Illustration of the construction used to create a line parallel to a given line.

An illustration showing the construction used to erect a parallel line. "With C as a center, draw the dotted arc ED, with E as a center, draw through C the dotted arc F.C. With the radius FC and E as a center, draw the cross arc at D. Join C with the cross at D, which will be the required parallel line.

Construction Of A Parallel

An illustration showing the construction used to erect a parallel line. "With C as a center, draw the…

Illustration used to show how to draw a parallelogram when given the sides and one of the angles.

Construction Of Parallelogram

Illustration used to show how to draw a parallelogram when given the sides and one of the angles.

An illustration showing the construction used to erect a parallelogram given two sides and an angle. "Draw the base line DE, and make the angle FDE = C; lines DE = B and DF = A; complete the parallelogram by cross arcs at G, and the problem is thus solved."

Construction Of A Parallelogram

An illustration showing the construction used to erect a parallelogram given two sides and an angle.…

An illustration showing how to construct a pentagon inscribed in a circle. "Draw the diameter AB, and from the center C erect the perpendicular CD. Bisect the radius AC at E; with E as center, and DE as radius, draw the arc DE, and the straight line DF is the length of the side of the pentagon."

Construction Of A Pentagon Inscribed In A Circle

An illustration showing how to construct a pentagon inscribed in a circle. "Draw the diameter AB, and…

Illustration used to show how to inscribe a regular pentagon in a given circle.

Construction Of Pentagon Inscribed In Circle

Illustration used to show how to inscribe a regular pentagon in a given circle.

An illustration showing how to construct a pentagon on a given line. "From B erect BC perpendicular to and half the length of AB; join A and C prolonged to D; with C as center and CB as radius, draw the arc BD; then the chord BB is the radius of the circle circumscribing the pentagon. With A and B as centers, and BD as radius, draw the cross O in the center."

Construction Of A Pentagon On A Line

An illustration showing how to construct a pentagon on a given line. "From B erect BC perpendicular…

An illustration showing how to construct a pentagon on a given line without resort to its center. "From B erect Bo perpendicular to and equal to AB; with C as center and Co as radius, draw the arc Do, then AD is the diagonal of the pentagon. With AD as radius and A as center, draw the arc DE; and with E as center and AB as radius, finish the cross E, and thus complete the pentagon."

Construction Of A Pentagon On A Line

An illustration showing how to construct a pentagon on a given line without resort to its center. "From…

Illustration used to construct a regular pentagon on a given line.

Construction of Regular Pentagon

Illustration used to construct a regular pentagon on a given line.

Illustration of the construction used to make a perpendicular bisector of a straight line.

Construction Of A Perpendicular Bisector Of A Straight Line

Illustration of the construction used to make a perpendicular bisector of a straight line.

Illustration of the construction used to create a perpendicular to a straight line at a given point.

Construction Of A Perpendicular To A Straight Line

Illustration of the construction used to create a perpendicular to a straight line at a given point.

Illustration of the construction used to create a perpendicular to a straight line from a given point not on the line.

Construction Of A Perpendicular To A Straight Line

Illustration of the construction used to create a perpendicular to a straight line from a given point…

An illustration showing the construction used to erect a perpendicular. "With C as a center, draw the dotted circle arcs at A and B equal distances from C. With A and B as centers, draw the dotted circle arcs at D. From the crossing D draw the required perpendicular DC."

Construction Of A Perpendicular

An illustration showing the construction used to erect a perpendicular. "With C as a center, draw the…

An illustration showing the construction used to erect a perpendicular from a point to a line. "With C as a center, draw the dotted circle arc so that it cuts the line at A and B. With A and B as centers, draw the dotted cross arcs at D with equal radii. Draw the required perpendicular through C and crossing D."

Construction Of A Perpendicular

An illustration showing the construction used to erect a perpendicular from a point to a line. "With…

An illustration showing the construction used to erect a perpendicular at the end of a line. "With the point D as a center at a distance from the line, and with AD as radius, draw the dotted circle arc so that it cuts the line at E through E and D, draw the diameter EC: then join C and A, which will be the required perpendicular."

Construction Of A Perpendicular

An illustration showing the construction used to erect a perpendicular at the end of a line. "With the…

Illustration used to show how to inscribe any regular polygon in a given circle.

Construction Of Polygon Inscribed In Circle

Illustration used to show how to inscribe any regular polygon in a given circle.

An illustration showing the construction used to divide the line AB in the same proportion of parts as AC. "Join C and B, and through the given divisions 1, 2, and 3 draw lines parallel with CB, which solves the problem."

Divide A Line Proportionately

An illustration showing the construction used to divide the line AB in the same proportion of parts…

Illustration used to draw lines which are radii of a circle where the center is inaccessible.

Construction of Radii of a Circle

Illustration used to draw lines which are radii of a circle where the center is inaccessible.

An illustration showing how to construct a regular polygon on a given line without resort to its center. "Extend AB to C and, with B as center, draw the half circle ADB. Divide the half circle into as many parts as the number of sides in the polygon, and complete the construction as shown on the illustration."

Construction Of A Regular Polygon On A Line

An illustration showing how to construct a regular polygon on a given line without resort to its center.…

Illustration used to show how to draw a regular polygon when given a side of the polygon.

Construction Of Regular Polygon

Illustration used to show how to draw a regular polygon when given a side of the polygon.

An illustration showing how to construct a screw helix.

Construction Of A Screw Helix

An illustration showing how to construct a screw helix.

A shaft in a building which serves as an air passage in a building.

Ventilation Shaft

A shaft in a building which serves as an air passage in a building.

An illustration showing how to construct Shield's anti-friction curve. "R represents the radius of the shaft, and C1, 2, 3, et., is the center line of the shaft. From o, set off the small distance oa; and set off a1 - R. Set off the same small distance from a to b, and make b2 = R. Continue in the same way with the other points, and the anti-friction curve is thus constructed.

Construction Of Shield's Anti-friction Curve

An illustration showing how to construct Shield's anti-friction curve. "R represents the radius of the…

An illustration showing how to construct a spiral with compasses and four centers. "Given the pitch of the spiral, construct a square about the center, with the four sides together equal to the pitch. Prolong the sides in one direction as shown by the figure, the corners are the centers for each arc of the external angles."

Construction Of A Spiral

An illustration showing how to construct a spiral with compasses and four centers. "Given the pitch…

An illustration showing how to construct an arithmetic spiral. "Given the pitch p and angle v, divide them into an equal number of equal parts, say 6; make 01 = 01, 02 = 02, 03 = 03, 04 = 04, 05 = 05, and 06 = the pitch p; then join the points 1, 2, 3, 4, 5 and 6, which will form the spiral required."

Construction Of An Arithmetic Spiral

An illustration showing how to construct an arithmetic spiral. "Given the pitch p and angle v, divide…

An illustration showing how to construct a square circumscribed about a circle. "Draw the diameters AB and CD at right angles to one another; with the radius of the circle, and A, B, C, and D as centers, draw the four dotted half circles which cross one another in the corners of the square, and thus complete the problem."

Construction Of A Square Circumscribed About A Circle

An illustration showing how to construct a square circumscribed about a circle. "Draw the diameters…

An illustration showing how to construct a square upon a given line. "With AB as radius and A and B as centers, draw the circle arcs AED and BEC. Divide the arc BE in two equal parts at F, and with EF as radius and E as center, draw the circle CFD. Join A and CB and D, C and D, which completes the required square."

Square Constructed Upon A Given Line

An illustration showing how to construct a square upon a given line. "With AB as radius and A and B…

An illustration showing how to construct a square inscribed in a circle. "Draw the diameter AB, and through the center erect the perpendicular CD, and complete the square as shown in the illustration."

Construction Of A Square Inscribed In A Circle

An illustration showing how to construct a square inscribed in a circle. "Draw the diameter AB, and…

Illustration used to show how to inscribe a square in a given circle.

Construction Of Square Inscribed In Circle

Illustration used to show how to inscribe a square in a given circle.

Illustration used to construct a square on a given line.

Construction of Square on Given Line

Illustration used to construct a square on a given line.

Illustration used to construct a square that shall be a multiple of any given square.

Construction of Multiple of a Square

Illustration used to construct a square that shall be a multiple of any given square.

Illustration used to construct a square that shall be in proportion to a given square.

Construction of Proportional Square

Illustration used to construct a square that shall be in proportion to a given square.

Illustration used to construct a square that shall be in proportion to a given square.

Construction of Proportional Square

Illustration used to construct a square that shall be in proportion to a given square.

Illustration used to show how to draw a straight line parallel to a straight line through a given point.

Parallel To Straight Line Construction

Illustration used to show how to draw a straight line parallel to a straight line through a given point.

Illustration used to show how to draw a perpendicular to a straight line from a given point on the line when the point is at or near the center of the line.

Perpendicular To Straight Line Construction

Illustration used to show how to draw a perpendicular to a straight line from a given point on the line…

Illustration used to show how to draw a perpendicular to a straight line from a given point on the line when the point is near the end of the line.

Perpendicular To Straight Line Construction

Illustration used to show how to draw a perpendicular to a straight line from a given point on the line…

Illustration used to show how to draw a perpendicular to a straight line from a given point that is not on the line and which lies nearly over the center of the line.

Perpendicular To Straight Line Construction

Illustration used to show how to draw a perpendicular to a straight line from a given point that is…

Illustration used to show how to draw a perpendicular to a straight line from a given point that is not on the line and which lies nearly over one end of the line.

Perpendicular To Straight Line Construction

Illustration used to show how to draw a perpendicular to a straight line from a given point that is…

Illustration used to show how to bisect a straight line.

Bisect A Straight Line

Illustration used to show how to bisect a straight line.

An illustration showing how to construct a talon, or two circle arcs that will tangent themselves, and meet two parallel lines at right angles in the given points A and B. "Join A and B; divide AB into four equal parts erect perpendiculars; then m and n are the centers of the circle arcs of the required talon."

Construction Of A Talon

An illustration showing how to construct a talon, or two circle arcs that will tangent themselves, and…

An illustration showing how to construct a tangent between 2 given circles. "Join the centers C and c of the given circles; draw the dotted circle arcs, and join the crossing m, n, which line cuts the center line at a. With aC as diameter, draw the half circle afC; and with ac as a diameter, draw the half circle cea; then the crossings e and f are the tangenting points of the circles."

Construction Of Tangent Between 2 Circles

An illustration showing how to construct a tangent between 2 given circles. "Join the centers C and…

An illustration showing how to construct a tangent to 2 given circles of different diameters. "Join the centers C and c of the given circles, and extend the line to D; draw the radii AC and ac parallel with one another. Join Aa, and extend the line to D. On CD as a diameter, draw the half circle CeD; on cD as a diameter, draw the half circle cfD; then the crossings e and f are the tangenting points of the circles."

Construction Of Tangent To 2 Circles

An illustration showing how to construct a tangent to 2 given circles of different diameters. "Join…

An illustration showing how to construct a tangent circle to 2 given circles. "Join centers C and c of the given circles, and extend the line to D; draw the radii AC and ac parallel with one another. Join Aa, and extend the line to D. On CD as a diameter, draw the half circle CeD; on cD as a diameter, draw the half circle cfD; then the crossings e and f are tangenting points of the circles."

Construction Of Circle Tangent To 2 Circles

An illustration showing how to construct a tangent circle to 2 given circles. "Join centers C and c…

Illustration used to draw a tangent to a circle.

Construction of Tangent to a Circle

Illustration used to draw a tangent to a circle.