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Illustration showing how to construct the bisector of an angle.

Construction Of Angle Bisector

Illustration showing how to construct the bisector of an angle.

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…

An illustration showing the construction used to divide an angle into two equal parts. "With C as a center, draw the dotted arc DE; with D and E as centers, draw the cross arcs at F with equal radii. Join CF, which divides the angle into the required parts."

Construction Of A Divided Angle

An illustration showing the construction used to divide an angle into two equal parts. "With C as a…

An illustration showing the construction used to divide an angle into two equal parts when the lines do not extend to a meeting point. "Draw the lined CD and CE parallel, and at equal distances from the lines AB and FG. With C as a center, draw the dotted arc BG; and with B and G as centers, draw the cross arcs H. Join CD, which divides the angle into the required equal parts."

Construction Of A Divided Angle

An illustration showing the construction used to divide an angle into two equal parts when the lines…

Illustration used to show how to bisect a given arc.

Bisecting an Arc

Illustration used to show how to bisect a given arc.

Illustration used to show how to "find an arc of a circle having a known radius, which shall be equal in length to a given straight line."

Construction Of Arc

Illustration used to show how to "find an arc of a circle having a known radius, which shall be equal…

An illustration showing how to construct the center and radius of a circle that will tangent a given circle and line. "Through the given point C, draw the line EF at right angles to AB; set off from C the radius r of the given circle. Join G and F. With G and F as centers draw the arc crosses m and n. Join mn, and where it crosses the line EF is the center of the required circle."

Construction Of A Center And Radius Of A Circle That Will Tangent A Given Circle And Line

An illustration showing how to construct the center and radius of a circle that will tangent a given…

An illustration showing how to construct the center and radius of a circle that will tangent a given circle and line. "From C, erect the perpendicular CG; set off the given radius r from C to H. With H as a center and r as radius, draw the cross arcs on the circle. Through the cross arcs draw the line IG; then G is the center of the circle arc FIC, which tangents the line at C and the circle at F."

Construction Of A Center And Radius Of A Circle That Will Tangent A Given Circle And Line

An illustration showing how to construct the center and radius of a circle that will tangent a given…

An illustration showing how to construct the center and radius of a circle that will tangent a given circle. "Through the given point C, draw the tangent GF; bisect the angle FGE; then o is the center of the required circle that will tangent AB at C, and the line DE."

Construction Of A Center And Radius Of A Circle That Will Tangent A Given Circle

An illustration showing how to construct the center and radius of a circle that will tangent a given…

An illustration showing how to construct a center and radius of a circle that will tangent the three sides of a triangle. "Bisect two of the angles in the triangle, and the crossing C is the center of the required circle."

Construction Of The Center And Radius Of A Circle Tangent To Triangle Sides

An illustration showing how to construct a center and radius of a circle that will tangent the three…

Illustration used to show how to find the center when given an arc and its radius.

Construction Of Center

Illustration used to show how to find the center when given an arc and its radius.

An illustration showing how to construct a circle arc without recourse to its center, but its chord AB and height h being given. "With the chord as radius, and A and B as centers, draw the dotted circle arcs AC and BD. Through the point O draw the lines AOo and BOo. Make the arcs Co=Ao and Do=Bo. Divide these arcs into any desired number of equal parts, and number them as shown on the illustration. Join A and B with the divisions, and the crossings of equal numbers are points in the circle arc."

Construction Of A Circle Arc

An illustration showing how to construct a circle arc without recourse to its center, but its chord…

Illustration used to construct a circle when given three points.

Construction of Circle Given 3 Points

Illustration used to construct a circle when given three points.

An illustration showing how to construct a circle tangent to a given line and given circle. "Add the given radius r to the radius R of the circle, and draw the arc cd. Draw the line ce parallel with and at a distance r from the line AB. Then the crossing c is the center of the required circle that will tangent the given line and circle."

Construction Of A Circle Tangent To A Line And A Circle

An illustration showing how to construct a circle tangent to a given line and given circle. "Add the…

An illustration showing how to construct a circle that tangents two given lines and goes through a given point c on the line FC, which bisects the angle of the lines. "Through C draw AB at right angles to CF; bisect the angles DAB and EBA, and the crossing on CF is the center of the required circle."

Construction Of A Circle That Tangents 2 Given Lines And Goes Through A Given Point

An illustration showing how to construct a circle that tangents two given lines and goes through a given…

An illustration showing how to construct a circle that tangents two given lines inclined to one another with the one tangenting point being given. "Draw the center line GF. From E, draw EF at right angles to AB; then F is the center of the circle required.

Construction Of A Circle That Tangents 2 Given Lines

An illustration showing how to construct a circle that tangents two given lines inclined to one another…

Illustration used to find the center of a circle.

Center of a Circle

Illustration used to find the center of a circle.

An illustration showing how to find the center of a circle which will pass through three given points A, B, and C. "With B as a center, draw the arc DEFG; and with the same radius and A as a center, draw the cross arcs D and F; also with C as a center, draw the cross arcs E and G. Join D and F, and also E and G, and the crossing o is the required center of the circle."

Find The Center Of A Circle Through 3 Points

An illustration showing how to find the center of a circle which will pass through three given points…

Illustration used to show how to pass a circumference through any three points not in the same straight line.

Construction Of Circumference

Illustration used to show how to pass a circumference through any three points not in the same straight…

Diagram showing how to construct a conic when given the focus and the auxiliary circle. If the focus is outside the circle, we get a hyperbola. If it's inside the circle, we get an ellipse. If the auxiliary circle is a straight line (radius is infinite), we get a parabola.

Construction of a Conic

Diagram showing how to construct a conic when given the focus and the auxiliary circle. If the focus…

Diagram showing how to construct a conic when given the focus and the auxiliary circle. The focus is on the left of the auxiliary circle, thus producing a very obtuse hyperbola.

Focus In Auxiliary Circle of Conic

Diagram showing how to construct a conic when given the focus and the auxiliary circle. The focus is…

Diagram showing how to construct a conic when given the focus and the auxiliary circle. As the focus moves inside the circle the ellipse broadens out until the focus reaches the center and becomes a circle.

Focus In Auxiliary Circle of Conic

Diagram showing how to construct a conic when given the focus and the auxiliary circle. As the focus…

An illustration showing how to construct a cycloid. "The circumference C=3.14D. Divide the rolling circle and base line C into a number of equal parts, draw through the division point the ordinates and abscissas, make aa' = 1d, bb' = 2'e, cc = 3f, then ab' and c' are points in the cycloid. In the Epicycloid and Hypocycloid the abscissas are circles and the ordinates are radii to one common center."

Construction Of A Cycloid

An illustration showing how to construct a cycloid. "The circumference C=3.14D. Divide the rolling circle…

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

Construction Of A Cyma

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

Illustration used to show how to divide a line into any number of equal parts by construction.

Construction Used to Divide a Line Into Equal Parts

Illustration used to show how to divide a line into any number of equal parts by construction.

Illustration used to show how to divide a given straight line into required number of equal parts.

Construction Of Dividing A Line

Illustration used to show how to divide a given straight line into required number of equal parts.

Illustration used to show how to divide a given straight line into required number of equal parts.

Construction Of Dividing A Line

Illustration used to show how to divide a given straight line into required number of equal parts.

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

Pattern for Dodecahedron

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

Illustration used to draw a an ellipse using string and pins by describing a circles with diameters equal to the minor and major axes of the ellipse.

Construction of Ellipse by Describing Circles

Illustration used to draw a an ellipse using string and pins by describing a circles with diameters…

An illustration showing how to construct an ellipse parallel to two parallel lines A and B. "Draw a semicircle on AB, draw ordinates in the circle at right angle to AB, the corresponding and equal ordinates for the ellipse to be drawn parallel to the lines, and thus the elliptic curve is obtained as shown by the figure."

Construction Of An Ellipse Tangent To Two Parallel Lines

An illustration showing how to construct an ellipse parallel to two parallel lines A and B. "Draw a…

Illustration used to draw a an ellipse using string and pins.

Construction of Ellipse Using String

Illustration used to draw a an ellipse using string and pins.

Illustration of half of an ellipse and its auxiliary circle used to construct an ellipse by points, having given its two axes.

Construction of an Ellipse

Illustration of half of an ellipse and its auxiliary circle used to construct an ellipse by points,…

An illustration showing how to construct an ellipse. "With a as a center, draw two concentric circles with diameters equal to the long and short axes of the desired ellipse. Draw from o any number of radii, A, B, etc. Draw a line Bb' parallel to n and bb' parallel to m, then b is a point in the desired ellipse.

Construction Of An Ellipse

An illustration showing how to construct an ellipse. "With a as a center, draw two concentric circles…

An illustration showing how to construct an ellipse using a string. "Having given the two axes, set off from c half the great axis at a and b, which are the two focuses of the ellipse. Take an endless string as long as the three sides in the triangle abc, fix two pins or nails in the focuses, one in a and one in b, lay the string around a and b, stretch it with a pencil d, which then will describe the desired ellipse."

Construction Of An Ellipse

An illustration showing how to construct an ellipse using a string. "Having given the two axes, set…

An illustration showing how to construct an ellipse using circle arcs. "Divide the long axis into three equal parts, draw the two circles, and where they intersect one another are the centers for the tangent arcs of the ellipses as shown by the figure."

Construction Of An Ellipse

An illustration showing how to construct an ellipse using circle arcs. "Divide the long axis into three…

An illustration showing how to construct an ellipse using circle arcs. "Given the two axes, set off the short axis from A to b, divide b into three equal parts, set off two of these parts from o towards c and c which are the centers for the ends of the ellipse. Make equilateral triangles on cc, when ee will be the centers for the sides of the ellipse. If the long axis is more than twice the short one, this construction will not make a good ellipse."

Construction Of An Ellipse

An illustration showing how to construct an ellipse using circle arcs. "Given the two axes, set off…

An illustration showing how to construct an ellipse. Given the two axes, set off half the long axis from c to ff, which will be the two focuses in the ellipse. Divide the long axis into any number of parts, say a to be a division point. Take Aa as radius and f as center and describe a circle arc about b, take aB as radius and f as center describe another circle arc about b, then the intersection b is a point in the ellipse, and so the whole ellipse can be constructed."

Construction Of An Ellipse

An illustration showing how to construct an ellipse. Given the two axes, set off half the long axis…

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.

Illustration used to draw a an ellipse with major axis AB and minor axis CD.

Construction of Ellipse

Illustration used to draw a an ellipse with major axis AB and minor axis CD.

Diagram showing how to construct an ellipse when given the two foci and the length of the major axis (2a).

Construction of an Ellipse

Diagram showing how to construct an ellipse when given the two foci and the length of the major axis…

An illustration showing the construction used to erect an equal angle. "With D as a center, draw the dotted arc CE: and with the same radius and B as a center, draw the arc GF; then make GF equal to CE; then join BF, which will form the required angle, FBG=CDE."

Construction Of An Equal Angle

An illustration showing the construction used to erect an equal angle. "With D as a center, draw the…

An illustration showing how to construct an equilateral triangle inscribed in a circle. "With the radius of the circle and center C draw the arc DFE; with the same radius, and D and E as centers, set off the points A and B. Join A and B, B and C, C and A, which will be the required triangle."

Construction Of An Equilateral Triangle Inscribed In A Circle

An illustration showing how to construct an equilateral triangle inscribed in a circle. "With the radius…

Illustration used to show how to draw an equilateral triangle when given one side.

Construction Of Equilateral Triangle

Illustration used to show how to draw an equilateral triangle when given one side.

Illustration used to show how to draw an equilateral triangle when given the altitude.

Construction Of Equilateral Triangle

Illustration used to show how to draw an equilateral triangle when given the altitude.

An illustration showing how to construct an evolute of a circle. "Given the pitch p, the angle v, and radius r. Divide the angle v into a number of equal parts, draw the radii and tangents for each part, divide the pitch p into an equal number of equal parts, then the first tangent will be one part, second two parts, third three parts, etc., and so the Evolute is traced."

Construction Of An Evolute Of A Circle

An illustration showing how to construct an evolute of a circle. "Given the pitch p, the angle v, and…

Frame used to frame tables, this is a small type design featuring shape.

Small Frame for Table Top

Frame used to frame tables, this is a small type design featuring shape.

Illustration used to show how to draw a helix when the pitch and the diameter are given.

Construction Of Helix

Illustration used to show how to draw a helix when the pitch and the diameter are given.

An illustration showing how to construct a heptagon, or septagon. "The appotem a in a hexagon is the length of the side of the heptagon. Set off AB equal to the radius of the circle; draw a from the center C at right angles to AB; then a is the required side of the heptagon."

Construction Of A Heptagon

An illustration showing how to construct a heptagon, or septagon. "The appotem a in a hexagon is the…

An illustration showing how to construct a hexagon in a given circle. "The radius of the circle is equal to the side of the hexagon."

Construction Of A Hexagon In A Circle

An illustration showing how to construct a hexagon in a given circle. "The radius of the circle is equal…

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

Construction Of Hexagon Inscribed In Circle

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

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

Construction of Regular Hexagon

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

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

Pattern for Hexahedron

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

An illustration showing how to construct a hyperbola by plotting. "Having given the transverse axis BC, vertexes Aa, and foci ff'. Set off any desired number of parts on the axis below the focus, and number them 1,2,3,4,,5,etc. Take the distance a1 as radius, and, with f' as center, strike the cross 1 with f'1=a1. With the distance A1, and the focus f as center, strike the cross 1 with the radius F1=A1, and the cross 1 is a point in the hyperbola."

Construction Of A Hyperbola

An illustration showing how to construct a hyperbola by plotting. "Having given the transverse axis…

An illustration showing how to construct a hyperbola by a pencil and a string. "Having given the transverse axis BC, foci f' and f, and the vertexes A and a. Take a rule and fix it to a string at e; fix the other end of the string at the focus f. The length of the string should be such that when the rule R is in the position f'C, the loop of the string should reach to A; then move the rule on the focus f', and a pencil at P, stretching string, will trace the hyperbola."

Construction Of A Hyperbola

An illustration showing how to construct a hyperbola by a pencil and a string. "Having given the transverse…

Diagram showing how to construct a hyperbola when given the two foci and the length of the major axis (2a).

Construction of a Hyperbola

Diagram showing how to construct a hyperbola when given the two foci and the length of the major axis…

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

Pattern for Icosahedron

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

An illustration showing how to construct an isometric ellipse by compass and six circle arcs. "Divide OA and OB each into three equal parts; draw the quadrant AC. From C, draw the line Cc through the point 1. Through the points 2 draw de at an angle of 45° with the major axis. Then 2 is the center for the ends of the ellipse; e is the center for the arc dc; and C is the center for the arc cf."

Construction Of An Isometric Ellipse

An illustration showing how to construct an isometric ellipse by compass and six circle arcs. "Divide…

An illustration showing how to use isometric perspective. "This kind of perspective admits of scale measurements the same as any ordinary drawing, and gives a clear representation of the object. It is easily learned. All horizontal rectangular lines are drawn at an angle of 30°. All circles are ellipses of proportion, as shown."

Construction Using Isometric Perspective

An illustration showing how to use isometric perspective. "This kind of perspective admits of scale…

Illustration of the construction used to create an isosceles triangle, given the bases and the sum of the altitude and a side.

Construction Of An Isosceles Triangle

Illustration of the construction used to create an isosceles triangle, given the bases and the sum of…