Science & Mathematics

The Museum's collections hold thousands of objects related to chemistry, biology, physics, astronomy, and other sciences. Instruments range from early American telescopes to lasers. Rare glassware and other artifacts from the laboratory of Joseph Priestley, the discoverer of oxygen, are among the scientific treasures here. A Gilbert chemistry set of about 1937 and other objects testify to the pleasures of amateur science. Artifacts also help illuminate the social and political history of biology and the roles of women and minorities in science.

The mathematics collection holds artifacts from slide rules and flash cards to code-breaking equipment. More than 1,000 models demonstrate some of the problems and principles of mathematics, and 80 abstract paintings by illustrator and cartoonist Crockett Johnson show his visual interpretations of mathematical theorems.

Planes APA’ and BQB’ (where A=B=c and A’=B’=d’) are given. Then line d’c’ is the vertical projection of the intersection of the two planes while line dc is the horizontal projection of the intersection.For more details, see COLL.1986.0885 and 1986.0885.01.01.Currently not on view
Description
Planes APA’ and BQB’ (where A=B=c and A’=B’=d’) are given. Then line d’c’ is the vertical projection of the intersection of the two planes while line dc is the horizontal projection of the intersection.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
Location
Currently not on view
date made
ca 1880
maker
Jullien, A.
ID Number
1986.0885.01.14
catalog number
1986.0885.01.14
accession number
1986.0885
The given planes are APA’ and BQB’. The vertical and horizontal projections of the planes meet at the points d’ and c on the vertical and horizontal planes respectively, with line of intersection of the two planes cd’, depicted by the red sting.
Description
The given planes are APA’ and BQB’. The vertical and horizontal projections of the planes meet at the points d’ and c on the vertical and horizontal planes respectively, with line of intersection of the two planes cd’, depicted by the red sting. Point n is the foot of the perpendicular from the line to the horizontal plane. The red string that runs left to right indicates the plane perpendicular to line cd’ with segments on the given planes. By rotating this perpendicular plane down to the horizontal plane, the angle between the two given planes is the angle tM2s.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
Location
Currently not on view
date made
ca 1880
maker
Jullien, A.
ID Number
1986.0885.01.28
catalog number
1986.0885.01.28
accession number
1986.0885
Plane APA’ (right construction) and line through (m, m’) parallel to the plane and to line cd’ on the plane are given (red strings). Then the plane BQB’ parallel to plane APA’ is constructed.For more details, see COLL.1986.0885 and 1986.0885.01.01.Currently not on view
Description
Plane APA’ (right construction) and line through (m, m’) parallel to the plane and to line cd’ on the plane are given (red strings). Then the plane BQB’ parallel to plane APA’ is constructed.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
Location
Currently not on view
date made
ca 1880
maker
Jullien, A.
ID Number
1986.0885.01.06
catalog number
1986.0885.01.06
accession number
1986.0885
Given plane APA’, c’ is a point on the intersection line of the plane with the vertical plane. Point b on the horizontal intersection of the plane is chosen so it that bc’ is perpendicular to PA. Connect b and c’ to from the red string.
Description
Given plane APA’, c’ is a point on the intersection line of the plane with the vertical plane. Point b on the horizontal intersection of the plane is chosen so it that bc’ is perpendicular to PA. Connect b and c’ to from the red string. The horizontal projection of bc’ is bc and the vertical projection is cc’. By rotating bc’ about bc to the horizontal, point C1 is found. Now angle cbC1 is the angle of the plane with the horizontal plane. Similarly, the angle bC1C is the angle with the vertical plane.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
Location
Currently not on view
date made
ca 1880
maker
Jullien, A.
ID Number
1986.0885.01.24
catalog number
1986.0885.01.24
accession number
1986.0885
The point (m, m’) on the left side of the relief is given. On the left side, two lines are given: ab’ depicted by the black string, and dc’ (black string missing).
Description
The point (m, m’) on the left side of the relief is given. On the left side, two lines are given: ab’ depicted by the black string, and dc’ (black string missing). By constructing the red lines hg’ and ef’ parallel to lines dc’ and ab’ respectively, the plane PQP’ containing the point (m, m’) is formed parallel to the two given lines.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
Location
Currently not on view
date made
ca 1880
maker
Jullien, A.
ID Number
1986.0885.01.20
catalog number
1986.0885.01.20
accession number
1986.0885
The given lines are the black strings: ab’ and dc’. They intersect at (m, m’). Segment ad on the horizontal plane creates a triangle with the given lines as sides. Point n on the horizontal plane is perpendicular to ad through point (m, 0).
Description
The given lines are the black strings: ab’ and dc’. They intersect at (m, m’). Segment ad on the horizontal plane creates a triangle with the given lines as sides. Point n on the horizontal plane is perpendicular to ad through point (m, 0). By rotating the triangle about line ab onto the horizontal plane, point (m, m’) maps to point M2. Angle aM2d is the angle between the two given lines.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
Location
Currently not on view
date made
ca 1880
maker
Jullien, A.
ID Number
1986.0885.01.25
catalog number
1986.0885.01.25
accession number
1986.0885
Plane APA’ is given. The line shown by the wire through (m, m’) and (c, c’) is constructed parallel to both the plane APA’ and the horizontal plane.For more details, see COLL.1986.0885 and 1986.0885.01.01.Currently not on view
Description
Plane APA’ is given. The line shown by the wire through (m, m’) and (c, c’) is constructed parallel to both the plane APA’ and the horizontal plane.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
Location
Currently not on view
date made
ca 1880
maker
Jullien, A.
ID Number
1986.0885.01.08
catalog number
1986.0885.01.08
accession number
1986.0885
The plane APA’ is intersected by line bc’ represented by the black string. The red string represents a line on the plane which bc’ intersects at point (m, m’).
Description
The plane APA’ is intersected by line bc’ represented by the black string. The red string represents a line on the plane which bc’ intersects at point (m, m’). Horizontal and vertical projections of these lines are shown.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
Location
Currently not on view
date made
ca 1880
maker
Jullien, A.
ID Number
1986.0885.01.17
catalog number
1986.0885.01.17
accession number
1986.0885
Planes CDD’C’ and ABB’A’ are both parallel to the x-axis (crease in the card). They intersect in line (e, e’)-(f, f’) (wire) which is also parallel to the x-axis. The planes can be visualize by imagining both red strings extending left and right.
Description
Planes CDD’C’ and ABB’A’ are both parallel to the x-axis (crease in the card). They intersect in line (e, e’)-(f, f’) (wire) which is also parallel to the x-axis. The planes can be visualize by imagining both red strings extending left and right. Both projections of this intersection are shown as well as the rotation of it about the horizontal line perpendicular to the x-axis PA.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
Location
Currently not on view
date made
ca 1880
maker
Jullien, A.
ID Number
1986.0885.01.16
catalog number
1986.0885.01.16
accession number
1986.0885
This relief shows four more special cases of lines. It is one of two reliefs that are about twice as long as the rest. The wires and strings are missing, so it is difficult to visualize the representations.
Description
This relief shows four more special cases of lines. It is one of two reliefs that are about twice as long as the rest. The wires and strings are missing, so it is difficult to visualize the representations. (Note that the wire coming out of the horizontal plane on the far right is not correct, it is in fact one of the support pieces. This is how the relief was configured when it arrived at the Smithsonian.)
Figure 1 on the left shows the vertical and horizontal projections of two lines as well as the intersection of the two lines projected onto the vertical plane.
Figure 2 shows the angle of inclination of the line with the horizontal plane by rotating it down onto the horizontal plane.
Figure 3 shows the angle of a line coming up through the horizontal plane with the vertical, again by rotating it onto the horizontal.
Figure 4 shows the vertical projection of a line and the horizontal projection of its vertical component.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
Location
Currently not on view
date made
ca 1880
maker
Jullien, A.
ID Number
1986.0885.01.04
catalog number
1986.0885.01.04
accession number
1986.0885
Planes APA’ and BQB’ are parallel in the horizontal plane (see their respective horizontal projections AP and BQ) and intersect along line (o, c’)-(d, d’) (wire).
Description
Planes APA’ and BQB’ are parallel in the horizontal plane (see their respective horizontal projections AP and BQ) and intersect along line (o, c’)-(d, d’) (wire). This intersection is also parallel to the horizontal projections of the two planes (observe that cd is also parallel in the horizontal plane).
For more details, see COLL.1986.0885 and 1986.0885.01.01.
Location
Currently not on view
date made
ca 1880
maker
Jullien, A.
ID Number
1986.0885.01.15
catalog number
1986.0885.01.15
accession number
1986.0885
Point (m, m’) is rotated about line ab. Point n on the horizontal plane is the foot of the perpendicular from the point to line ab.
Description
Point (m, m’) is rotated about line ab. Point n on the horizontal plane is the foot of the perpendicular from the point to line ab. Point M1 is the result of rotation of the point about line nm; M2 is the result of rotation about line ab.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
Location
Currently not on view
date made
ca 1880
maker
Jullien, A.
ID Number
1986.0885.01.11
catalog number
1986.0885.01.11
accession number
1986.0885
Figure 1 shows the rotation and projections of point (m, m’) about a horizontal line perpendicular to the vertical plane through point a’.
Description
Figure 1 shows the rotation and projections of point (m, m’) about a horizontal line perpendicular to the vertical plane through point a’. Figure 2 shows the rotation and projections of point (m, m’) about the vertical line perpendicular to the horizontal at point a.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
Location
Currently not on view
date made
ca 1880
maker
Jullien, A.
ID Number
1986.0885.01.10
catalog number
1986.0885.01.10
accession number
1986.0885
The black string represents the given line bc’, while the point (a, a’) at the bend of the wire represents the given point. The horizontal line coming out of the vertical plane denoted cd’ is perpendicular to line bc’.
Description
The black string represents the given line bc’, while the point (a, a’) at the bend of the wire represents the given point. The horizontal line coming out of the vertical plane denoted cd’ is perpendicular to line bc’. Point P is the intersection of the vertical and horizontal projections of the wire with the x-axis. It follows that plane FPF’ which contains the line (c,0)-(0,d’) (wire) is also perpendicular to line bc’.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
Location
Currently not on view
date made
ca 1880
maker
Jullien, A.
ID Number
1986.0885.01.21
catalog number
1986.0885.01.21
accession number
1986.0885
Plane APA’ is given. The line perpendicular to the plane is represented by the oblique wire passing through (m, m’).
Description
Plane APA’ is given. The line perpendicular to the plane is represented by the oblique wire passing through (m, m’). The point of intersection of the line and the plane would be about halfway along the wire between (m, m’) and (c,0).
For more details, see COLL.1986.0885 and 1986.0885.01.01.
Location
Currently not on view
date made
ca 1880
maker
Jullien, A.
ID Number
1986.0885.01.07
catalog number
1986.0885.01.07
accession number
1986.0885
Two projections are shown. The left shows the vertical and horizontal projection of a line.
Description
Two projections are shown. The left shows the vertical and horizontal projection of a line. The right shows a line rotated to the horizontal and vertical plane at a point of contact with each plane to show the angle of the line with each plane.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
Location
Currently not on view
date made
ca 1880
maker
Jullien, A.
ID Number
1986.0885.01.02
catalog number
1986.0885.01.02
accession number
1986.0885
This relief shows the special case of a line that passes through the origin (0, 0, 0) and another point (a, b, c). The line is represented by the wire.For more details, see COLL.1986.0885 and 1986.0885.01.01.Currently not on view
Description
This relief shows the special case of a line that passes through the origin (0, 0, 0) and another point (a, b, c). The line is represented by the wire.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
Location
Currently not on view
date made
ca 1880
maker
Jullien, A.
ID Number
1986.0885.01.03
catalog number
1986.0885.01.03
accession number
1986.0885
Plane APA’ is a plane perpendicular to the horizontal plane with point (m, m’) on APA’ (at corner of wire).
Description
Plane APA’ is a plane perpendicular to the horizontal plane with point (m, m’) on APA’ (at corner of wire). Vertical and horizontal projections are shown, as well as rotation about line AP in the horizontal plane.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
Location
Currently not on view
date made
ca 1880
maker
Jullien, A.
ID Number
1986.0885.01.12
catalog number
1986.0885.01.12
accession number
1986.0885
The horizontal line is represented by the wire coming out of the vertical plane at c’. The second line would run from point a on the horizontal plane to b’ on the vertical, however the black string that should represent this line is missing.
Description
The horizontal line is represented by the wire coming out of the vertical plane at c’. The second line would run from point a on the horizontal plane to b’ on the vertical, however the black string that should represent this line is missing. The two lines intersect at point (m, m’) at the bend in the wire. Lines cd and ab are the projections of the lines on the horizontal plane, with line nm perpendicular to cd at m. By rotating about these three lines as in relief 25, the angle between the given lines is shown on the horizontal plane as angle aM2D1.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
Location
Currently not on view
date made
ca 1880
maker
Jullien, A.
ID Number
1986.0885.01.26
catalog number
1986.0885.01.26
accession number
1986.0885
This pamphlet accompanies a set of Jullien models for descriptive geometry and includes a full description of the models, an account of how to assemble them, and mathematical details.For related objects, see COLL.1986.0885 and 1986.0885.01.01 through 1986.0885.01.30.Currently not
Description
This pamphlet accompanies a set of Jullien models for descriptive geometry and includes a full description of the models, an account of how to assemble them, and mathematical details.
For related objects, see COLL.1986.0885 and 1986.0885.01.01 through 1986.0885.01.30.
Location
Currently not on view
date made
1880
maker
Jullien, A.
ID Number
1986.0885.02
accession number
1986.0885
catalog number
1986.0885.02
Plane APA’ and point (m, m’) are given. Construct the line on the plane with largest slope or inclination from the horizontal. Theory says that this line would be perpendicular to the horizontal trace of the plane, line PA.
Description
Plane APA’ and point (m, m’) are given. Construct the line on the plane with largest slope or inclination from the horizontal. Theory says that this line would be perpendicular to the horizontal trace of the plane, line PA. So the result is the black string from point c on the horizontal plane to point A’ on the vertical plane. The red string from point A is in the plane; the red string from point d forms the plane perpendicular to plane APA’ that the line lies on. All three lines meet at point (m, m’).
For more details, see COLL.1986.0885 and 1986.0885.01.01.
Location
Currently not on view
date made
ca 1880
maker
Jullien, A.
ID Number
1986.0885.01.09
catalog number
1986.0885.01.09
accession number
1986.0885
Suppose one is given plane APA’ and point (m, m’) not on the plane. To find the distance, one must find the perpendicular from the point to the plane. This is done by finding the shortest vertical and horizontal distances from the point to the plane.
Description
Suppose one is given plane APA’ and point (m, m’) not on the plane. To find the distance, one must find the perpendicular from the point to the plane. This is done by finding the shortest vertical and horizontal distances from the point to the plane. Segment mn on the horizontal plane is the projection of the shortest distance of point (m, m’) to the plane horizontally, often referred to as the perpendicular foot. Line de’ (red string) is the image of this foot up onto the plane. Likewise, segment m’n’ is the vertical perpendicular foot and its image on the plane is the wire coming out of the horizontal plane. Point (n, n’) where these two lines meet is the perpendicular from (m,m’) to the plane, and thus the shortest distance.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
Location
Currently not on view
date made
ca 1880
maker
Jullien, A.
ID Number
1986.0885.01.22
catalog number
1986.0885.01.22
accession number
1986.0885
Three points, a, b, and c on the horizontal plane make the triangular base of the pyramid. Point (s, s’) at the bend in the wire will be the apex. The three black strings represent the three remaining edges of the pyramid. Notice that the apex is not above the base.
Description
Three points, a, b, and c on the horizontal plane make the triangular base of the pyramid. Point (s, s’) at the bend in the wire will be the apex. The three black strings represent the three remaining edges of the pyramid. Notice that the apex is not above the base. The various projections after rotation to the horizontal plane allow the lengths of the sides to be found. The height of the pyramid is segment sS3.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
Location
Currently not on view
date made
ca 1880
maker
Jullien, A.
ID Number
1986.0885.01.30
catalog number
1986.0885.01.30
accession number
1986.0885
Figure 1 on the left shows plane APP’ cutting obliquely through the space with the black string showing a line on the plane.
Description
Figure 1 on the left shows plane APP’ cutting obliquely through the space with the black string showing a line on the plane. The vertical and horizontal projections of the plane are also depicted.
Figure 2 on the right shows the vertical and horizontal projection of a line in the plane BQB’.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
Location
Currently not on view
date made
ca 1880
maker
Jullien, A.
ID Number
1986.0885.01.05
catalog number
1986.0885.01.05
accession number
1986.0885

Our collection database is a work in progress. We may update this record based on further research and review. Learn more about our approach to sharing our collection online.

If you would like to know how you can use content on this page, see the Smithsonian's Terms of Use. If you need to request an image for publication or other use, please visit Rights and Reproductions.