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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.

"Science & Mathematics - Overview" showing 2805 items.

Page 101 of 281

## Model for Descriptive Geometry by A. Jullien - Through a Given Point Construct a Plane Parallel to Two Given Lines

- 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

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Model for Descriptive Geometry by A. Jullien - Through a Given Point Construct a Plane Perpendicular to a Given Line

- 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

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Model for Descriptive Geometry by A. Jullien - Distance from a Point to a 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

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Model for Descriptive Geometry by A. Jullien - Distance from a Point to a Line

- Description
- Given point (a, a’) and line L, the slanted wire coming out of the horizontal plane at c and extending through (m, m’). Construct the horizontal line through (a, a’) that is perpendicular yet above to line L (the wire coming out of the vertical plane at d toward the right.) Then the plane FPF’ is a perpendicular to L at (m, m’). The vertical projection of the intersection of the plane and L is point e’ while the horizontal projection is point g. The red string is the line joining these two points which passes through (m, m’). Line eg is the horizontal projection of this line. By rotating points (a, a’) and (m, m’) about eg onto the horizontal plane, we get their images A’ and M’. The length of segment A’M’ is the distance from point (a, a’) to the line L at its perpendicular foot (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
- 1986.0885.01.23

- catalog number
- 1986.0885.01.23

- accession number
- 1986.0885

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Model for Descriptive Geometry by A. Jullien - Angle of a Plane with Planes of Projection

- 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 C
_{1}is found. Now angle cbC_{1}is the angle of the plane with the horizontal plane. Similarly, the angle bC_{1}C 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

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Model for Descriptive Geometry by A. Jullien - Angle between Two Lines

- 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 M
_{2}. Angle aM_{2}d 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

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Model for Descriptive Geometry by A. Jullien - Angle between a Horizontal Line and another Line

- 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 aM
_{2}D_{1}.

- 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

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Model for Descriptive Geometry by A. Jullien - Angle between a Line and a Plane

- Description
- The given plane is CPC’ and the line goes from b on the horizontal plane to a’ on the vertical plane. The holes can be seen in the image, but the black string is missing. Point (m, m’) is any point on the line. Construct the line from (m, m’) to point d on the horizontal plane that is perpendicular to the plane. This line is the wire protruding out of the horizontal plane. Through the use of several projections seen in the relief, point M
_{2}on the horizontal plane is the image of the rotation of point (m, m’). Then angle fM_{2}d on the horizontal plane is the angle between the given plane and line.

- 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
- 1986.0885.01.27

- catalog number
- 1986.0885.01.27

- accession number
- 1986.0885

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Model for Descriptive Geometry by A. Jullien - Angle between Two Planes

- 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 tM
_{2}s.

- 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

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Model for Descriptive Geometry by A. Jullien - Angle between Two Planes with Parallel Horizontal Traces

- Description
- The two planes are APA’ and BQB’, both perpendicular to the vertical plane. As can be seen in the relief, the horizontal images are the parallel lines PA and QB. Each red string represent a line on each plane that is perpendicular to intersection of the plane with the horizontal plane. These lines meet at (m, m’). The locus of all such intersection points is the horizontal line (wire) coming out of the vertical plane. By rotating (m, m’) about segment sm, the image of the angle of intersection of the planes is given by angle sM
_{1}n.

- 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
- 1986.0885.01.29

- catalog number
- 1986.0885.01.29

- accession number
- 1986.0885

- Data Source
- National Museum of American History, Kenneth E. Behring Center