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.
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.
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.
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.
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.
As with relief 17, APA’ is again the plane and the red string de’ is on the plane. In this relief, the line is represented by the wire coming out of the horizontal plane and away from the vertical plane (it intersects the vertical plane below the horizontal plane). The point of intersection is at (m, m’) where the wire, the string and the bent wire meet. The horizontal and vertical projections are shown.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
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 M2 on the horizontal plane is the image of the rotation of point (m, m’). Then angle fM2d 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.
Plane APA’ is any plane in space with point (m, m’). The two red strings, the black string and the horizontal wire are all lines on the plane. Vertical and horizontal projections are given, as well as the results of rotation of the plane about lines AP, nm, cn, and ce.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
The three points in space are represented at the bends in the three wires at points (a, a’), (b, b’) and (c, c’). The red lines connect the points in pairs showing the resulting triangle that lies on the plane that was to be constructed.
For more details, see COLL.1986.0885 and 1986.0885.01.01.
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.
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.
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.
This roughly built wooden case that is lined with cloth and pink paper. It holds thirty models for descriptive geometry. For a description of the general collection, see COLL.1986.0885. For a description of the individual models, see 1986.0885.01.01 through 1986.0885.01.30.
A paper sticker glued to the inside of the lid reads: METHODE NOUVELLE (/) POUR L'ENSEIGNEMENT (/) DE LA GOMTRIE DESCRIPTIVE; COLLECTION DE RELIEFS (/) A PIECES MOBILES (/) AYANT OBTENU UN DIPLOME DE MRITE A L'EXPOSITION (/) UNIVERSELLE DE VIENNE, 1878 (/) Comprenant 32 cartons, 118 piéces métalliques et une [/] instruction practique ou notice explicative. Another mark on the sticker reads: A. JULLIEN. A third mark on the sticker reads: PARIS.
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.
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.
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.
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.
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.
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.