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# Serie XVII, Nr 2b

## The seven types of plane curves of order three principal.

**Mathematical description**

This models represents a sphere with three of the seven principal types of plane curves of order three
on it.
The equations from the three plane curves are from the inside til the outside:

y^{2} = 4/9 [(x+3)^{2} - 20 x^{3} / (x-4)]
y^{2} = 4/9 [(x+3)^{2} - 25 x^{3} / (x+6)]
y^{2} = 4/9 [(x+3)^{2} - 20 (4x)^{3} / (x+3)]

This plane curves are projected on the sphere with projective geometry.
**Title model and translation**

Die sieben Haupttypen der ebenen Curven 3. Ordnung.

The seven types of plane curves of order three principal.

**Text on Sticker and translation**

Kugelprojection d. ebenen Curven 3.Ord. II 3 typen

II. Three types spherical projection even curves of order three.

**Designer**

Dollinger under the supervision of Dr. Brill

Tübingen in 1886

**Company**

Martin Schilling in Halle a.S.

**Original price**

Mark 12 (two pieces)

**Dimension**

10 cm

**Material**

Plaster

**Literature**

Schilling, M., Catalog mathematischer Modelle für den höheren
mathematischen Unterricht, Leipzig: Verlag von Martin Schilling, 1911