THOMAS U. TAYLOR-PRISMOIDAL FORMULAE. 
35 
2. DEFINITIONS. 
I here append the following historic definition: 
A prismoid is a solid whose parallel bases are polygons of the same 
number of sides, and whose side faces are trapezoids. 
The term prismatoid was introduced by Wittstein in 1860, in “ Das 
Prismatoid, eine Erweiterung der elementaren Stereometric.” It was 
defined as a solid with any two parallel polygonal bases, and whose 
side faces are triangles formed by joining the vertices of the bases so 
that each line with the preceding forms a triangle with that line and one 
side of one of the bases. 
When the bases are closed curves in parallel planes and the mantle is 
generated by a straight line whose end points move on the two curves 
and which finally returns to its initial position, the volume generated 
has been called a cylindroid. 
Ein Korper, welcher von zwei parallen Vielecken, als Grundflachen, 
und von Trapezen, als Seitenflachen, ein geschlossen ist, soil den namen 
eines Obelisk erhalten. [Koppe’s Neuer Lekrsatz der Stereometric, 1843, 
page 2.] 
If a line passes through a fixed point in the plane of one of the bases 
of the cylindroid (prismoid) and moves so that it is always parallel to 
the generating line of the cylindroid, it will cut out between the bases a 
cone (pyramid) which is called the associate cone (pyramid). 
The mean area (M) of a prismoid is such an area which multiplied by 
the altitude gives the volume. 
It would be sufficient to group all of these solids (prismoid, prismatoid, 
and cylindroid) under the general name of prismoid. When we use the 
term “ prismoidal formula” it carries with it this general meaning. 
3. The mean area of a prismatoid is equal to the half sum of the bases 
less one-sixth of the base of the associate pyramid. 
c 
Fig. 1. 
Fig.2. 
