How theorem paintings were made 

The nineteenth-century student artist did not set up a still life arrangement and paint a picture of it the way students do today. They painted from copies of pictures, from their memories, or from theorems (a set of instructions). Theorem painting was done by following a set of steps or rules. The steps included how to make the oiled paper for cutting stencils, how to mix colors, and how to practice brushstrokes. Theorem paintings were done on paper, velvet, wood, silk, cotton, linen, or bristol board. Less talented amateurs could use stencils to paint the decorative elements such as fruit in a bowl or basket. Talented amateurs could paint freehand while copying from prints. 

Materials and tools

The materials needed for theorem painting were paints, brushes, paper or cloth, a print to copy, and stencils. Private painting tutors, who taught in their own home or the student's, provided materials for their students. They advised students to use the colors red, yellow, blue, brown, orange, purple, green, and verdigris (gray-green). The paints were powdered colors mixed with gum tragacanth (sap of a plant) and water. If "fancy color shops" did not exist in a student's part of the country, it was necessary to prepare some of these materials at home. One popular recipe for purple watercolor includes six ounces of logwood chips, tragacanth gum, alum, and a pint of water -- boiled down to half its quantity and strained through a cloth. The artist used a hog-hair brush cut down to a nub for stenciling, and a camel-hair brush for adding details. 

Stencil making

Students made their stencils from horn paper, a type of drawing paper coated with linseed oil to make it transparent. They coated the paper with a varnish that sealed the paper and prevented paint from leaking through. The students cut out each stencil shape from the horn paper with a sharp knife. An easy method of painting with stencils was to cut individual stencil shapes for each piece of the picture. Each stencil could be placed into any composition.

Painting Technique

The artist practiced stencil painting on scratch paper until he or she could add the color delicately and evenly, perhaps shading to create the illusion of three dimensions. The artist held the brush vertically over the stencil, and made circular motions of the hand or arm to apply steady but light pressure on the brush. Very small amounts of almost dry paint were used to prevent paint from creeping under the edge of the stencil and creating blobs of color. The stencil was then carefully lifted off the paper.