History of Mathematics Project | Derby Museum Hornbook

History of
Mathematics

Project

1545

Derby Museum Hornbook

Primer for study

In William Shakespeare's Love's Labour's Lost, one character asks another, "Yes, he teaches boys the hornbook. What is a, b, spelt backward with the horn on his head?" Shakespeare is referring to a hornbook or a crib book, which is a device that serves as a primer for study. Usually, the hornbook is in the shape of a paddle with a handle. One side contains study materials, while the other side is either blank or decorated. Hornbooks typically had a hole in the handle for a leather thong that could be attached to one's belt.

Hornbooks could have only the alphabet, as in this instance, the alphabet plus numbers or the Lord's Prayer and phonetics in some cross pattern. As an educational tool, the hornbook became popular in England as early as the 15th century. Often illustrations in manuscripts, such as one in Gregor Reisch's Margarita Philosophica (1503), show a student holding a hornbook or having a hornbook at their hip.

Artifact origin

Derby, United Kingdom

Current artifact location

Derby Museum and Art Gallery, Derby

Timeline

Interactive Content

Computational Explanation

To construct a graphical representation of the Derby Museum hornbook, begin by constructing the board portion containing the letters of the alphabet. With the exception of the first and last lines (which contain ABC and XYZ, respectively), all other lines contain four letters. Interestingly, in the second-to-last row, the letters U and V are transposed:

In[]:=

letters={{"A","B","C"},{"D","E","F","G"},{"H","I","J","K"},{"L","M","N","O"},{"P","Q","R","S"},{"T","V","U","W"},{"X","Y","Z"}};

Define a small utility function to position the letters on a rectangular board:

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letterposition[{r_,c_}]:=Module[{rowlength=Length[letters[[r]]]},.1{4.8c-4-2rowlength,4r-1}]

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board=Graphics[{Blend[{Yellow,Brown},.7],Rectangle[{-1,0},{1,3},RoundingRadius.1],Darker@Brown,MapIndexed[Text[Style[#,FontFamily"Times",FontSize50],letterposition[#2]]&,Reverse@letters,{2}]}]

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To add the ornate handle, zoom in:

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handleimg=

;

Place points along the right edge:

Now visualize the resulting set of points placed on top of the image:

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pts=

;

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Show[{handleimg,Graphics[{Yellow,Line[pts]}]},ImageSizeMedium]

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Fit the resulting points with a B-spline function:

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fn=BSplineFunction[pts,SplineDegree2]

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BSplineFunction

Argument count: 1

Output dimension: 2



Plot together with the actual points, showing good agreement:

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Show[{ListPlot[pts],plot=ParametricPlot[fn[x],{x,0,1}]}]

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Now extract the curve from the parametric plot:

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curve=FirstCase[plot,Line[l_]l,None,∞];

Shift vertically downward to pick up the small vertical portion of the handle just below the board:

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AppendTo[curve,curve[[-1]]+{0,5}];

Shift to be symmetric around the origin:

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shiftedcurve=(#-{curve[[1,1]],0})&/@curve;

Reflect around the y axis and display as a polygon:

In[]:=

Graphics[Polygon[poly=Join[Reverse[shiftedcurve],{-1,1}#&/@shiftedcurve]],FrameTrue,AspectRatioAutomatic]

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Attach the handle to obtain the final form of the hornbook:

In[]:=

Show[{Graphics[{Blend[{Yellow,Brown},.7],Polygon[.01{1.2#,#2-109}&@@@poly]}],board}]

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(We leave the addition of the floral and leaf motifs on the handle in the corners as an exercise to the reader.)

Additional Reading

Plimpton, G. "The Hornbook and Its Use in America." Proceedings of the American Antiquarian Society, Vol. 26, pp. 264–272, 1916.
Tuer, A. W. History of the Horn-Book. London: Leadenhall Press, 1896.

Additional Links

Image Credits

Wikimedia (cropped, background adjusted, contrast enhanced)