ABSTRACT
In the last chapter we studied operations of adding and subtracting areas and saw how the ability to effect an additive composition of the set of parts brought about conservation of the whole. We saw too how that conservation preceded measurement, which involves a synthesis of subdivision and change of position. Here we shall carry that analysis one stage further by studying the beginnings of division in the field of area, using concrete models, like cakes to be divided among a number of children. This should enable us to see once more how part-whole relations are constructed and also how they are quantified as fractions. Here again we will meet the key problems of subdivision and conservation of the whole, but we shall also be dealing with metrical phenomena since the subdivision we require is particularly conducive to such quantification.
