Goitre in 1835. The German Karl Adolph von Basedow also independently reported the same constellation of symptoms in 1840, while earlier reports of the disease were also published by the Italians Giuseppe Flajani and Antonio Giuseppe Testa, in 1802 and 1810 respectively, and by the English physician Caleb Hillier Parry (a friend of Edward Jenner) in the late 18th century. Paracelsus (1493–1541) was the first person to propose a relationship between goitre and minerals (particularly lead) in drinking water. Iodine was later discovered by Bernard Courtois in 1811 from seaweed ash. Goitre was previously common in many areas that were deficient
Trace field of a representation of formula_4 (see for example in ). The "invariant trace field" is equal to the trace field of the subgroup formula_7 generated by all squares of elements of formula_4 (a finite-index subgroup of formula_4). The invariant trace field of Fuchsian groups is stable under taking commensurable groups. This is not the case for the trace field; in particular the trace field is in general different from the invariant trace field. Let formula_4 be a Fuchsian group and formula_11 its trace field. Let formula_12 be the formula_11-subalgebra of the matrix algebra formula_14 generated by the preimages of elements of formula_4. The