The quinto acuto profile demanded in
1367 is a geometrical figure produced
when the radius of curvature in the
intersecting arches is four-fifths of the
resulting span. The radius of curvature
m a semicircular vault, by contrast, is
only one half the diameter, leading to
a much shallower and more rounded
profile. It was this figure about which
Giovanni da Prato raised the alarm. In
a submission to the Opera del Duomo
he maintained that the dome had been
'falsely built* because Filippo was
constructing it 'half round' and not as
the specified pointed fifth. It was being built, that is, as a mezzo acuto, halfway between a semicircular arch and a
pointed fifth. The result would be a dome incapable of reaching the
required height. And Giovanni attributed this error not to some fault in
the system of curvature control but, instead, to Filippo's ignorance.