hes
(identified in plan and perspective sketch as A, B, C, D), and the
lines which are taken by the various arches shown by dotted lines.
Looking at the perspective sketch, it will be apparent that the
intersection of the two cross vaults produces two intersecting arches,
the upper line of which is shown in the perspective sketch (marked _e_
and _f_); underneath, this intersection of the two arches, which forms a
furrow in the upper side of the construction, forms an edge which
traverses the space occupied by the plan of the vaulting as two
oblique arches, running from A to C and from B to D on the plan.
Although these are only lines formed by the intersection of two cross
arches, still they make decided arches to the eye, and form prominent
lines in the system of vaulting; and in a later period of vaulting
they were treated as prominent lines and strongly emphasized by
mouldings; but in the Roman and early Romanesque vaults they were
simply left as edges, the eye being directed rather to the vaulting
surfaces than to the edges. The importance of this distinction between
the vaulting surfaces and their meeting edges or _groins_[2] will be
seen just now. The edges, nevertheless, as was observed, do form
arches, and we have therefore a system of cross arches (A B and C D[3]
Fig. 95), two wall arches (A, D and B C), and two oblique arches (A C
and B D), which divide the space into four equal triangular portions;
this kind of vaulting being hence called _quadripartite_ vaulting. In
this and the other diagrams of arches on this page, the cross arches
are all shown in positive lines, and the oblique arches in dotted
lines.

[Footnote 2: A _groin_ is the edge line formed by the meeting and
intersection of any two arched surfaces. When this edge line is
covered and emphasized by a band of moulded stones forming an
arch, as it were, on this edge, this is called a _groin rib_.]

[Footnote 3: The "D" seems to have been accidentally omitted in
this diagram; it is of course the fourth angle of the plan.]

We have here a system in which four semicircular arches of the width
of A B are combined with two oblique arches of the width of A C,
springing from the same level and supposed to rise to the same height.
But if we draw out the lines of these two arches in a comparative
elevation, so as to compare their curves together, we at once find we
are in a difficulty. The intersection of the two circular arches
produce