CRON. 
“when a conic furface is employed for the intrados of a vault 
it fhould be femi-conic, with a horizontal axis, or the furface 
of the whole cone with its axis vertical. 
All vaults, which have a horizontal ftraight axis, are 
called ftraight vaults 
All vaults, which: have their axis horizontal, are called 
horizontal vaults. 
roin is that in which two geometrical folids may be 
tranfverfely applied one after the other, o that a portion of 
the furface of the groin will have been in contaé& with a 
portion of the furface of the firt folid, and the remaining 
part in a — the furface of the fecond folid, when 
the firft is rem 
The moft sted kind of groins is one cylinder piercing 
another, or a cylinder and eylindroid piercing each other, 
having their axis at right angles 
The axis of each fimple vault forming the intrados of a 
groin, is the fame with the ax 
which the intrados of the rein is compofe 
When the breadths of the crofs paflages or openings of a 
groined — are equal, the groin is faid to be equilateral. 
Wh e altitudes of the crofs vaults are equal, the groin 
is faid to be equi-altitudinal. 
Groing have various names according to — a of 
the geometrical bodies a form the fimple va 
A cylinder groin is th ich is formed by the interfec- 
tion of one portion of a linger with another, 
A cylindroidic groin is that which is formed by the in- 
terfeCtion of one portion of a cylindroid with another 
A fpheric groin is that which is formed by thé interfeGtion 
of one portion of a {phere with another. 
A conic groin is that which is formed by the iaterieQtion 
of one portion of a cone with another. 
The {pecies of at groin, or fingle arch, formed by the 
thbbeteleion: of a vaults of unequal heights, is denoted by 
two prece $3 he former of which ending in o in- 
dicates the imple vault, which has the greater oe and the 
ending in ic, indicates -_ fimple vault of the lefs height. 
When a groin is the interfection of two un- 
equal cylindric vaults i . is Wied a Se ame geome groin, 
and each arc lindro-cylindric arch. 
When a groin is by the faterleaion of a cylindric 
vault, with a fpheric ‘eau the f{pheric portion being of 
er height than the cylindric sees, the groin is called 
oa He roin, 
When a groin is formed by the interfeétion of a cylindric __ 
wault with a fpheric vault, and the fpheric portion of lefs al- 
titude than the cylindric portion, fe is called a cylindro- 
gota groin; and each arch is called a cylindro-{pheric arch. 
hen one conic vault pierces another of Es con altitude, 
ed a cono-conic 
ipple vaults in two vertical Eo at right abs to each 
A multangulie groin is that which is formed by three or 
more {imple vaults piercing each other, fo that if the feveral 
folids which form edch fimple vault be is. aint? A applied, 
“only one at a time to fueceeding portions of the groined fu 
face, every portion of the groined furface will have formed 
fucceffive an with certain Sorettportd ing portions of 
bron ve ot 
: sipiibes ge roin is shat? = n which the fevedss axes of 
patie form sonal les around the fame point, 
horizo 
+ ellets adobe: vor laces are pone i co 
‘with groins of brick foes ct 
attached to a wall; the baer bose ae 
i & 
% 
* 
fi 
the geometrical folids, of 
d. 
{quare, or 1 re@angular, inflated 
res and from thofe of the pila 
t 
Mefeation —~A,A and fiz. 1. No, 1. are the piers, 
upon which the groin ‘a bitte —No, 2. is the elevation of the 
nave, exhibiting one of its ribs, and the edges of the com- 
mon and jack-ri s of the tranfept. In this groin the fec- 
tion, or generating figure, acrofs the nave, is a ferni-ellipfis, 
and that acrofs the tranfept a femi-circle. It may eafily ey 
= _ that the line in which two vau ults meet in 
“ey from thé Conierd “of 
ers {pring the fquandrals 
ouble ordi- 
For this 
HD, . 2 
0. 0. 2; and let t 
_ A D and E G, be bifeGted, each in c, and divided - 
n the points B and F, fo that AB: EF ;: AC: EC, 
alfo let the two ree C,H, be a to each other, then 
will their parallels BK, and F L, be alfo Be to each 
other, for by a property of the ellipfis a C*:ABx BD: 
BD 
Chi: BKt= 
= and by the fame pro~. 
BAS : 
perty EC?:EFx FG: : cH: FL: EF F x EO LEAT 
but to fhew the equality of B K’, and FLY, it is 
to have the value of F L, inthe fame as with BK 
for this tt we have A B;:BD-: 
we x et and AB: AC:: EF:EC= _ ACKER EF 
BD x EF 
by fubftituting ee 
for E C* in the quantity — 
BD x RE 
A 
for F G and 
EF x F x FGxCH* 
ae oe 
Therefore, 
ae RM RE 
A B- 
A B 
“ACXEF 
—- = EL the fame, value as found, 
a 
for BK » therefore FL is equal to BK. Now it is evident, 
that if two feétions, BKHD, and ELHG, be moved 
poe their worn fe as has already been defined, nae the — 
KB t, the point K, will coincide wi ; 
caufe 3B mult Lacie: with F, upon the diagonal ig con- 
fe uently the points K and L, = — in the c poe a 
iho, perpendicular to the ow all 
mn two points fo crcumflancsd, ould tfewife on meet ina 
it will then be EF x CH x . 
oe ee ee, 
he. ame 
he common line is an ellipfis, whofe centre is in the 
iddle of the diagonal line. _ Now it has 
the nave is compl ‘ee 
fpe&t to the tranfept.—In eles to get the fot of the pe ic "I 
ribs, it is found conven prithabelaed the two di upon 
