83 A R C H I T 
points (c. c) in the arch as there are joints required, and 
from the points c. c, where thefe lines interfeit the arch, 
dr aw c e, c e, &c. parallel to the axis of the feftion G D. 
The lines b c, b c, which bifedl the feveral angles e c a, 
will then be the true joints of the' parabolic arch; as in 
fig. 19. 
Proei.em III. Of the Hyperbola. Let F and G be the 
focus points of two oppofite hyperbolas given in pofition, 
from the focus G, draw lines through the feveral joints 
(c. c) of the arch, and through each of the points where 
they inter left the arch, as at c. c, &c. draw Fa, Fa; pro¬ 
ceed, as in the two former problems, to bifeift the angles 
a c G, and you will determine the joints required; as in 
fig. 20. 
Of DOMES. 
The above problems, efpecially the two latter, will be 
found of great ufe, wherever arches of the parabolic or 
hyperbolic kind are required ; their properties are well 
known to every mathematician, and their utility in con- 
firmftion universally admitted, particularly in magnificent 
domes, and in fituations where great weight is to be At¬ 
tained without much lateral refinance ; they have alfo the 
advantage of requiring no centring, or at lead not fo much 
as the arches in common ufe. The concave of St. Paul’s 
was turned upon a centre, which was judged necelfary to 
keep the work even and true, though a cupola might be 
built without a centre : but this is obfervable, that the 
centre was laid without any ftandards from below to fup- 
port it; and, as it was both centring and fcaffolding, it re¬ 
mained for the ufe of the painters. The claim of Sir 
Chrifiopher Wren to the firft rank in his profefiion, depends 
more, perhaps, upon his knowledge of the properties of 
thefe curves, than upon all his other attainments in archi¬ 
tecture. Hence he was enabled to defign and execute the 
fuperb cupola of St. Paul’s, one of the nobleft fpecimens 
of conftruction exifting, and the chef-d’oeuvre of this artift. 
This edifice, continues Mr. Murphy, if deprived of that 
noble feature, would have very little remaining, befides 
the weftern portico, that any ingenious architect of this 
age would be ambitious to own ; and the church of St. 
Bunftan in the Eaft would have few admirers, were it not 
for the geometrical ingenuity of its fpire. In that branch 
of architecture which relates to conftruction, Sir Chrifto- 
pher Wren may be confidered as equal, if not fuperior, to 
any artift that has appeared in Europe thefe two hundred 
years; and what contributed not a little to give him this 
fuperiority, was his living in an age enlightened by the 
genius of a Newton, a Leibnitz, a Huyghens, &c. His 
mind was enlarged by the fublime difeoveries of thofe great 
philofophcrs ; lie was one of the firft geometricians of the 
age ; and if to his knowledge in mathematical fcience, he 
had united, in an equal degree, the true principles of the 
art of defign, the world, for the firft time, would have 
feen a complete architect. 
Since the death of that great man, the art of conftruc¬ 
tion has been much neglected in England ; and perhaps 
there are but very few recent fpecimens of it in Europe, 
of bold execution, befides the cupola of St. Genevieve at 
Paris. Yet, it is remarkable, that four of the greateft ar¬ 
chitects that have appeared fince the reftoration of the arts, 
are chiefly indebted, for their fame in this art, to their 
knowledge of conftruction. Thefe were Filippo Brunel¬ 
lefchi, Michael Angelo, Jacques Germain Soufflot, and 
Sir ChriftopherWren. To the firft we owe that ftupendous 
machine, the cupola of the church of S. Maria del Fiore, 
one of the mod aftonifhing and difficult performances in 
Europe, being in magnitude not inferior to any thing of 
the kind, perhaps, the ancient world ever faw. The know¬ 
ledge of conftruCtion gradually declined in Italy, by the 
death of the old Gothic architects, and finally expired 
with Arnolfo Lappi, who began this church according to 
the Gothic rules ; this prevented the completion of its cu¬ 
pola for upwards of a century, during which time, there 
was not to be found in Florence, nor throughout all Italy, 
any architect who would undertake to finilh it. This ar» 
E C T U R E. 
duous talk was referved for the genius of Brunellefchi, 
who has rendered his name memorable in the hiftory of the 
arts, by the execution of that cupola; which Lappi, who 
began the work, would have confidered as a firnple opera¬ 
tion, and would, as M. Felibien juftly obferves, havefi- 
niflied it, had he lived, with more eafe than Brunellefchi, 
though he had been pofleired of all the rules of the ancient 
Greek and Roman architects. 
But Filippo Brunellefchi, however great his merit may 
have been, has no title to the invention of the modern 
manner of building cupolas ; for this we are indebted to 
Anthemius and Ilidorus, the two celebrated architects 
who, by order of the emperor Juftinian, built the prefent 
Santa Sophia, at Conftantinople; and to prevent its de- 
ftruCtion by fire, as had already happened four feveral 
times, they employed no combuftible materials in its fa¬ 
brication. From this epoch we may date the origin of 
cupolas refting upon the four pillars of a fquare, w hich 
fquare is gradually formed into a circle by pendentives, 
or thofe parts in the angles between the arches of the nave 
which fpring from a point, and gradually advance in a con¬ 
cave direction to receive the circular entablature of the 
cupola ; an idea fuggefted by the figure of the crofs repre- 
fented in the plans of all Chriftian churches. The vene¬ 
ration in which this church has long been held, and the 
advantages which appeared to refnlt from its new mode of 
conftruCtion, are to great, that it has fince been imitated 
by all the nations of Europe. The Venetians were the 
firft who fet the example to the Italians, by ereCting the 
church of St. Mark, at Venice, upon a fimilar plan, about 
the year 973. St. Mark’s, together witli the cathedral of 
Pila, built after the fame model at the commencement of 
the eleventh century, probably lupplied Brunellefchi with 
much information in the conftruClion of the cupola of Santa 
Maria del Fiore, which laft Michael Angelo feems to have 
copied, in the dome of that immenfe fabric Saint Peter’s 
at Rome. 
Hence we are enabled to trace through Gothic veftiges, 
the origin of thofe ftately domes which crown the princi¬ 
pal facred edifices of Europe ; a mode of conftruction, of 
which there is not a Angle inftance to be found among the 
remains of the buildings of ancient Rome, or of Greece; 
nor in thofe of the Egyptians ; nor in the writings of Vi¬ 
truvius. The abbe Winckelmann does not appear to have 
invpftigated this fubjeCt with his ufual care, or he w'ould 
not have attributed the above invention to the ancient 
Greeks, without being able to refer to a pofitive inftance 
to eftablifli the fait; his conclufion to this effeft refts up¬ 
on the authority of a piece of fculpture which is upon an 
antique farcophagus found in the villa Moirani. But, 
granting that this farcophagus bears the model of a tem¬ 
ple crowned with a fort of cupola, the original may, not- 
withftanding, have refted upon a circular bafe ; for how 
is it pollible to determine to the contrary, by any'external 
rep relent ation in painting or fculpture? The fait appears 
to be, that we are not warranted to conclude, from any 
exifting model, that the ancients ufedany fuch termination 
to their edifices as a cupola refting on a fquare bafement : 
their round temples, it is true, were often covered with a 
femicircular vault, to which they gave the name of Tholus, 
fuch as that we now fee in the Pantheon at Rome; but 
this form is very different from that which we have adop¬ 
ted from Santa Sophia, as may be feen by comparing the 
vault of the Pantheon at Rome with the dome of the Au- 
guftins’ church in the fame city. 
We may conceive fome idea of the difficulty the moderns 
find in executing any bold defign of this nature, by what 
we colleCt from the Life of M. Soufflot. This artift, tho 5 
one of the belt that ever appeared in France, experienced 
more difficulty in conftruCting the cupola of the church of 
St. Genevieve, than in all the edifices that ever rofe be¬ 
neath his direction. Notwithstanding its weight, impulfe, 
and refiftance, were afeertained, and the whole demonftra- 
ted to be perfectly fecure by two able mathematicians, 
M. Ganthey, and the abbe Boflut; yet this was not fuf- 
3 ficient 
