P A R 
were the nohleft families of Perfia, in the number of 
which were the Achaem6nides. Herodut. c. 125. 
PASAR'NA, a town of Afia, in Armenia Minor, at 
fome diftance from the Euphrates, in the Lavinian pre- 
fe&ure. 
PASCAGOO'LA, a river of Weft Florida, which runs 
into the gulf of Mexico, forming a bay at its mouth, 
in lat. 30. 23. N. Ion. 88. 30. W. 
PAS'CAL (Blaife), a very diftinguiftied French ma¬ 
thematician and philofopher, was born at Clermont in 
Auvergne, in the year 1623. His father, who was pre- 
fident of the court of aids in his province, was alio a 
man of confiderable learning, and an able mathematician. 
As Blaife was his only fon, fo great was his aft eft ion for 
him, that in the year 1631 he relinquilhed his official 
fttuation and fettled at Paris, in order that he might 
liimfelf undertake the employment of being his tutor. 
From his infancy young Pafcal gave evidence of a very 
extraordinary capacity. What we are told concerning 
his manner of learning the mathematics, and his rapid 
progrefs in that fcience, is very aftonilhing. His father, 
perceiving in him an extraordinary inclination to reafon- 
ing, was afraid left the knowledge of the mathematics 
fhould prevent him from learning the languages. He 
therefore refolved to keep from him, as much as he 
could, all notions of geometry, locked up all the books 
that treated of it, and refrained even from fpeaking of it 
in his prefence. Yet he could not refufe to give this ge¬ 
neral anfwer to the importunate curiofity of his fon : 
“ Geometry is a fcience which teaches the way of making 
exaft figures, and of finding out the proportions between 
them but at the fame time he forbade him to fpeak or 
think of it any more. The flight idea which had been 
thus conveyed to him of the fcience occupied young 
Blaife’s thoughts, who was now only twelve years of 
age, and led him in his hours of recreation to make fi¬ 
gures on the chamber-floor with charcoal, the propor¬ 
tions of which he fought out, laying down definitions 
and axioms, and then going on to demonftrations. So 
far had he proceeded with his enquiries, that he had 
come to what was juft the fame with the thirty-fecond 
propofition of the Firft Book of Euclid, when he was 
one day furprifed by his father in the midft of his figures, 
who alked him what he was doing. He replied, that he 
was fearchingfor fucli a thing, which was juft that pro¬ 
pofition of Euclid. When afked afterwards how he came 
to think of this, he anfwered that it was becaufe he had 
found out fuch another thing; and fo, going backwards, 
and ufing the names of bar and round, he at length came 
to the definitions and axioms which he had formed to 
liimfelf. From this time young Pafcal had full liberty to 
indulge his genius in mathematical purfuits, and was 
furnifhed by his father with Euclid’s Elements; of which 
he made liimfelf mafter in an incredibly ftiort time, with¬ 
out any affiftance. So wonderful was his proficiency in 
the fciences, that at the age of fixteen he wrote a Trea- 
tife on Conic Se£Iions, which, in the judgment of the 
nioft learned men of the time, was confidered to be a 
great effort of genius. Des Cartes, who had been in 
Holland for a long time, having read it, added his opi¬ 
nion to the univerfal verdidft in its praife: but, when 
informed of the age of the author, he rather chofe to be¬ 
lieve that it was the produbfion of M. Pafcal the father, 
than to admit that fo young a perfon was capable of 
writing a book with fuch ftrength of reafoning. At the 
age of nineteen, our young mathematician had contrived 
his admirable Arithmetical Machine, furnifliing an eafy 
and expeditious method of making all forts of arithme¬ 
tical calculations without any other affiftance than the 
eye and hand. This was efteemed a very wonderful 
thing, and would have done credit to any man verfed in 
fcience, and much more to fuch a youth. About this 
time the ftate of his health becoming impaired, owing 
molt probably to the intenfenefs of his ftudious applica¬ 
tion, he was obliged to fufpend his labours for the fpace 
Vol. XVIII, No. 1*77. 
P A R 729 
of four years. At the age of twenty-three, having feen 
Torricelli’s experiment refpefting a vacuum and the 
weight of the air, he dire&ed his attention to thofe fub- 
jeffs, and made feveral new experiments. He likewife 
made many experiments with fyphons, fyringes, bellows, 
and all kinds of tubes, ufing different fluids, fuch as 
quickfilver, water, wine, oil. &c. and, having publilhed 
an account of them in 1647, difperfed his work through 
all countries. Thefe experiments, however, only afeer- 
tained effects, without demonilrating the caufes. Pafcal 
knew that Torricelli conjedtured that thofe phenomena 
which he had obferved were occafioned by the weight 
of the air, though they had formerly been attributed to 
nature’s abhorrence of a vacuum ; but, were Torricelli’s 
theory true, he concluded that the liquor in the tube of 
the barometer ought to ftand higher at the bottom of a 
a hill than at the top of it. In order to afeertain the faft, 
he made an experiment at the top and bottom of a 
mountain in Auvergne, called Ie Puy de Dome, the re- 
fult of which gave him reafon to conclude that the air 
was indeed heavy. Of this experiment he publilhed an 
account, of which he fent copies to moft of the learned 
men in Europe. He alfo repeated it at the top and 
bottom of feveral high towers, as thofe of Notre Dame at 
Paris, St. Jaques de la Boucherie, See. and always re¬ 
marked the lame difference in the weight of the air at 
different elevations. 
M. Pafcal, being now fully convinced of the general 
preffure of the atmofphere, drew many Important and 
ufeful inferences from this difeovery. lie alio compofed 
a large treatife, in which he fully explained the fubjedl, 
and anfwered the objections which were preferred againlt 
that theory; but afterwards, confidering it to be too pro¬ 
lix, he divided it into two fmall treatifes, one of which 
he entitled a Differtation on the Equilibrium of Fluids; 
and the other, an Elfay on the Weight of the Atmofphere. 
Thefe treatifes were not publilhed till after the author’s 
death. 
The reputation which M. Pafcal had acquired by his 
fcientific labours, occafioned his being frequently con- 
fulted by fome of the greateft mathematicians and philo- 
fophers of the age, who applied for his affiftance in the 
refolution of various difficult queftions and problems. 
Among other fubjedls on which his ingenuity was em¬ 
ployed, was the folution of a problem propofed by father 
Merfenne, which had baffled the penetration of all who 
attempted it. This problem was, to determine the curve 
deferibed in the air by the nail of a coach-wheel, while 
the machine is in motion : which curve was then called 
a rouillctte, but is now commonly known by the name of 
cycloid. As a fpur to genius, M. Pafcal offered a reward 
of forty piftoles to any one who (hould give a fatisfadlory 
anfwer to it. No perfon having fucceeded, he publilhed 
his own folution at Paris; but, as he now began to grow 
difgufted with the fciences, he would not fend it into the 
world under his own name, but prefixed to it that of A. 
d’Ettonville. This exertion of his genius was a triumph 
overall the old mathematicians of Europe; and it was 
made in circumftances which cannot but excite aftonifli- 
ment. For his filler informs us, that he made the difeo¬ 
very, as it were, in fpite of himfelf, and to his own great 
furprife, while palling fleeplefs nights in his bed, tor¬ 
mented by fevere paroxyfms of the tooth-ache. Before 
this time he had drawn up a table of numbers, which, 
from the form in which the figures in it are difpofed, he 
called his “ Arithmetical Triangle.” Of this table he 
has been fpoken of as the inventor; but Dr. Hutton has 
fliown, in the firft volume of his Mathematical Trails, 
that fuch a table of numbers, and many properties of 
them, had been treated of more than a century before by 
Cardan, Stifelius, and other arithmetical writers. 
When M. Pafcal was in the twenty-fourth year of his 
age, and the higheft expeditions were entertained of the 
advantages to Icience from his future labours, he all at 
once renounced the ftudy of the mathematics and natu- 
8 Z ral 
