1802. ] 
bere, the Jefuit. Huygens* fquared the 
fegment comprehended between the vor- 
tex of the cycloid and the fourth of the 
diameter of the generating circle Slufust 
meafured the area of that curve in a very 
elegant manner, and Wrezf found its rec-. 
tification, But all thofe refearches did 
not entirely anfwer the queltions in the 
Programma circulated by Pafcal, under 
‘the name of A. Dettonville. He affirmed 
that Wallis and Father Lallouere were 
miftaken in feveral particulars, and there- 
fore he withheld the promifed rewards. 
He himielf, however, gave perfect folu- 
tions of the problems which he had pro- 
poled, and of feveral others, which were 
neceffary to complete the theory of the 
cycloid. 
that, by unaided ftrength- of memory, he 
could perform multiplication, divifion, &c. 
to 20, 30, or 40 figures; and particularly 
that in the dark, on the night of Decem- 
ber 22, 1669, he extraéted the fquare root of 
three to 20 places of decimals 3 and farther, 
that, at the requeft of a foreign gentleman, 
on the 18th of February, 1670, being in bed, 
and in the dark, he propofed to, himfelf a 
number, confifting of 53 figures, the {quare 
root of which he extraéted to 27 places, and 
the next morning di€tated the whole to the 
gentleman !—-See Lowthorp’s Abridgment of 
the Phil. Trans. vol. iii. p. 661. ‘This exer- 
tion of memory far exceeds that of Hender- 
fon, the player, when, fora wager, he got a 
whole newfpaper by heart in a day 5 nor is it 
equalled by that of the prefent Mr. T———-r, 
who, I am told, can multiply nine figures by 
nine figures, by mere dint of memory, 
*  Chriftian Huygens was born at the 
Hague on the 14th of April, 1629. His fa- 
ther was fecretary and counfellor to the Prince 
of Orange. At th age of 13, young Huy- 
gens gave proofs of that profound genius, 
which was one day to conduct him through 
the moft obfcure refearches.. Having been 
invited by Louis XLV. to fettle in France, 
he repaired to Paris in 1666, and, during his 
refidence in that city, he was one of the 
principal ornaments of the Academy of Sci- 
ences. Anticipating the revocation of the 
Edié&t of Nantz, he retired into his native 
country, where he died in 1695. 
+ Renatus Francis Walterus Slufius, a ca- 
non of the cathedral of Liege, was born in 
1623, and died in 1685. He pofleffed a fu- 
perior genius for the mathematics, joined to 
great erudition and literary tafte. . 
} Sir Chriftopher Wren, a celebrated Eng- 
lifh mathematician and architeét, was born in 
1632, and died in 1723. He conducted the 
erection of St. Paul’s Church, in London, and 
his remains lie interred in it. 
. 
| Shetch of the Hiftory of Pure Mathematics 525 
66. About the fame time, the Low 
Countries produced Gregory Saint Vin- 
cent*, a geometrician, who acquired great 
reputation by his work on the Quadrature 
of the Circle. In purfuing this chimera, 
which he could not attain, he reaped an 
ample harveit of new truths and important 
difcoveries. Huygens publicly refuted 
the pretended quadrature, and having been 
then very young, he foon afterwards took 
a more-elevated flight, and the moft difh- 
cult problems became the objeé& of his 
labours. In contemplating the logarith- 
mic curve, the firft idea of which was 
given by Edmund Gunter+, the contempo- 
rary of Briggst, Huygens found that the 
tangent of that curve is a conftant quan- 
tity. Heafterwards invented the Theory 
of the Evolutes of Curves, which will al- 
ways be regarded as one of the moft im- 
portant difcoveries in.geometry, and which 
conducted the avthor to that fine property 
of the cycloid, namely, that its evolute is 
a cycloid equal to the firft; but, placed in 
a contrary direction, and that at every 
point the radius of the evolute is equal to 
double the correfponding chord of the ge- 
nerating circle. "4 
67, It was by help of the ancient me- 
thods, that the geometricians made the 
difcoveries of which we have hitherto been 
fpeaking. But the means by which they 
effected fuch great things were infufficient 
to elevate them to more fublime fpecula- 
tions, and to enable them to difentangle 
more complicated relations. The aid of 
the modern analyfis was neceflary to enable 
them to gvercome with facility difficulties 
which were infurmountable by the ordi- 
nary methods. 
* Gregory de Saint Vincent was born at 
Bruges in 1534, became a Jefuit at 20 years. 
of age, and died at Prague in 1667. He was 
a diftinguifhed profeflor of the mathematics, 
and was as eminent for his virtues as for his 
learning. 
+ Edmund Gunter, Profeffor of Aftronomy 
in London, died in 1626, having acquired ce~ 
lebrity by his leétures (in Grefham College ?) 
and by his writings. 
t Henry Briggs, Profeffor of the Mathes 
matics at Oxford, died in 1631. That inde 
fatigable calculator, who lived content with 
his lot,, a ftranger to envy, pride, or ambi- 
tion, publifhed, in 1624, a Table of the Lo- 
garithms of the natural Numbers from 1 to 
20,000, and from 90,000 to 101,600. Death 
prevented him from finifhing his table of the 
logarithmic fines and ‘tangents for every de- 
gree, and hundredth part of a degree, of the 
quadrant, which he had far advanced. 
34 # Thomas 
