1802.] 
all parts of the mathematics, applied him- 
felf particularly to the fummation ef feve- 
rai feries, fuch as thofe of the natural 
numbers, triangular numbers, &c. 
49. At the jame time Geometry was 
cultivated in France, but with lefs fuccefs | 
than in Italy, and the French mathema- 
ticians of that period are {carcely known, 
except by particular anecdotes. 
so. Le Pelletier, of Mans, acquired fome 
degree of celebrity by his controverfy with 
Father Clavius, the Jefuit, concerning the 
angle of contact, that is, the angle inter- 
cepted between a right jine and a curve 
which it touches. 
51. Oronce Finee* publifhed fome ele- 
mentary books, and. Peter Ramust fig- 
nalized himfelf by his zeal for the mathe- 
matics. 
2. In the Low Countries, Peter Metius 
difcovered, that the diameter of the circle 
is to the circumference, nearly as 113 to 
355. 
53. His cotemporary, 
Ceulez,$ was more fuccefsful ; 
Ludolph-Van- 
for he 
with reputation in his native country, having 
poflefled the happy art of rendering the moft 
abftraé&t queftions plain, by his clearnefs and 
perfpicuity of expreffion, 
* Oronce Finée, born at Briancon, in 1494, 
was chofen by Francis I, as Profetiar of the 
Mathematics in the Royal College. He ri- 
diculoufly pretended to have found out the 
quadrature of the circle, and to have folved 
the problem of two mean proportionais, and 
that of the trife€tion of an angle. He was 
vigoroufly refuted by Father Butesd; one of 
his own pupils, a circumftance very humi- 
liating to Finée. 
+ Peter Ramus was Born, about 1502, at 
the village of Vermandois; but came to Paris 
in his eighth year. Having been endued 
with a found judgment, he perceived that 
the philofophy then taught in the univer- 
fities, was nothing but a vain collection of 
words. It was his wiih to difcard thofe un- 
profitable {peculations, and to introduce the 
ftudy of the mathematics into the Univerfity 
of Paris. Some works which he publithed 
excited againft him an hoft of enemies — His 
difpute with the Peripatetics of the Univer- 
fity was decided by Commiffioners appointed 
by the King, and who condemned Ramus. 
The fentence in favour of Arifictle - was 
affixed to all the yates of the Univerfity, and 
Rearnus was expofed toa thoufand indignities. 
As the unfortunate ‘mathematician publicly 
profeffed the opinions of the Proteftants, he 
was included in the number of thofe who 
_ perished in the mailacre of St. Bartholomew, 
in 1572. 
{ Lucolph Van Ceulen, fo called becaufe 
he was from Cologhe, which is called Ceulen 
Sketch of the Hiftory of Pure Mathematics. 
SOF 
fhewed that,the diameter of the circle being 
unity, the circumference will be exprefled 
by 3514159, &c. which number he car- 
ried to thirty-five places of decimals. 
54. In Germany, Werner,* a mathe- 
matician who deferves to be better known 
than he is, contributed, by his works 
on trigonometry and other parts of the 
mathematics, to diffufe a: talte for thofe. 
{ciences. 
55. Rheticus, whofe work was publifhed 
by Valentine Otho, one of his fcholars, in- 
troduced the ufe of the fecants into trigo- 
nometry ; and Fu/ftus Byrgius invented the 
fector.F 
in Dutch, was long a Profeffor of the Ma- 
thematics in Holland. To tranfmitto pofte- 
rity the memory of his invention, he gave 
orders that the number exprefling the pro- 
portion of the diameter of the circle to its 
Circumference, fhould be engraved on his 
monument. It is faid, that his order was 
executed after his death, in the church of 
Leyden. 
Note by the Traaflator.—The approximation 
of Van Ceulen was an extraordinary mathe- 
matical atchievement, eipecially as it was 
performed by the ancient operofe method of 
bife€&tion; fo that the attainment of his 35 
places of decimals probably coft him more 
labour than Mr. A. Sharp, of Bradford, 
Yorkfhire, beftowed in carrying the calcula 
tion to 72 places, or even than Mr. Machin 
experienced in extending it to rco. For, fo 
much have the methods of fluxions and infi- 
nite feries facilitated this, among many other 
abftrufe calculations, that Dr. Halley affures 
us, and we have not the leaft doubt, that in 
an hour’s time he obtained 12 decimal places, 
which exhibit the proportion of the diameter 
to the circumference fo nearly, as not to err 
the breadth of a grain of fand ina great circle 
of the earth—a fufficient degree of exactnefs 
in all confcience! See Gardiner’s edition of 
Sherwin’s Tables, p. 53, and Jones’s Synop- 
Jisy p- 243- Hence, if we durff, we would 
call the incomprebenjibly accurate, and, at beft, 
frightfully laborious, calculations of Van 
Ceulen, Sharp, and Machin, difficiles nuge, 
mere contrivances to waite one’s time and 
{pirits. 
* Werner was born in 146% and died in 
1528 
va Note by the Tranflator.—The fir work 
on the feétor, called by the French, Ger- 
mans, and I believe moft other nations, the 
compals of proportion, was publifhed at Frank- 
fort on the Maine, in 1603, by Lewin Hulie, 
who candidly fays, that is was invented long 
before by Juftus Byrgius, anenginecr in the 
fervice of the Landgrave of Heffe. But that 
honour was claimed, and even contended for, 
by Galileo, and Balthafar Capra of Milan, 
The former publithed a Tra&t on that admi- 
Uys : * rable 
