History. 
Chinese _ 
geonietry. 
Roman 
geometry. 
yol. x. p. 455, ma 
192 
the Christian era. Interwoven with many absurdities, 
this book contains a rational system of trigonometry, 
which differs entirely from that first, known in Greece 
or Arabia: In fact, it is founded on a geometrical theo- 
rem, which was not known to the mathematicians of Eu- 
rope before the time of Vieta, about two hundred years 
ago. And it employs the sines of arcs, a thing un- 
known to the Greeks, who used the chords of the 
double arcs. The invention of sines has been attribu- 
ted to the Arabs, but it is possible that they may. have 
received this improvement in trigonometry, as well as 
the numeral characters, from India. " 
According to the natural progress of knowledge, the 
sciences of astronomy and geometry must have been 
long cultivated, and carried to some degree of perfec- 
tion, before a system of trigonometry would be formed ; 
we may therefore infer, that geometry had an earlier 
origin in India than the Surya Sidhanta, It is, how- 
ever, proper we should state, that the high antiquity 
both of the Indian astronomy and the Surya Sidhanta 
has been controverted ; but we cannot find room to en- 
ter on this point here. The antiquity of the Indian 
geometry has been asserted by Bailly in his Astrono- 
mie Indienne, and Professor Playfair in his Remarks on 
the Astronomy of the Brahmins, Edin. Trans. vol. ii, 
and Observations on the Trigonometry of the Brahmins, 
Edin. Trans. vol. iv. with great eloquence and strength 
of reasoning: (See our article Astronomy, p. 585.) 
On this side of the question, the Edinburgh Review, 
also be consulted. And on the 
opposite side, La Place, Systeme du Monde, 2d edit, 
. 239; Bentley On the.Hindoo Systems. of Astronomy, 
“Gn the Asiatic Researches, vol. viii. ; Edinburgh Review, 
vol. xviii. p. 210; Leslie’s Geometry, 2d edit. p. 456. 
Mr Leslie is of opinion, that the Hindoos derived 
their knowledge of mathematics from, the West. In 
opposition to this, consult Strachey, in the Preface to 
ija Ganita; and a review of the work in Edinburgh. 
Review, vol. xxi. p. 364. 
The Chinese are well known to have observed the 
heavens from the most remote ages, yet they appear to 
have made little progress in geometry: When the Eu- 
ropeans came among them, it consisted of little more 
than the rules of mensuration : it is true, they have long 
known the famous property of a right angled triangle, 
and in this they have even gone before the Greeks; ~ 
but this property, which, on account of its various ap- 
plications, well deserved the sacrifice said to have been 
offered by Pythagoras to the Muses, has remained ste- 
rile in their hands. They did not become acquainted 
with spherical trigonometry before the 13th century ; 
and then they probably learned it from the Arabs or 
Persians. 
The Romans fell far short of the Greeks in their at- 
tention to the sciences. The mathematics, in particu- 
lar, were greatly neglected at Rome ; so that geometry, 
hardly known, went little beyond the measuring of 
land and the fixing of boundaries. The celebrated 
Varro, although no mathematician, had some know- 
ledge of geometry, and wrote a treatise on the science, 
which has been cited by Frontinus and Priscianus un- 
der the title of Mensuralia. Cicero was not unac- 
quainted with mathematics ; although he did not write 
on the subject, his works contain expressions of es- 
teem for the science. The pains he took to discover 
the tomb of Archimedes, in Sicily, was a proof that he 
could estimate the high merit of that illustrious man. 
Vitruvius has displayed considerable knowledge in 
mathematies, particularly in the ninth book of his ar- 
GEOMETRY. : 
chitecture. We owe to him many notices relating to 
the mechanics and gnomonies of his time. . |. nae 
. The fifth, sixth, and seventh centuries poaaeat hard- 
ly any mathematicians, The senator and Roman con- 
sul Boetius, so well known by his misfortunes. and. his 
Consolations of Philosophy, was, in, 1 to the time, 
‘one of the most versed in mathematics. It was by his 
care that the Greek authors, as Nicomachus, - : 
Euclid, &c. begin to be a little known ‘in. the L 
tongue. His geometry is a kind of free translation of 
Euclid. Aah oii kien 
ighth century was brightened. 
500 
The beginning of the 
by the learning of Beda; he understood all the bi 2S Bed 
of mathematics, then’so little known, but he atten 
chiefly to astronomy. It is a curious fact, that at this 
period mathematics were more cultivated in Britain 
than in any other part of Euro ‘his country pro- 
duced Alcuin, who studied under Beda; he was well Ale 
skilled in mathematics, and master to Charlemagne, 
The exertions of Alcuin and his exalted pupil to re- 
vive the sciences were unavailing: the light of science 
was almost extinguished, and the human mind enye-. 
loped in the darkness of ignorance ; insomuch, that) 
there is no trace of a single mathematician to be found. 
during a period of 150 years preceding the middle of 
the tenth century. However, about that period a few. 
scattered rays shot across the gloom. The monk Abbo,. 
a man eminently endowed with a taste for knowledge, 
and in particular for mathematics, then hardly known, 
had made the monastery of Fleuria school celebrated - 
for its learning. Among his scholars was Gerbert, af=' gerbe 
terwards elevated to the pontificate by the name of Sil- 960 
vester II. His desire for learning could not be grati« 
fied by what was known among the Christians; he. 
therefore travelled into Spain, and studied mg the. 
Arabs, in their celebrated schools of Cordova and Gre=. 
nada. He soon went beyond his masters in mathema« 
tics, and on his return to France he wrote a book on. 
geometry, which has been published by the learned. 
authors of Thesaurus Anecdotorum Novissimus, anc “ 
which it appears that he was acquainted with the geo-' 
metry of Euclid and Archimedes. It is a work on. 
practical geometry, in which he gives rules for measur= 
ing heights and distances, by means of an instrument 
which he calls Horoscopus. . fA onl 
Gerbert had imitators in his own age, and in that which 
followed it. Among the first was Adelbold, who wrote a Ad 
small treatise on the solidity of the sphere. It appears 
he re what had been done in this matter by Archi- 
medes, but his own reasoning is vague and ungeome- _ 
trical. About the year 1050,. Hermann Contractus , Her 
wrote several treatises.on mathematics, and in parti-. 
cular one on the quadrature of the circle. sn eee 
The twelfth century, notwithstanding the ignorance. _ 
of the period, presents some mathematicians.. The | 
English monk Adhelard travelled into Spain and Egypt; or 
and on his return he translated Euclid from Arabic n= ~~ 
to Latin.. He appears to have been the first that made 
this author known in the West; but his work exists 
only in the libraries. . Adhelard had various imitators ; 
among his countrymen, as Daniel Morlay, Robert of Rober 
Reading, William Shell, Clement Langtown: They Readi 
lived towards the end of this century, as did also Ro- 1148: 
bert, bishop of Lincoln, called Grotshead, the author of 
a short treatise on the sphere, and his brother Adam 
Marsh. Roger Bacon, himself a mathematician, and pace 
their cotemporary in his youth, speaks highly of their gon 
skill in geometry. Passing over various writers on as- 
tronomy, we shall only farther mention Plato of Ti- 
