GEOMETRY. 191 
as of no use. Isidore is said, by Eutocius, to have in- Mahomet Al-Bagdadi, (of Bagdad,) the author of an History. 
vented an instrument for describing a parabola, by con- elegant work on mensuration, which has been transla. “—~-— 
eromme, : J ted and published in 1570; and Alhazen, the celebra- Bagdadin. 
__ It would appear that Diocles lived about this period ; 
he was the inventor of the cissoid, a curve contrived 
for the purpose of ng two mean proportionals. 
Eutocius also attributes to this geometer a solution of 
the Archimedean problem concerning the division of 
‘a sphere, which we have already noticed ; it is highly 
ereditable to him, and shews that he was skilful in the 
ancient analysis. We may place Sporus, and his mas- 
ter Philo, about this period ; the former gave a solu- 
tion of the problem of two mean proportionals, and the 
latter extended Archimedes’ approximation of the ratio 
of the diameter to the circumference of a circle, as far 
as 10,000th parts, , ; 
' The labours of Proclus, and the eters that fol- 
lowed him, were the last rays which the ancient ma- 
thematics scattered upon Chedai The long night 
of ignorance which elapsed from this time, until the de- 
struction of the Greek empire, produced merely ele- 
men writers, such as in better times would scarce 
have deserved the name of mathematicians. The school 
of Alexandria, however, yet existed, and the brilliant 
times of Euclid and Apollonius might have been re- 
newed, had it not been for the troubles which agitated 
the East. The taking of Alexandria by the Saracens, 
ve a mortal blow to the sciences, not only in that ce- 
febrated capital, but also Prougl out the Greek empire. 
This happened in the year 640 A.D. The Alexandrian 
library, a treasure of inestimable value, was delivered to 
destruction, and the finest monument of human ge- 
nius, the accumulated store of knowledge produced by 
the exertion of the most enlightened minds in many 
ages, was expended in heating the public baths of the 
city. See ALEXANDRIA. ; ee 
~ It is consoling to reflect, that although the followers 
of Mohammed, at this period, destroyed the sciences, 
yet they afterwards were entitled to the gratitude of 
owe , for the care with which oe cherished them. 
ithin less than a century, we find the Arabs cultiva- 
ting astronomy and geometry. Many of the Greek ma- 
thematicians, chiefly such as treat of astronomy, as 
Euclid, Theodosius, Hypsicles, Menelaus, were trans- 
lated into’ Arabic in the reign of Almamon, or soon 
after ; they even then began to study the more sublime 
geometry, for the four first books of the conics of Apol- 
lonius were translated by order of that enlightened 
prince. Ata later period, the remaining books were 
translated, also Archimedes’ treatise on the sphere and 
cylinder, and probably his other works ; and it deserves 
to be remarked, that the Arabs cite several works of the 
Greek geometers, concerning which we know nothing ; 
a8 a treatise on parallel lines, another on triangles, and a 
third on the division of the circle. Weare indebted to 
the Arabs for the form under which trigonometry is 
now known. Ptolemy had greatly simplified the theory 
of Menelaus, yet he employed a laborious rule, called 
the rule of six quantities. 
Geber ben Aphla, who lived in the 11th century, 
substituted, instead of the ancient method, three or four 
_ theorems, which are the foundation of modern trigono- 
metry. The Arabs also simplified tri etrical cal- 
_ culation, by substituting the sines of arcs, instead of 
_ the chords of the double arcs ; and this was even one 
_ of their earliest inventions, for it is found in the writ- 
ings of Albatenius, who flourished about the year 880 
our era. The names of many Arabian 
eometers are 
known, we shall, however, only mention ‘Bagdadin, or 
ted author of a work on optics, which shews him to have 
been an excellent geometer. In general, the Arabian 
geometers had little invention, they were almost all 
compilers or commentators on the ancients, 
Persia has also had its geometers. The most cele- 
brated was Nassir-Eddin Al-Tussi ; he wrote a learned 
commentary on Euclid, which was printed in 1590 at 
the ae of the Medici. He also revised_the conics uf 
Apollonius, and wrote a commentary on the subject ; 
this was useful to Dr Halley, in restoring the fifth, 
sixth, and seventh books of that precious work. The 
geometer next in esteem was Maimon-Reschid: he 
Wrote a commentary on Euclid, and is said to have in- 
dulged in a singular whim: he had conceived such 
an affection for one of the propositions of the first book 
of the Elements, that he wore the diagram as an ovna- 
ment embroidered on his sleeve. Geometry has, in mo- 
dern times, been respected among the Persians, but they 
have not made any improvements inthe science. The 
traveller Chardin has given some traits of the pedantry 
of their literati. ‘« They have given,” says he, “a name 
to every proposition. of the Elements. “They call the 
47th proposition of the first book of Euclid ‘the figure 
of the bride, probably because it is to become the mo- 
ther of a humerous progeny of other theorems. The 
48th proposition, again, they call the bride’s sistor; 
and they, with reason, denominate geometry the difficult 
science. 
‘The Turks have not altogether neglected geometry. 
Tn.the libraries of Constantinople, the greater number of 
the Greek mathematicians may be found translated into 
Arabic, and some into the Turkish language ; but it 
does not appear that they pay attention to any thing 
beyond what is contained in Euclid’s Elements, and ine 
indeed they have never made one discovery in the 
sciences, : 
There are hardly any traces of geometry among the 
aneient Hebrews. Every one knows that when Solo- 
mon’s temple was built, Hiram king of Tyre furnished 
architects and navigators, a proof that geometry must 
then have been very little known in Palestine. “It was 
not until the second dispersion among the nations that 
they began to cultivate the sciences. In the ninth 
century, the Jews, after the example of the Arabians, 
began to translate the Greek geometers into their lan- 
guage; but they have discovered nothing whatever in 
geometry. 
The researches of the learned have brought to light 
astronomical tables in India, which must have been 
constructed by the principles of geometry ; but the pe- 
riod at which they have been formed has by no means 
been completely ascertained, Some are of opinion, that 
they have been framed from observations made at a 
very remote period, not less than three thousand 
years before the Christian era; and if this opinion be 
well founded, the science of geometry must have been 
cultivated in India to a considerable extent, long 
before the period assigned to its origin in the West : 
so that many of the elementary propositions may have 
been brought from- India to Greece. - The Hindoos 
have a treatise called the Suryd Sidhanta, which pro- 
fesses to be a revelation from heaven, communicated 
to Meya, a man of great sanctity, about four. million 
of years ago; but setting aside this fabulous origin, it 
has been supposed to be of great antiquity, and to 
have been written at least two thousand years before 
Alhazen, 
1100. 
Persian 
geometry. 
Nassir- 
Eddin, 
1270. 
Turkish 
geometry. 
Hebrew 
geometry, 
Geometry 
of India. 
