ries in its language, and established their truth by its 
liar mode demonstration. The conic sections, 
one of its earliest and most profound theories, acquired 
a value by its application to astronomy, far he 
what it ever had when considered merely as an object 
of intellectual lation ; and the learning and genius 
of Halley and y eee were employed in rs and 
____ bringing into view the precious remains of Euclid and 
®->* Apollonius , ‘ 
1 For upwards of a century, the physico-mathematical 
sciences have very much en, the attention of ma- 
thematicians ; but in these, the ancient geometry af- 
fords a very limited degree of aid in comparison to the 
modern: hence no doubt it has happened, that the ve- 
nerable theories of the ancients have been less noticed. 
There have, however, been some who have sedulously 
cultivated them, and endeavoured to restore them to 
their former importance ; and this spirit has been par- 
ticularly manifested in Britain. It is a curious circum- 
stance, that when the subtile reasonings of the inge- 
nious Bishop of Cloyne had raised doubts as to the 
justness of the high claims of the doctrine of fluxions, 
the boast of the modern analysis ; the ingenious Mac- 
in. laurin thought the safest course he could follow, was 
» to call geometry to its aid, and to explain its principles 
in the clear style, although circuitous manner, of the 
Passing over several foreigners who have cultivated 
y in the 18th century, as well as natives of Bri- 
tain, for whose particular rs we cannot find room, 
we must notice the celebrated Scottish geometer Dr 
Robert Simson. To him we are indebted for a treatise 
on conic sections, composed on the model of the an- 
** cients ; also for restorations of the Plane Loci of Apol- 
 lonius, and the books of determinate sections ; but more 
especially for his restitution of the Porisms of Euclid: 
a task which we are not certain was ever accomplished 
by any geometer before his time ; although Albert Gi- 
rard, as we have already observed, claimed a like honour. 
His edition of the first six, and the eleventh and twelfth 
__ books of Euclid’s Elements, has now in a manner su- 
epeneeied all others in this country, and is almost uni- 
_versally taught in our schools. 
Listiliew Stewart, the friend of Simson, was an- 
own in 
. They were given 
without demonstrations, except a few of the more eagle, 
Which he has proved with w degree of elegance that ren 
ders them the finest models of geometrical reasoning. 
His tracts, physical and mathematical, his essay on the 
_- gun’s distance, and his solution of Kepler’s problem, are 
attempts to apply | geometry to the subli inqui- 
ries in-astronom: etnies se reps iiis-ahahen ab 
y 
may be accom by the force of genius; and the 
points Page Say failed serve also to shew, that 
even in such a masterly hand, the geometrical method 
is still limited in its application, and can by no means 
be compared in power with the modern etry. 
This excellent few oo published also a en 4 entitled 
itiones. rice, More Veterum. demonstrate, 
ad vam Antiquam illustrandam et endam 
idonew, which we reckon one of the most valuable that 
}: agama the hands.of a student that is pre- 
toe acquainted with the elements, and is desirous 
_ of learning the true spirit of the ancient geometry. 
To such of our readers as wish to appreciate the high 
3 
GEOMETRY. 
merit of these two geometers, we recommend the Rev, _ History. 
Dr Traill’s excellent life of Dr Simson’ (1812), and an “"Y"" 
197 
elegant biographical account of Dr Stewart, composed 
by Mr Playfair, and read before the Royal Society of 
Edinburgh, (Edin. Phil. Trans. vol. i.) See also the ar- 
ticles Simson and Srewart in our Work. 
Regretting that our limits oblige us to omit many 
Britis eters, whose names deserve preservation, _ 
we shall yet mention two; the Rev. Mr Lawson, au- Lawson. 
thor of a Dissertation on the Geometrical Analysis of 
the Ancients, and English editions of the Tangencies 
and Determinate Section of Apollonius ; and Dr Hors- Horsley. 
ley, Bishop of St Asaph. This learned prelate has Born 1732. 
given a restoration of Apollonius’ work on Inclinations, Died 1806, 
also a neat edition, in Latin, of Euclid’s Elements, be- 
sides other works on geometry. For farther informa- 
tion relative to the history of geometry, the reader may 
consult the articles ANatysis, ARITHMETIC oF SINEs, 
Conic Sections, Curves, Dratine, Ericyciorp, and 
other branches of mathematics that are to follow the 
present article; also the biographical accounts: of ma- 
thematicians contained in our work. We shall»now 
give a select catalogue of the principal works which 
have been written on geometry, particularly those 
which exhibit the progress of its improvement. Such 
as relate to conics have been already enumerated in 
Conic Sections, and those that treat of Trigonome- 
TRY, will be indicated in that article. 
On the history of geometry, consult Montucla, His- List of Wri- 
(ba it.) Bossut’s General His- ters on Geo= 
toire de Mathematiques, 
of Mathematics in French, of which there is an ™*'Y- 
English translation, and Dr Hutton’s Dictionary, (2d 
edit. 1815. ). 
Euclid, The Elements of Geometry: Of this there are 
very many editions; the first is that of Ratdolt, 1482. 
There is an elegant Greek and Latin edition of his 
works by Dr Gregory, Oxford 1703. Perhaps the most 
valuable isthat of Peyrard, in Greek, Latin, and French, 
of which the first six books are now published. Dr 
Barrow’s edition of all the books, and the Data, and Dr 
Horsley’s of the first 12, from the Latin versions of Com- 
mandine and Gregory, and the Data, are valuable. Sim~- 
son’s edition of the first six, and the 11th and 12th 
books, and the Data; and Playfair’s edition, the first 
six, (the same as Simson’s,) and three additional books 
on solids, are most commonly used. 
Euclid’s Porisms have been restored by Dr Simson in 
his Opera Religua, 1776. 
Archimedes ; the best editions are Torelli’s in Greek 
and Latin, Oxford, 1792 ; and Peyrard’s French trans- 
lation, Paris, 1808. The: first edition of the Greek 
text was that of Venatorius in 1544. 
Apollonius ; the writings that have been recovered of 
this celebrated eter are :—. 
1. The Section of a Ralio; and, 2. The Section of a 
Space. These have been restored by Snellius, 1607 ; 
and by Dr Halley, 1706. 
3. Determinaie Section ; Snellius restored these in his 
Apollonius Batavus, 1601. There is an English trans- 
lation by Lawson, to which is added a new restoration 
by Wales, 1772. . Simson has restored this work in his 
+ ae Reliqua, 1776 ; and Gianinni, an Italian geome-« 
ter, in 1773. ; 
4. Tangencies ; Vieta restored this in his Apollonius 
Gallus, 1600. Some additions were made by Ghetal- 
dus, and others by Alexander Anderson, in 1612. The 
labours of Vieta and Ghetaldus have been given in Eng- 
lish by Lawson, 1771. 
5. The Plane Loci; these have been. restored by 
