1809.] [ 
PROCEEDINGS OF 
v3 | 
LEARNED SOCIETES, 
Le 
NATIONAL INSTITUTE. 
* Report on the Progress of the Sciences 
Sroim the Epoch of the French Revolu- 
tion (1789) to the Year 1808, made by 
a commussion of the Instituteof France, 
by order of the Emperor Napoleon. 
} 1S Majesty bemg in council,t a de- 
at putation from the class of Mathe- 
matical and Physical Sciences of the In- 
stitute, composed of M. M. Bougainville, 
president of the Institute; Terron, vice- 
president ; Delambre, Cuvier, secreta- 
ries; M. M, Lagrange, Monge, Messier 
de Fieurieu, Charles. Berthollet, Haug, 
Lamarck, ‘Thoum, de Lacepede, and 
Dessesarts, members of the Institute ; 
was presented by his excellency the mix 
nister of the home department, and ad- 
mutted to the bar of the council. 
Introductory Speech of M. Bougainville, 
President of the Institute. 
SIRE 
Your imperial and royal majesty has 
erdered that the several classes of the 
Enstitute should appear in your council, 
and report to you on the present state of 
the sciences, literature, and the arts, 
and on their progress since the yeat 1789, 
The class of the mathematical and 
physieal seiences now perform that duty, 
and im présenting myself at the head of 
the learned men who compose it, [ain 
indebted to my ave for that hours 
But, site, such is the variety of objects 
with which this class has been occupied, 
that even with all the conciseness of 
which profound knowledge and a spirit 
of analysis afford a facility, the report 
containing a bare statement ‘of facts 1s of 
great extent. 
it is therefore only the sketch of their 
labours that M. M. Delainbre and Cuvier 
are about to read. 
I shafl ake only asingle observation, 
Which is, that at the same'time that the 
period from 1789 to 1808 will be, for 
political and military events, oue of the 
most memorabie in the annals of natious, 
* Asit is probable that the discoveries, 
the labours, and writings of Englishmen, are 
noliced in too cursory a manner, or wholly 
omitted in this Report, we shall cheerfully 
insert such explanations or observations as 
may be sent us by ovr own countrymen on 
particular passages of these reports. 
t The sitting of Saturgay, the 6th of 
February, 1808. : 
3 
it will also be’ one of the most brilliant 
in the records of the arts and sciences. 
The share which the French have 
had in the improvement of those ana- 
lytical methods, which have led ta 
the great discéveties of the system oF the 
world: atid even to those of the three 
kingdoms of nature, will shew that if che 
influence of one mah alone has’ niade 
lreroes of all our warriors, our learned 
nien, honoured by the protection of your 
inajesty, whom they have sec in their 
ranks, have a claim to add some rays to 
the national glory. 
Report of M. Delambre, Secretary of 
the Class for the Maihemutical Sciences: 
SIRE, 
Upon an occasion as memiorable as 
glorious for the sciences, at the rnoment 
when their representatives and or¢ans 
are admitted to the honor of depositing, 
at the foot of your throne, a view of the 
acquisitions made by them, of the m- 
teresting facts by which they have been 
enriched, the desire so natural of laying 
before your majesty, in the rose fave 
able light, the new discoveries, will not 
lead us to forget that each Branch of 
human knowledge has a language and 
style ees to “feel cloak the branch 
oF inathematics can have no other merit 
than that of conciseness and simplicity, 
Bot if reason did not induce ws sere 
pulously to adhere to this principle, the 
abundance of tle materials which we 
Nave to presetit to your majesty would 
render it a matter of indispensable ne- 
cessity. 
“Allthe parts of the mathematics arg 
intimately connected together, and mi- 
tually afford assistance to each other. 
We shall begin with those which were 
first cultivated, and which serve a5 an 
introduction to ll the others, 
The elementary part farnisies us with 
two works ednaliv worthy of their suc- 
cess. In the one, M. Legendre recalls 
geometry to its ancient severity, aiid 
presents new ideas for treating sonre 
parts of it ina manner entirely analytie 
eal; in the other, Hl. Tacroix proposed 
a8) himself to preserve as] thar is essential 
m the ancient inethod, but eo that his 
book may Itkewise serve as an introduc- 
tion Lo modern analysis. 
The beautiful collection of the Greek 
mathematicians was completed im 1791, 
bythe Archimedes of Tareli, of weicir 
wi. Peyrard 
