1816.) Royal: Institute of France. 153 
manner in which he considers his subject enabled him to findin the first 
place all the theorems already known, andthen many other theorems 
which are new. We shall quote the following, which is at once sim- 
pleand remarkable. According as the position of the equilibrium ts 
stable or not stable, the distance of the centre of gravity of that body 
from the centre of the keel is either a minimum or a maximum, with 
respect to all the neighbouring positions which floating bodies can 
take. And this. The directions of the greatest and least stability 
of any body whatever increase always at right angles. . The con- 
clusion of the report is that the new work of M. Dupin confirms 
the hopes which this philosopher has already given by his first 
labours. We cannot but applaud his continual efforts to direct 
their results towards the practice of the great art to which he has 
devoted himself. 
Small Machine for grinding Corn, for the Use of the Armies, 
by M. Cagniard Latour. 
The conclusions adopted are that the machine is good, that it 
may be useful in towns or citadels besieged, and to private families 
in times of scarcity, or when the mills are stopped by ice, and 
labourers are not employed. 
Greek, Latin, and French Edition of the 15 Books of the Ele- 
ments, and the Book of the Lata of Euclid, by M. Peyrard, 
Commissioners MM. Prony and Delambre, reporter. 
The Class had already given its approbation to a complete trans- 
Jation of all the works of Euclid remaining to us. M. Peyrard, 
author of this book, had compared the 23 Greek manuscripts 
which are in the king’s library. The result of this comparison was, 
that none of these manuscripts is entirely conformable to the Oxford 
edition ; that this edition, which is considered the best, and which 
is without doubt the most beautiful, is only, as far as the Greek 
text goes, a copy of the edition of Bale, from which it has taken 
even the most obvious faults; that most part of the manuscripts 
offer variations which fill up some blanks or elucidate some pas- 
sages of the two principal editions; but that in general all these 
manuscripts differ little from each other, but considerably from the 
oldest manuscript marked No. 190, and taken from the library of 
the Vatican, from which it was sent into France by M. Monge. 
The text in it appears more pure, more clear, less prolix, and 
more intelligible. M, Peyrard has attached himself chiefly to this 
manuscript, and has mostly followed it in the edition of the Greek 
text, which he has joined to his Latin aud French translations, 
At the request of his Excellency the Minister of the Interior, 
the Class has named a commission to examine the fidelity of the 
translation, and the merit of the numerous variations which 
M. Peyrard has introduced into the text, or rejected at the end of 
the work. Another commission of the class of history and ancient 
literature had been at the same time invited by the Minister to con- 
sider the new translation relative to style and execution. The re- 
porters of both Classes, after several conferences, were of the same 
Vor. VII. N° Il. L 
