It may not be improper here to caution learners against some inaccuracies in style and expression which are often met with in scientific works published in this country To matters of this kind much attention is paid by the French mathematicians. By this means, as may naturally be expected, accuracy is produced in thought as well as in style, and hence it is, that many of their recent works exhibit a perspicuity and simplicity, and a logical clearness of arrangement, which enhance their value in a very considerable degree. To put the student on his guard against faults of this kind, some instances of the inaccuracies above referred to are subjoined; and he will find that, by avoiding the use of them and of similar modes of expression, he will soon acquire a comparatively correct style, instead of the careless and random one that is so common in this country Some of these instances will doubtless be found in the works of authors of the present day, but they have been purposely selected from the writings of authors no longer living.