70 G. FLEURI. 



Number — Arithmetic. 

 Amongst the magnitudes considered in science, some, such as a 

 volume, a weight, an atmospheric pressure, etc., are completely 

 known when the number which measures them is known. 



Those magnitudes are called absolute magnitudes, and the 

 numbers which measure them are called their moduli or tensors.* 



. , Any of these magnitudes has same tensor 



"! *" as a certain straight line AB and therefore 



lg ' ' the line AB can be considered as represent- 



ing that magnitude. Consequently, any question on absolute 

 magnitudes of any kind can be transformed into a similar question 

 on straight lines representing these magnitudes. 



For simplicity in this representation we will agree to take these 

 straight lines — in the same plane, always horizontal and moreover 

 of same direction, the direction of the arrow, from left to right. 



(%• i.) 



This idea of direction may be made quite clear in the following 

 manner : Let us suppose that a point moves along our line from 

 A to B^the straight line AB can then be considered as the result 

 of that motion (translation) and even as representing that motion 

 or in other words as the symbol of that motion. 



Ir is this way of considering a straight line which we choose — 

 (and I may point out here that it is the way which tends to pre- 

 vail in modern geometry). A straight line AB is therefore the 

 symbol of the translation of a point moving along the line from 

 A to B. Please notice the order of the letters AB. A is the 

 starting point, B the terminal point and in denoting our lines we 

 will always carefully put the starting point first and then the 

 terminal point. 



The properties of operations on absolute magnitudes are the 

 properties of operations on their tensors, i.e., on numbers and are 



* We adopt the word tensor preferably to ' modulus/ as the latter word 

 is u*ed in quite a different acceptation in the theory of Elliptic and in 

 general Abelian functions. 



