158 TERMINOLOGY. . 144. 



in which tLe faces of the two first forms meet. Hence the 

 algebraic expression of the Line of Combination must be 

 exactly the same for the third form and the first, or the 

 third and the second, which is found when calculating the 

 Line of Combination for the first and the second form 

 among themselves. 



After these preparations, the length of the Line of Com- 

 bination EF or EF' must be calculated from the known or 

 given dimensions of the two first forms. An expression 

 will be obtained for it, finite or infinite, positive or nega- 

 tive, in which every single quantity is determined. 



The same line EF or EF' must also be calculated 

 from the dimensions, either of the first and the third, or of 

 the second and the third form. An expression similar to 

 that mentioned above will be found, in which every thing 

 is known, except what refers to, or is dependent upon, 

 the dimensions of the third form, to ascertain whose re- 

 lations is the object of the inquiry. The two values of 

 EF. or EF' being equal to each other, they maybe joined 

 in an equation to be resolved for one of the unknown quan- 

 tities. 



If this equation contains only one unknown quantity, 

 the resolution yields its value at once, and by this the 

 perfect determination of the third form is obtained. But 

 if there are two unknown quantities, the process must be 

 repeated, by constructing another equation, for a case in 

 which the unknown form which is to be determined com- 

 bines in the same way with other known forms ; the second 

 equation is procured in the same way as the first. 



In the application of this process, we may take advantage 

 of many circumstances, which may very often render the 

 second equation superfluous ; this, however, is so obvious 

 in every particular case, that it will not be necessary here 

 to enter upon this subject more at large. 



. 144. MAGNITUDE OF THE EDGES OF COMBINATION. 



To a complete knowledge of a combination is also 



