

(6) 



(4) 



Si per extremitatem abscissae x ducatur planum normale axi AX , hujus 

 plani aequatio ope coordinatarum #', y 1 ', z' expressa , erit 



x = x'cosa -}- y'cosaf -f- z'cosct," ..... (i) 

 eodem modo invenientur 



y x'cosfi +y' cos/3' 4- z' cos/3" .... (2) 

 z = x' cosy +.7' cosy' -j- z'cosy" .... (3): 



quod si attendamus novas coordinatas x f , y' , z' esse respective normales 

 prioribus x, y , z, sex orientur relationes. 



cos* a + cos*/3 4- cos*y = i 

 cos* a 4* cos*/3 4" cos*y = i 

 cos* a 4" cos*/3 4" cos*y = i 

 cosa cosa' 4" cos/3 cos/3' 4" cosy cosy' = o 

 cos a cos a" 4- cos/3 cos/3" 4- cosy cosy" = o 

 cos a' cos a" 4~ cos/3' cos/3" 4~ cosy' cosy" = o 

 Si multiplicetur (i) per cosa, (2) per cos/3, (3) per cosy, respectu 

 habito ad aequationes (4) , orientur vicissim hse relationes 

 x' = xcosa 4"J{ cos /3 4~ zcos y } 



y' = xcosaf +^cos/3' 4" -scosy' > (5) 



z' = xcosx" -{-ycos(3" -\- zcosy" \ 

 ex quibus emergunt sequentes praecedentibus similes 



COS'fl! 4~ COS a a' 4" COS a a" = I 



cos'/S 4- cos"/3' 4- cos'/S" = i 



cos"y 4~ cos*y' 4" cos'y" = i 



cosa cos/3 4- cosa' cos/3' 4- cosa" cos/3" = o 



cos# cosy 4~ cos#' cosy' 4~ cosa" cosy" = o 



cos/3 cosy 4" cos/3' cosy' 4~ cos/3" cosy" = o 



Transeamus ad aliam investigationem valorum coordinatarum x , y> z 



ope coordinatarum x' , y' , z' , ideoque ponamus relationes generalissimas 



x = m' x' 4- n' y' -\- p' z' 



y = m "x' +n'y+p"z' 



(6) 



z = m'"x' 



(7) 



Cum duo systemata x, y , z, et x' , y' } z' sint orthogonalia , quadra- 

 turn lineas ductse a puncto quocumque ad initium commune , erit , in 



