RESPONSIO AD QUAESTIONEM MATJIEMATICAM. 



*'* + /'' + 2'* = 1 . 



« ergo 2'^ (i +«'* + **; = I 

 1 



et z' = 



, + «2 ^. i^ 

 I 



1/ti + «^ + b^y 



qiiod si hoc substituamus in aequationibiis 



x' = «a' y' = ^2;' 



habebimus 



, a , _, b ^ . 



*~VCi+«^ + ^=) ^ ~ i/Ci + «^ + ^==)* 



Sint y, ^", 2" puncti M' coordinatae, aequationes erunt 



x" = «'2", y = b'z", 1 — *"^ + y"^ + 2"% 



et erunt 



* -vci+«'"+^'o ^ "i/ci +«''+*'") * ~vo+«"+n* 



Deducta a distantia M'^ = x"^ + y"^ + 2'^ 

 distantift M"^ = x"^ + y"^ + 2"^ 



■"■ I " -■■' ■ " ■ . I - I !■— I ■ I ■!■■■ I 11 1 ) 11 ■ ■ 



remanet M'^ — M"= = (;«;' — ^c"/ + iy' — y"f + («' — 2"/. 



vel M' — M" = i/^^*'— *"/ + iy'—y"T + (2' — O'')* 

 Sit nunc V angulus quaesitus, tunc erit 



Cos. V = I — 2 Sin.2(— ) (i). 



= I - / C^'-^")' + (y'-y"Y 4- rz'-z"Y \ ^ 



~ I (2-(£M2'f+£!^ - c^"'+y'M^'") + 2(*'.^"+/y'+^'^")) 



( I ) Vid. y. Swinden , /. /. VIII Boek 34 Voprst. No. iii. pag. 375- 



( 2 ) Nam Sin. ( I ) = I V^( (*' - x"f + (/ - j")^ + (2' - 2")» ) 



. ^z' V 



Sin 



( - ) = i( c*'-*")^ + c/-y')= + c^'-^"/) 



et a Sin."( J ) = C«' -^")- + C/- 3'".- 4- (2 -2"); 



