4 PETRI LEONARDI RIJKE, 



lum ad illuJ planum pertinentium ; atque 



»" + y^ + ■=' = R' 

 aequaiio sphaerae. 



Colli quorum apicium coordinatae sunt «' , y' , 2' ; *" , y" , z" ; *'" , y'" , c'" 

 spheram secundum circulos tangent, qui siti suut in planis quorum aequamenia 

 sunt (1 ) 



tax + y/ + ss' — R2 . . . . («) 



**" +jy' + i2"=R^ . . . . (/3) 

 »*'"+ jy"+ 2s"'= R* . . . . (y) 



quaeramus coordlnatas puncti in quo illa tria plana se secant ; aequaiione ( « ) in-^ 

 veiiitur 



*= -f. .... (S) 



Habeblßius si loco * hunc valorem in aequationem (ß) transponamus 

 x" CR' -yf - ^^' ) 



x' 

 «"RS _ yy'x" — zz'x" + yx'y" + zz"x' = R^»' 



+ yy" + zz" = K^ 



R^ {x' — *") + z(z'x" — z"x') , , 



y = y^'-^ry^' ^'^ 



atriue in aequationem (y)^ 



.,'■' Q' - yj; - '^ '^ + ^y ^. ^,. = R. 



ä"'R^ - y/.v'" + zz'x'" -f. jj'^' + S2'x' = S^^x' 

 loco y in lianc aequationem ejus valor ponendus est , atque ergo 

 _,„^^ f."-y'x"'{x'-x ")+z y'x"'{z'x"-z"x' ) , ,„ _^ Ky"x'{x'- x")+zy"x'( /x"-z"x') 

 y'x'—y^- *'"' "* y'V -jV 



+ zz"'x'-= RV 

 x"K-^{y"x'—y'x") — 'KYx"'{x' — x'') — zfx'" {z'x" — z"x') — zz'x" {y"x' —fx")-^ 

 Ry"x' (»' — a:") + zy"x' C= V — ="x') + zz"'x' {fx'—y'x"') r= R^jc' (/V —/*"}• 

 _ R' (x'^y" — x'y'x" — x'"y'V + x"'y'x" +y'x"'x' —y'x"x"' —fx"" +y"'x"x') 

 "" ~ y"'x' (z'x"— z"x') -f. z"'x' (fx- —y'x") — z'x'" {y"x') +y'x"'z"x' ^^^' 



Nondum autem analytice expressimus tria puncta ad planum pertinere , cujus 

 aequaiio est 



ax + by + cz ^ d 

 at({ue nos hanc ob causam habere 



ax.' + 



{ i) Vid, 5Ij F. Le Roy, Analyse appliquee a la geonietrie des trois Jinieiisions §. ms. 



