n 
JlcmwtS(fBook^. ( I he grand ^fameux Prohleme dd 
' la Quadrature flfii C^vdcrefolu Geometriquement par 
le Cercle c^^la Ligne droite^par Monfieur Mallement 
, de Meflange. A Paris, in i^'' i6%6. IVith a Re- 
futation of the fame j by Mr. D. Cluverius. Jleg* 
S. Soc. 
His Author is one of thofe unhappy Geometricians, 
who without having acquired a through Underftan- 
Mdingof the Principles, have yet thought themfelves able to 
matter the abftruleft Difficulties in this nice Mathematical 
•Science , where the leaft overfight or miftake fubverts the 
'.whole fuperftrudure. Hence it is, that the true Quadrature 
H the Circle here pretended to, is loft upon the fame Rock 
•with thofe many others, which the leis knowing and more 
opinionated of their own Skill have produced, in this and 
the laft Century : But briefly to Ihew wherein the Paralo- 
gifm of our Author confifts, we muft firft lay down the con- 
ftru£iion, whereby he pretends to do the Bufinefs : In Tab,2» 
Fig. 2. \Qtfk be a Circle, f az, the Diameter, a the Cen- 
ter, k z,k an equilateral Triangle infcribcd y Bb z line e- 
qual to the three fides of that Triangle, and dividing the 
Archfk equally in/, the line/ ^ wiU be half the fide of a 
Hexagon infcribed, which fide taken 6 times, is the Une /£ 
=to the circumference of the Hexagon ; and dividing the 
,Arch //in the fine hd is half the fide of the Dodecagon 
infcribed, and D d 2^ h d hi the circumference of the 
J)odecagon; and proceeding after the fame manner , the cir- 
jeumfercnces of Polygons of 24,48, 96 fides, &c. may be 
j ^ound, approaching fliill nearer and nearer to the circumfe- 
I rence of the Circle, which at length will be equal to the 
I line /fin the Tangent ; but how to find the Point Fis all 
I ihe Skill : Here our Author tells us, that the Points BEDF 
are all in the Arch of a Circle, whofe center is in the line 
Hh fz 
