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Calculus, as it is ie Ae creme oso and invent his Method of Indivisibles, in which he con- 
no further back than the 17th century ; but the inquiries sidered lines as composed -of an infinite number of 
which have led to it, must have occurred to Geometers we er omni of an infinite number of 
from the earliest peri tay void yew of; a re pen as Ant of an infinite ni end 
was cultivated. It rs from the writings o i e to have is theor 
and Archimedes, hit ven the ancients considered cur- the year 1629, att he Lin awn net with ti. 
vilineal , or the solids formed by the rotationof tle, Geometria sndlivisibélium isibilium conlinuorum novd quaédam 
curves, they established the truth of thei itions ratione : e of his method was at- 
by a peculiar mode of demonstration, whi was indi« tacked by Guildinus in 1640, and then he shewed, that 
Eudiits Elements, is arriustence of this kind ofdemon: lines; of drhidh Ga valetidis eocisillored thie! ratice"ana tiie 
stration. It is there to prove, that circles sums, are no other than the little solids, or the’ inscri- 
haye to each other the ratio of the squares of their dia~ bed and circumscribed ‘parallelograms of 
i > ‘differ 
lar gons inscribed in circles, have to each other cluded between them, by less than any given quantity ; 
RES Es coil ‘hace, by a mode of reasoning rather wae tiie investnette, anyone eaten, 
artificial, although quite accurate, the truth of of a curvilineal to another known one, employs 
ion is proved to extend to the circles ves, many words, an “indirect turn of demonstration ; 
Soe negte: Shere baad yt Deg om tageraye item the modern eter, i 
not be to the square of the other diameter, as the one ni in’ 
circle to a space either Jess, or greater than the other 
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