3o jMtfcelianea Curioja. 



ny Segments as they thought fit j (or fuppofed 

 it to be fo parted.) ~ 



3. Thefe Segments were fo many wanting one, 

 aa was the number of thofe Parallels. 



4. To each of thefe Parallels, wanting one ; 

 they fitted Parallelograms, of fuch breadths a* 

 .were the Intervals (equal or unequal) between 

 each of them (refpe&ively) and the next fol- 

 lowing. Which formed an Adfcribed Figure 

 made up of thofe Parallelograms. 



5. And, if they began with the Greateft 

 (and therefore negleded the leaflj flich Figure 

 was Circumfcribed, ("as Fig. 1:) and therefore 

 Bigger than the Curvilinear propofed. 



6. If with the Leaft (neglecting the great- 

 efl;) the Figure was Infcribed (as Fig, 2. ) 

 and therefore Lefs than that propofed. 



7. But, as the number of Segments was in- 

 creafed, (and thereby their breadths diminifh- 

 cd } ) the difference of the Circumfcribed from 

 the Infcribed (and therefore of either from 

 that propofed) did continually decreafe, fo as 

 at laft to be lefs than any alfigned.- 



8. On which they grounded their Method 

 of Exhauftions. 



9. In cafes wherein the Breadth of the Pa- 

 rallelograms,, or Intervals of the Parallels, is 

 not to be confidered, but their length only ; 

 (or, which is much the fame, where the Inter- 

 vals are all the fame, and each reputed = f . ) 

 Archimedes >(inftead of Infcribed and Circum- 

 fcribed Figures) ufed to fiy, All except the 

 Greateft, and All except the Leaft. As Prop. 1 1 . 

 Lin. Spiral. 



Particular Cafe. 

 10/ Though it be well known, that, in the 

 Terrelfrial Gfobe, all the Meridians meet at 



the 



