[418] 
tion ADE. Which Semi-quadrate, is 
a Uh Figure^ and a liJ^ fituate to 
^ AE, asisACBtoAB. 
And therefore ( becaufe like Fi- 
gures are in the Duplicate Proportion 
of their refpedive Sides ) If we fo 
infcribe AE, as that the Square of 
A E be to the Square of AB, in fuch 
Given Proportion, the Lunula will 
C at DE, be fo divided as is required. 
And this will hold ( if duly appli- 
ed, according as the different Cafes may require ) though E be 
taken ( in the Continuation of the Semi-circle ) beyond B. For 
{ ftill ) Like Figures, will be in Duplicate Proportion of their 
Refpedive Sides ; and CE = CD±DE. And the fame is yet im- 
proveable much further. 
I forbear to Apply this to the feveral Parts of the whole Sy- 
fleme, confidered by Dr Gregorie^ ( Or to that of Mr Cajwelly ) 
that I be not too Teadious. 
Much lefs fhall I give my felf the trouble to confider the Solids 
to be made by the Converfion of it, or of its parts, about a given 
Axis, (as MN, or AB, or AC, or BC, &c. ) with their Surfaces and 
Centers of Gravity ; as I have done elfewhere for the Cycloid : 
But fuch as are at Leifure ( and think it worth the while, ) may 
-do it by fuch like Methodes as I have made ufe of for the Cydoide, 
lam SIR, 
Tours to ferve you, 
JOHN JVALLIS. 
Pofl-fcript. 
In the TranfaBms for the Month of Auguji laft pafl; Numb. i fS'- 
A Letter of mine, is very faulty ly Printed. I defire that the Errata 
may be thus Corrected. 
P<tg. 280. /. 24. ut ait./'. 281./. I J. differentias infinitefimas. f. 28*. /. 12. (ut 
antea) reram Novitas. /. 14. Melfis. /.15. Et quidem. /. 16, Atque hinc. 
/. 17. natura. /. 22. Academia. /.25. reapfe. /.53. mifi. 285. /. defperatum. 
/. II. Sued. /. 17. itinere. /. 2j. adomat. /. 33. Coeno. 284. /. i. fita. /.15. 
redeundo ) fenfim, /. 17. motibus. /. 19. penitius. /. 22. materia?. L 23. per- 
pendiculum ere6los ) ad. /.24. longo traftu. Lz%, praefe. /.29. Multaque. /. 30. 
annos. / 31. deprompta) raihi videntur hue. /.32. alio. /.34. coenofum, torbi- 
dum. /.35. Ifthmo./. uh.ThzWordsV. S. Aug. 29. \6<)^. Jhouldhxvz fiood^ lin. 20. 
Numb. 257.^. 346./. iiAheSolarTr(>pkalyear,j^. 349. /. 2, fuggeftedby./'. 3JI. 
i. 34. ftands thus. 
