IIL An ExtraSl of a Letter from the Ke^erend 
Dr. John VVallis to Richard Waller, Efq-, 
Secretary to the Royal Society^ concerning the 
Spaces in the Cycloid, which are ferfeBly 
Quadrable. 
Oxford^ Augufl a i . 1 69 > . 
SIR, 
I Find it is thought by moft, that there is no other 
part of the Semicydoid Figure (adjacent to the Curve) 
that is capable of being Geometrically Squared, but thefc 
two, viz, 
I. The Segment^ ^F, Figur. I. taking ^ r= j i4 a, 
( which was firft obferved by Sir Chrijiopher Wren, and 
after him by Hugenius 9XidL others) and it is=! 
a. The Trilinear AdD (taking dD^ in the Parallel 
dDC^ paffing through the Center C,) which is ~R\ 
But it is other wife (as I have fliewed in my Treatife 
De Cycloide^ and that De M&tu; the Figures of which 
latter I retain here, Co far as they concern this occafion ; ) 
there being other portions of it, equally capable of Qua- 
drature. 
In order to which, I there Ihew (De Motu, Cap, 5-. 
Prop.zo, A, 801, 805, 804.) that not only the 
Cycloid is Triple to the Circle Generant , ( which was 
known before) but that the refpe^lve parts of that are 
Triple tothoft of this : which is the Foundation on 
which 1 build my whole Procefs concerning the Cychid 
in both Treatifes, ( and which is not pretended, that I 
know of, to have been obferved, or known, by any 
body before me :) That xs h^aA Figur. i, triple to 
the Sedor B<zA (taking h ^ parallel 10 Bet) where - 
ever, in the Curve ^r, we take the point k 
I then i 
