out of his owa fenfes, and the experience of fomany 
years. Bat he is fatistyed in this ; that, what Mr. Hook, 
flights and undervalues , is by divers eminent, worthy^ 
and learned men, well approved and commended j 
(who's praife he more values, as being from praife- 
worthy perfons^ ) and doubts not but that they will be 
found more accurate than to one, two, or three in- 
tire Minutes (as Mr. /iTj^^?^ pretends, before he fees them ) 
And hopes that, of the 'E^yal Society (of whom he ex- 
preffeth a great efteemj there are who will be ready to 
vindicate him from Detradlors. 
The 12^^. is from Dr. Wallis, to the ^^^^or, the ip^H, 
to him from Titus Lwius Burattini (which latter had 
for lome time been with the Author, and affiftant at 
his ObfervationSi ) v/hich (^befide Gratulations, and 
juft commendations of his Inftruments, and his Obfer- 
vations) fpeak particularly of the Divifions in the limb 
by Diagonals (nkd hy Tyc/jo, the La n dt^r a vs, this jiutbor^ 
and divers others i ) to this purpofe : That, the Divi- 
fion of an Angle into equal parts by ftreight Diago- 
nals obhquely cutting concentrick Arches in the Iimb^ 
would require, in Mathematical rigor, that the con- 
centrick circles be fet at fomewhat unequal diftances.r 
and in fmal Inftruments, where the breadth of the di- 
vided limb is aconfiderable part of the Radius, |^as|, 
or ^5 thereof) and the Angle to be fo divided, of a confi* 
derable greatnefs (luppole, lo minutes or more) it may 
^•equire fome httle difference of intervals j fas the Ju- 
thor was well aware 5 and had himfelf given notice Afar^. 
Cosleji. p. 139, 140,) But where the Inftrument is large 
(as here, 6^ 8, or 10 foot Radius,) and the breadth 
ot the limb to be divided, but narrow (as here, about 
half An incbj and (as here) the angle to be fo divided 
but f minutes i the true intervals according to Maths^ 
mamal xlgor.are undiftinguifliable, to the fubtileft lenfe, 
from equal diftances. Aad, here, it is indifferent to 
F f f lay, 
