419 
Now serupulus = = is scrupulus; because —— cateis = igin 
calcis 5 calcis 
; . serupulus 
.“. scrupulus = calcis.———— - 
P 8° calcis 
scrupulus eS > 3 ies 
But ———— = sil . 8C lus = cailcis , siliqua. 
pans siliqua rupu alcis , siliqua 
— . scrupulus . .. serupulus 
and semis. siliqua = semis. ——_-—_ = semtuncia . —~;-— 
calcis calcis 
= semiuncia. 2 . scrupulus. 
: calcis 
igin _ andras.igin _ 
But, by the integral notation, —— Pe, cadena aaa” 
igin andras __ igin — igin 
andras’ caleis — andras* ormis 
: Therefore, 
semis . siliqua = semiuncia . semiuncia . duella . scrupulus. 
= semiuncia . duella. 
| We have now to reduce the 
igin igin _ igin 
andras’ andras — arbas 
and, semis . siliqua = sicilius . duella . scrupulus. 
semiuncia . semiuncia = = sicilius. 
We have thus the required quantity in a very compli- 
cated form. To effect the reduction of this is the work of ~ 
another long operation, which it is unnecessary to repeat here, 
as the above will sufficiently serve for an example of the la- 
borious, though ingenious, plan which was pursued. 
Gerbert, in his Treatise on Geometry,* makes use of this 
notation, and adds, quod abaciste facillimum est.t The MS. 
Burney, 213, in the British Museum contains an express 
treatise on it. Added to which, the Alabaldine contractions | 
are constantly occurring in mathematical manuscripts, and 
till very lately no one had the slightest idea of their true 
nature. 
Are tivters peli ll 36a. atten ey ol 
® Pezri Thesaurus, t. i. p. ii. col. 13. + Ib. col. 30, 
