Mathematical Collections of Pappus. 
19 
nis, hoc est semidiameter tropiei est 55023, liabet autem 
23924 ad 55023earidem fere proportionem quamlO ad 23.” 
( 2 ) “ H’abet enim sphserae diameter ad diametrum tropiei earn 
fere proportionem quam 25 /j ad 23.” 
The general fidelity of the translation will be evident from a 
comparison of the Latin with the Greek, and their agreement 
is most favourable to the text as it now stands. It is worthy of 
observation, likewise, that, with respect to the numerals, there is 
no difference whatever in the manuscripts, excepting that some 
of them have won ryoc, in the place of which only confirms 
the accuracy, in this instance, of the present reading. But it 
may be said, that one transcriber often copies the errors of ano- 
ther, and that these may be detected by the internal evidence 
from the context. This is very true, but it is wholly inappli- 
cable to the support of the proposed correction. On the contra- 
ry, the internal evidence is, I conceive, conclusive against any 
alteration. M. Delambre says very justly, “ Pappus dit que le 
diametre de la sphere est en puissance a celui du tropique 
comme 629 : 529, d’ou je tire cos. — 
2 =23° 29' 50"*;” 
but he omits all allusion to the latter part of the passage, and this, 
I think, if he had attended to it, would have prevented him 
from suggesting the conjectural emendation. It wall be obser- 
ved that 629, 529 are not the original numbers, on which the 
reasoning is founded. They are derived from the other ratio 
of 10 to 23 : this is clearly pointed out by the use of the con- 
conjunction g7iws£. Now, this being ad- 
mitted, which can hardly be disputed, 
it follows that the larger numbers could 
be none other than as they now stand. 
For, let C be the centre of the sphere, 
CP its axis, CE the radius of the equa- 
tor, A B the radius of the tropic; join 
AC, and then, by the conditions of the £ 
P 
It is hardly worth mentioning, but the quantity strictly is greater by 5". 
Log. 529 2.72345.57 
Log. 629 2.7986507 
2)9^9248050 
9.9624025 which is the Cosine of 23° 29' 557. 
