28 Book XIII. 15.* 7. The number of propositions and their order in some Adhyayas is different. In Book III. our text has 86 propositions, propositions 11 and 12 being included in proposition 11 as under If two circles touch one another internally or externally, the athraight line which joins heir centers being produced shall pass through the point of contact' In Book . proposition8 12 and 18 in the Sanskrit text are found to be propositions 18 and 12 respectively in Bil.s edition. of 10 alternative proofs in all bhe books taken together, the following are exctio d Aberd':- Book Prop.20, 2, 34. Book III. Prop. 3, 4, 5, 10, 1l, I2, 18, 17. Book vtProp. 2, 4, 5, 6. Boo VII. Prop. 7, 28. The following are found in Bil. (I. 5 ), (I. 12 ), (I. 20 one alternative ), (I. 25), ( v1. 18). Book I. Prop. 11 is only a particular easo. Prop. 2 contains three cases . Prop. 25 gives the direct proof. Book II. Prop. 8 gives a common proof to Propositions ? and 8. Prop. 9 gives the direct proof fonnd in recent editions of Juclid. Prop. 30 gives the converse of the 1st part of the Proot. Book IV. Prop. I is the converse of Prop. I. 5
