...one another. IX. The whole is greater than its part. X. All right angles are equal to one another. " Two straight lines, which intersect one another, cannot be " both parallel to the same straight line." Book I. PROPOSITION I. PROBLEM. TO describe an equilateral triangle upon a given finite straight line....

...appeared more obvious, and better entitled to be accounted an Axiom, has been introduced, viz. " that two straight " lines, which intersect one another,...be both parallel to the •" same straight line." On this subject, however, a fuller explanation is necessary, for which see the note on the 29th Prop....

...and equal to all its parts taken together. X. — All right angles are equal to one another. XI. — Two straight lines, which intersect one another, cannot be both parallel to the same straight line. XII. — The shortest distance between two points is a straight line. OF GEOMETRY. Book I. PROPOSITION...

...another. 9. The whole is greater than its part. 10. All right angles are equal to one another. 11. " Two straight lines which intersect one another, cannot be both parallel to the same straight line." PROP. IV. If two triangles have two sides of the one equal to two sides of the other, each to each...

...parallels is founded on the following axiom, suggested by Ludlam in his Rudiments of Mathematics : " Two straight lines which intersect one another, cannot be both parallel to the same straight line :" and from this he derives, indirectly, in a very simple manner, the proof of the first part of the...

...another. 9. The whole is greater than its part. 10. All right angles are equal to one another. 11. "Two straight lines which intersect one another, cannot be both pa"rallel to the same straight line." PROPOSITION I. PROBLEM. To describe an equilateral triangle upon a given finite straight lint.' Let...

...— 9. nition. Unfortunately, however, he is obliged afterwards to assume the truth of another axiom, viz. " two straight lines which intersect one another...cannot be both parallel to the same straight line."* 3, The definition is exceedingly complex and difficult to be understood. It appears to me, then, that...

...parallels is founded on the following axiom, suggested by Ludlam in his Rudiments of Mathematics : " Two straight lines which intersect one another, cannot be both parallel to the same straight line. From this the author derives, indirectly, in a very simple manner, the proof of the first part of the...

...the converse of Prop. 27, Book i. Professor Playfair has adopted in his Elements of Geometry, that " Two straight lines which intersect one another cannot be both parallel to the same straight line." This apparently more simple axiom follows as a direct inference from Prop. 30, Book I. But one of the...

...appeared more obvious, and better entitled to be accounted an Axiom, has been introduced, viz. " that two straight lines, which intersect one another, can"not be both parallel to the same straight line." On this subject, however, a fuller explanation is necessary, for which see the note on the 29th Prop....