12. What is Plane Geometry?
13. What portion of plane geometry forms the subject of the “First Six Books of Euclid’s Elements”? Ans. The geometry of the point, line, and circle.
14. What is the subject-matter of Book I.?
15. How many conditions are necessary to fix the position of a point in a plane? Ans. Two; for it must be the intersection of two lines, straight or curved.
16. Give examples taken from Book I.
17. In order to construct a line, how many conditions must be given? Ans. Two; as, for instance, two points through which it must pass; or one point through which it must pass and a line to which it must be parallel or perpendicular, &c.
18. What problems on the drawing of lines occur in Book I.? Ans. ii., ix., xi., xii., xxiii., xxxi., in each of which, except Problem 2, there are two conditions. The direction in Problem 2 is indeterminate.
19. How many conditions are required in order to describe a circle? Ans. Three; as, for instance, the position of the centre (which depends on two conditions) and the length of the radius (compare Post. iii.).
20. How is a proposition proved indirectly? Ans. By proving that its contradictory is false.
21. What is meant by the obverse of a proposition?