EXERCISES CXXXVI (Page 522).

1. Four.

2. Six.

3. Seven. 4. Eight.

EXERCISES CXXXVII (Pages 532, 533).

1. § 407. section of the planes ABC, ADE.

2. Cf. Ques. 1.

3. §§ 401, 402.

5. § 401.

4. The inter6. See Ques. 4.

8.

§ 407.

9.

§§ 402, 406,

11. § 401.

12. § 406.

13. § 402.

17. § 410

7. An infinite number: see § 405. 407. 10. SS 406, 408.

15. §§ 400, 401. 16. §§ 401 (Cor.), 402.

18. §§ 400, 407. 19. § 410. 20. §§ 401, 402. 23. See Ques. 18.

24. See Ques. 18.

plane. 16. SS 411, 416. 18. If AB and CD are the two given straight lines, suppose AC and BD are each to both AB and CD. Draw CE, DF each || AB. Prove AC, BD each plane ECDF, etc. 19. Use Fig. 550; draw AK1 GF; prove ▲ BFD=AKC. 20. § 418. 21. §§ 154, 155, 411.

6. § 418. 10. §§ 402, 415, 418. 418. 13. §§ 401, 402, 417, 418. 14. § 426. 16. Use Ex. CXXXVIII, 3. 17. Use Ex. CXXXVIII, 3. 19. § 418; eight. 20. §§ 426, 209. 21. §§ 411, 426.

7. Use Ques. 6. 8. Prove that opposite edges of the parallelopiped are opposite sides of a rectangle. 9. 70.5°. 12. § 400. 13. § 435. 14. (iii)

§ 426.

18. 1.41".

15. 1.63".

16. 54.7°, 70.5°.

17. 1·22", 41′′. 19. 158", 4.74", 3 67"; 1·58", 4.74", 3.67". 20. 2".

22. 2.43".

21. § 437. 24 S$ 402, 407; (a) when the two opposite edges are perpendicular; (b) when in addition the distances of the plane of section from these two edges are proportional to the edges. 25. §§ 399, 406. 26. See Ex. CXXXVIII, 17. 27. Let AG be a diagonal of the cube; bisect each of the six edges which do not meet AG; all these middle points are equidistant from A and G and therefore lie in the plane bisecting AG at right angles, 28. See Ex. CXXXVIII, 19. 29. (iii) § 443, converse. 30. (i) Yes; (ii) no; (iii) no.

etc.

31. § 440. 32. § 440.

[The letter s may be added to an abbreviation to form the plural, e. g. ms may be used for parallelograms.]

The following list shows the Greek letters used in this book for naming angles, with their English equivalents and their Greek names :

a, a, alpha; B, b, beta; y, g, gamma; d, d, delta; e, th, theta; λ, 1, lambda; μ, m, mu; σ, s, sigma; 4, ph, phi.

New Books and New Editions published since July 1, 1907, are underlined.

Select List of Books

IN THE

University Tutorial Series.

University Tutorial Press L

W. B. CLIVE, 157 DRURY LANE, LONDON, W.C.

The General Catalogue (32 pages); Sectional Catalogues in (1) Mathematics and Mechanics, (2) Science, (3) Classics, (4) English and French, with History, Philosophy, etc.; and Special Catalogues for London University and other Examinations, may be had post free on application.

SEPTEMBER 1908.