Euclid. # Euclid's Elements of geometry, the first six books, chiefly from the text of Dr. Simson, with explanatory notes; a series of questions on each book ... Designed for the use of the junior classes in public and private schools online

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Online Library → Euclid → Euclid's Elements of geometry, the first six books, chiefly from the text of Dr. Simson, with explanatory notes; a series of questions on each book ... Designed for the use of the junior classes in public and private schools → online text (page 37 of 38)

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on the line joining these points, describe a square ; the Imes drawn from

the center through the opposite angles of the square to meet the circular ;

arc, will determine two points of the square inscribed in the sector.

100. Let ABCDE be the given pentagon. On AB, AE take equal!

distances AF, AG, join FG, and on FG describe a square FGKH.

Join AH and produce it to meet a side of the pentagon in L. Draw

LM parallel to FH meeting AE in M. Then LM is a side of the

inscribed square.

101. Let ABC be the given triangle. Draw AD making with the

base BC an angle equal to one of the given angles of the parallelogram.

Draw AE parallel to BC and take AD to AE in the given ratio of the

sides. Join BE cutting AC in F.

102. The locus of the intersections of the diagonals of all the

rectangles inscribed in a scalene triangle, is a straight line drawn from the

bisection of the base to the bisection of the shorter side of the triangle.

103. This parallelogram is one half of the square in the circle.

104. Analysis. Let ABCD be the given rectangle, and EFGH that

to be constructed. Then the diagonals of EFGH are equal and bisect

each other in P the center of the given rectangle. About EPF describe

a circle meeting BD in K, and join KE, KF. Then since the rectangle

EFGH is given in species, the angle EPF formed by its diagcmals is

given ; and hence also the opposite angle EKF of the inscribed quadri-

lateral PEKF is given. Also since KP bisects that angle, the angle

PKE is given, and its supplement BKE is given. And in the same way,

KF is parallel to another given line ; and hence EF is parallel to a third

given line. Again, the angle EPF of the isosceles triangle EPF is given ;

and hence the quadrilateral EPFK is given in species.

105. In the figure Euc. in. 30 ; from C draw CE, CF making with

CD, the angles DCE, DCF each equal to the angle CDA or CDB, and

meeting the arc ADB in E and F. Join EF, the segment of the circle

described upon EF and which passes through C, will be similar to ADB.

106. The square inscribed in the circle may be shewn to be equal to

twice the square on the radius ; and five times the square inscribed in

the semicircle to four times the square on the radius.

107. The three triangles formed by three sides of the square with

segments of the sides of the given triangle, may be proved to be similar.

Whence by Euc. vi. 4, the truth of the property.

108. By constructing the figure, it may be shewn that twice the

square inscribed in the quadrant is equal to the square on the radius,

and that five times the square inscribed in the semicircle is equal to four

times the square on the radius. Whence it follows that, &c.

109. By Euc. i. 47, and Euc. vi. 4, it may be shewn, that four times

the square on the radius is equal to fifteen times the square on one of the

equal sides of the triangle.

110. Constructing the figure, the right-angled triangles SCT, ACB

ON BOOK VI. 355

may be proved to have a certain ratio, and the triangles ACB, CPM in

the same way, may be proved to have the same ratio.

111. Let 13 A, AC be the bounding radii, and D a point in the arc of

a quadrant. Bisect BAG by AE, and draw through D, the line HDGP

perpendicular to AE at G, and meeting AB, AC, produced in H, P.

From H draw HM to touch the circle of which BC is a quadrantal arc ;

produce AH, making HL equal to HM, also on HA, take HK equal to

HM. Then K, L, are the points of contact of two circles through D

which touch the bounding radii, AB, AC.

Join DA. Then, since BAC is a right angle, AK is equal to the

radius of the circle which touches BA, BC in K, K' ; and similarly, AL

is the radius of the circle which touches them in L, L'. Also, HAP

being an isosceles triangle, and AD drawn to the base, AD* is shewn

to be equal to AK . KL. Euc. iii. 36 ; ii. 5, Cor.

1 ] 2. Let E, F, G be the centers of the circles inscribed in the triangles

ABC, ADB, ACD. Draw EH, FK, GL perpendiculars on BC, BA, AC

respectively, and join CE, EB ; BF, FA ; CG, GA. Then the relation

between E,, r, r', or EH, FK, GL may be found from the similar triangles,

and the property of right-angled triangles.

113. The two hexagons consist each of six equilateral triangles, and

the ratio of the hexagons is the same as the ratio of their equilateral

triangles.

114. The area of the inscribed equilateral triangle may be proved to

be equal to half of the inscribed hexagon, and the circumscribed triangle

equal to four times the inscribed triangle.

115. The pentagons are similar figures, and can be divided into the

same number of similar triangles. Euc. vi. 19.

1 16. Let the sides AB, BC, CA of the equilateral triangle ABC touch

the circle in the points D, E, F, respectively. Draw AE cutting the

circumference in G ; and take O the center of the circle and draw OD :

draw also HGK touching the circle in G. The property may then be

shewn by the similar triangles AHG, AOD.

INDEX

TO THE

PROBLEMS AND THEOREMS

IX THE

GEOMETRICAL EXERCISES.

ABBREVIATIONS.

Senate House Examination for Degrees.

S. H.

Smith's Mathematical Prizes. S. P.

Bell's University Scholarships. B. S.

St Peter's College. Pet.

Clare College. Cla.

Pembroke College. Pern.

Gonville and Caius College. Cai.

Trinity Hall. T. H.

Corpus Christi College. C. C.

King's College. Ki.

Queen's College. Qu.

St. Catharine's College. Cath.

Jesus College. Jes.

Christ's College. Chr.

St. John's College. Joh.

Magdalene College. Mag.

Trinity College. Trin. -

Emmanuel College. Emm.

Sidney Sussex College. Sid.

Downing College. Down.

In the years the centuries are omitterl,

and the places are supplied by a comma

prefixed, thus ,45 means 1845.

EXERCISES ON BOOK I, p. 69, &c.

1 Emm. ,22. ,35. ,46.

Sid. ,30. Trin. ,37.

2 Trin. ,40. Cai. ,57.

Chr. ,58.

3 Trin. ,32. ,37. ,50.

T.H.,52. Joh. ,54.

S. H. ,54.

4 Sid. ,30., 43. Jes.

,50. ,58. Qu. ,34.

Trin. ,40. Cla. ,47.

Emm. ,56.

5 Emm. ,21. Qu.,23.

,40. ,42. Trin. ,26.

,27. ,29. C. C. ,30.

,55. Pem. ,32. ,38.

6 S. H. ,17. Trin.

,24. ,37. Qu. ,25.

Emm. ,27. ,48.

Cath. ,29.,48.Pem.

,39. ,47. Sid. ,40.

Chr. ,45. Cla. ,56.

7 S. II. ,19. Trin.

,29. Qu.,35. Pem.

,44. Jes. ,49. B. S.

,55.

8 Qu. ,26. ,28. S.H.

,49. ,50. Pet. ,56.

Emm. ,50. C. C.

,57. Cai. ,55.

9 Mag. ,38. Joh. ,58.

10 Emm. ,34.

11 Cai. ,40. Joh. ,50.

12 S H. ,40. ,54.

13 Cath. ,31. S.H. ,50.

14

15 Pet. ,57.

16 Cath.,22.,33. Trin.

,37.

17 Cai. .57.

18 Chr. ..iH.

19 Emm. ,56.

20 T. H. ,51.

21 Jes. ,58.

22 S. H. ,50.

23 Qu. ,19. T. H.,51.

Emm. ,51. Pem.

,57.

24 Jes. ,58.

25 S.H. ,14. Cla. ,55.

26 Cai. ,41.

27 Chr. ,26. ,41. ,52

Jes. ,52. Joh. ,31.

Pet. ,38. Trin. ,39,

,50. Mag. ,51.

28 S. H. ,58.

29 C. C. ,53. S. H.

,59.

30 C, C. ,53. Qu. ,54.

Chr. ,56.

31 Trin. ,31.

32 S.H. ,36. ,48. Mag.

47. Chr. ,54.

33 Emm. ,25.

34 Joh. ,19. Qu. ,25.

35 Chr. ,28. Pem. ,42,

Jes. ,51.

36 Trin. ,26. Sid. ,43.

C. C. ,57.

37 Pem. ,29. B. S.

,48. Qu. ,52.

38 Qu. ,50.

39 Qu. ,31. Cath. ,35.

Emm. ,35. Sid.

,38. B. S. ,40.

Trin. ,27.

I

40 Trin. ,34.

41 S. H. ,55.

42 S. H. .04. C. C.

,23. Chr. ,29. ,5C.

Cath. ,35. Jes. ,52.

Pet. ,36. Qu. ,39.

Trin. ,37. ,49. Cai.

40. Pern. ,48.

43 Trin.,54. Emni.,54.

44 Trin. ,58.

45 Cai. ,55.

46 Pet. ,58.

47 Chr. ,55.

48 Cai. ,49.

49 Jes. ,54.

50 S. H. ,53.

61 Trin., 39., 51. Pern.

,51.

52 Trin. ,43.

53 Joh. ,26. Pem. ,47.

Chr. ,52. ,53.

64 Cai. ,46. Qu. ,48.

65 Cai., 31. Joh. ,30.

66

67 Jes. ,52. Cai. ,56.

68 Jes. ,55.

69 Pet. ,51.

60 Chr. ,39.

61 Pet. ,36.

62 Trin. ,52. ,54. T.II.

.52.

63 Pet. ,51.

64 Trin. ,51.

65 Jes. ,54.

66 Pet. ,51.

67 S. H. ,48.

68

69 T. H. ,54.

70 Trin. ,40.

71

72 Cai. ,33. Qu. ,33.

73 Trin. ,49.

74 Qu. ,31. Chr. ,56.

Sid. ,36. Pet. ,53.

75 Qu. ,19.

76 Qu. ,24.

77 Cla. ,51.

78 Qu. ,32. Jes. ,36.

S. H. ,49. ,50.

79 S.H.,49. Mag. ,52.

80 Qu. ,37.

81 Trin. ,48.

82 Chr. ,58.

8'3 Chr. ,52.

84 Trin. ,52.

85 Cath. ,49.

INDEX.

86 Cla. ,57.

87 Pet. ,46.

88 C. C. ,50. Cai. ,53.

89 Mag. ,51. ,58.

90 Jes. ,54.

91 Cath. ,49. S. H.,54.

92 Jes. ,55.

93 Cai. ,46.

94 Jes. ,41.

95 Chr. ,43.

96 Joh. ,31.

97 Cai. ,36. Cath. ,55.

98 Emm. ,30. Cath.

,57.

99 Trin. ,59.

100 Pet. ,51.

101 Qu. ,29. ,35. ,37.

P.S. ,39.

102

103 Mag. ,52.

104 Chr. ,47. Cla. ,48.

105 Pet. ,51.

106 Sid. ,45. Chr. ,47.

Emm. ,47.

107 S. H. ,52.

108 Emm. ,57.

109 S. H. ,04. Cai.

,34. Emm. ,39.

110 Qu. ,25. Trin.

,25. ,38. Pet. ,39.

Jes.,52. Pem. ,42.

111 S. H. ,03. ,18.

Trin. ,25. ,44. Cla.

,31. ,36.

112 Qu. ,29. ,37. ,26.

Trin. ,27. ,33. ,36.

,40. ,49. ,50. Chr.

,44. Pem. ,45.

Cath. ,58. Emm.

,54. Jes.,52. S.H.

,50. C. C. ,58.

113 Emm. ,32.

114 Qu.,19.,37.Emm.

,25. ,53. Mag. ,29.

,32. Cai., 34. Trin.

,37. ,38. Pet. ,44.

52

115 S. H. ,48.

116 Qu. ,39. Mag. ,54.

S. H. ,59.

117 Trin. ,29.

118 Emm. ,22. C. C.

,58.

119 Pet. ,45.

120 S.H.,35.,48. Joh.

,37.

357

121 Pet. ,38. Chr., 39-

122 S. H. ,53.

123 Joh. ,58.

124 C. C. ,46.

125 Pem. ,46.

126 S. H. ,54.

127 Emm. ,31 Chr.

38

128 Trin.,48. Cath.,46.

129

130 Pem. ,47.

131 Cla.

132 Ki. ,48. S.H. ,53.

Chr. ,55. ,57.

133 Qu. ,30. Chr. ,46.

134 Pet. ,58.

135 Jes. ,57.

136 Mag. ,57.

137 Cai. ,52.

138 Trin. ,37. ,50. ,52.

Joh. ,47. Emm.

,52. ,53. ,56. Chr.

,50. T. II. ,52.

139 Cla. ,36.

140 Mag. ,49.

141 Cla. ,36.

142 Joh. ,58. Chr. ,58.

143 Trin. ,53. ,54.

144 Joh. ,16. Qu.,30.

Pem., 33. ,49. Jes.

,46. Trin., 47. ,58.

C. C. ,58.

145 Pet. ,27.

146 S. H. ,36.

147 Chr. ,54,

148 Cla. ,56.

149 Jes. ,20. Qu. ,32.

,48. Cath. ,35.

S. H. ,59.

150 Trin. ,40.

151 Pet. ,32. ,35.

152 Pet. ,49.

153 S. H. ,55.

154 Jes. ,53.

155 Chr. ,56.

156 T. H. ,52.

157 Joh. ,20. Emm.

,26.

158 Sid. ,46. Mag. ,58.

159 Cai ,37.

160 Emm. ,32. Qu.

,35. ,59. C. C.

,36. ,59. Mag. ,39.

B. S. ,47.

161 Trin. ,21. ,50.

162 Jes. ,35.

358

INDEX.

EXERCISES ON BOOK II, p. 113, &c.

1 S.H. ,U. ,50. Joh.

,18. Trin.,35. Chr.

,55.

2 Joh. ,17.

3 S.H. ,16.,59. Trin.

,27. ,30. ,37. ,47.

,48. Mag. ,31. .43.

Pet. ,29. ,38. Sid.

,34. Emm. ,21, ,27.

,37. ,44. Cai. ,43.

Qu. ,37. T.H. ,55.

4 Emm. ,34. Pem.

,46. Mag. ,51.

5 S.H. ,03. Joh., 18.

Qu. ,21. Trin. ,37.

Sid. ,42. Chr. ,45.

,46. ,48.

6 Pet. ,52.

7 Pet. ,58.

8 Jes. ,54.

9 S. H. ,50.

10 Cai. ,58.

11 Jes. ,53.

12 Pet. ,25.

3 Chr. ,40.

14 Trin. ,42.

15 Pet. ,37.

16 T. H. ,40. ,54.

17 Qu. ,37.

18 S. H. ,38.

19 Chr. ,48. ,54. Jes.

,48. Sid. ,49. Pet.

,55. Pem. ,58.

20 Emm. ,56.

21

22 Qu. ,50.

23 Qu. ,24.

24 Chr. ,49.

25 S.H.,10.,04. Trin.

,29.

26 Pet. ,43.

27 Chr. ,49.

28 Qu. ,55.

29 Qu. ,57.

30 Qu. ,51.

31 Mag. ,57.

32 Cai. ,59.

33 Chr. ,57.

34 Cai. ,44.

35 Joh. ,44.

36 Trin. ,49. Cai. ,57.

37 Joh. ,13. Emm.

,25. ,36. Trin. .32.

Mag. ,33. ,40. Pet.

,52. S. H. ,53.

38 Joh. ,21. S. H.

,50. Pet. ,54.

39 Joh. ,25.

40 Cai. ,42.

41 S H. ,53.

42 T. H. ,58.

43 Joh. ,26. Jes. ,37.

Mag. ,42.

44 Pet. ,44.

45 Emm. ,23. ,26. ,28.

,43. ,51. Trin. ,27.

,44. ,49. ,50. Pet.

,30. Mag. ,33. ,43.

,46. ,52. B. S.,38.

C. C. ,51. Chr.

,41. ,47. ,50.

46 Emm. ,28. Sid.

,33. C. C. ,39.

47 Joh. ,19. Qu. ,29.

,30. ,48.

48 Chr. ,30. Emm.

,36. S. H. ,45.

Cath. ,52.

49 S. H. ,07. T. H.

,44. Pem. ,52. Joh.

,41. Trin. ,53.

Emm. ,52. S. H.

,59.

50 Emm. ,28, ,46.

Trin. 32. Pem. ,47.

51 Chr. ,51.

52 Pet. ,53.

53 Cai. ,28.

54

55

56

57 Jes. ,58.

58 S. H. ,59.

EXERCISES ON BOOK III, p. 160, &c.

1 Chr. ,28. S. H. ,36.

,59. Cai. ,44.

2 Qu.,23. T.H.,54.

Mag. 53.

3 Trin. ,27.

4 Mag. ,53.

5 S. H. ,04. Sid. ,41.

6 Trin. ,19, ,23. Qu.

,21., 22. Pem. ,30.

,39. Sid. ,.36. Pet.

,31. Emm. ,34, ,42.

,44. T. H. 54.

7 Emm. ,22. Pem.

,36. Joh. 57. S. H.

,o3.

8 Pet. ,29. Cla. ,46.

9 Qu. ,56.

10 Mag. ,46.

11 Mag. ,47.

12 S. H. ,43.

13 S. H. ,48.

14 Cath. ,53.

15

16

17 Joh. ,57.

18 Trin. ,19. Sid. ,33.

Cai. ,34. Emm., 34.

Qu. ,36. S.H. ,53.

Chr. ,56. Joh. ,57.

,58.

19 Emm. ,24.

20 C. C. ,42.

21 Joh. ,21.

22 Trin. ,52.

T. H. ,58.

23 Joh. ,17.

24 Joh. ,21.

25 Chr. ,27.

26 S. H. ,48.

27 Pet. ,47.

28 S. H. ,49.

29 Trin. ,39.

SO Emm. ,54.

31 S. H. ,53.

32 S. H. ,59.

33 Qu. ,57.

34 Pet. ,55.

INDEX.

359

35 Trin. ,30. ,39. C. C.

80 Trin. ,35.

123 Pet. ,48. Joh. ,58.

,35. ,45. Emm. ,37.

81 S.H. ,59.

124 Qu. ,54.

Chr. ,39. Pern. ,40.

82 Ki, ,50.

125 Pet. ,52.

36 Sid. ,35.

83 S. H. ,03. Qu. ,22.

126 Trin. ,42.

37 Joh. ,30.

Emm., 27. Sid. ,30.

127

38 Joh. ,20. Emm. ,26.

Cath. ,30. ,35.

128 S.H. ,04. Joh. ,16.

39 Cath. ,31.

Mag. ,34. ,37. ,45.

Qu. ,20. ,35. ,29.

40 Qu. ,36.

B.S.,39.,43. C.C.

Trin. ,22., 23 Pet.

41 Joh. ,28. Qu. ,35.

,57.

,31. B.S. ,30.,34.

42 Emm. ,56.

84 Pet. ,37.

129 Pet. ,43.

43 Trin. ,57.

85 Qu. ,33.

130 Trin. ,33.

44

86 Joh. ,47.

131 Pem. ,44.

45 Qu. ,58.

87 Cai. ,48.

132 Trin. ,20.

46 Pem. ,45.

88

133 Sid. ,35.

47 S. H.,14. Qu. ,20.

89 Joh. ,19. Qu. ,26.

134 T. H. ,58.

,32. Joh. ,25.

90 S. H. ,58.

135 Qu. ,49.

Emm., 32. Chr. ,45.

91 Qu. ,52.

136 Qu. ,54.

Cai. ,44.

92 Qu. ,39. Pem. ,43.

137 Joh. ,58.

48 Pet. ,56.

93 Joh. ,30.

138 Emm. ,47.

49 Trin. ,57.

94 Trin. ,24.

139 Jes. ,49.

50 Trin. ,34.

95 Qu. ,54.

140 Joh. ,41. ,42. ,49.

51 Cai. ,32. ,41.

96 Joh. ,17.

141 Qu. ,33.

52 Emm. ,21. Pem.

97 Sid. ,35. Pem. ,42.

142 Joh. ,20.

,32. Cla. ,36. Cai.

98 Qu. ,38.

143 Joh. ,25. T. H.

,45.

99 Cai. ,31.

,55.

63 S. H. ,53.

100 S.H. ,48. Qu.,57.

144 T. H. ,58.

54 Cla. ,56.

101 S. H. ,50. Qu.

145 S. H. ,48.

55 S. H. ,55.

,54. Pem. ,50.

146 Cath. ,58.

56 Cla. ,56.

102 Cai. ,47.

147 T. H. ,54.

57 Emm. ,57.

103 Cai. ,40.

148 Cla.

68 Trin. ,43.

104 Emm. ,56. ,57.

149

69

105 T. H. ,58.

150 Jes. ,56.

60 Trin. ,11,

106 Pet. ,52.

151 Mag. ,49.

161 Qu. ,36.

107 Cai. ,39. Jes. ,26.

152 Joh. ,18. ,19. Qu.

62 Cai. ,44.

C. C. ,38.

,26., 39. Mag. ,29.

63 Jes. ,33.

108 Pet.,39.Pem.,45.

Emm. ,30. Pem.

64 Joh. ,22.

109 Chr. ,40.

,44.

65 S. H. ,29.

110 Trin. ,29. ,32. ,38.

153 Mag. ,35.

66 Joh. ,42. Chr. ,53.

S. H. ,08. Pet.

154 Cath. ,30.

B7 S. H.,25

,19. ,20. ,21. Qu.

155 Joh. ,34.

B8 Cai. ,43. Emm. 44.

,20. ,28. Mag. ,30.

156 Trin.,26. Pem.,34.

59 Joh. ,14. Chr. ,26.

B.S.,39. Chr.,51.

157 C. C. ,46.

C. C. ,55.

Ill S. H. ,49.

158 Joh. ,35.

JO Trin. ,29. Sid. ,45.

112 Joh. ,31.

159 Trin. ,38. Joh. ,19.

S. H. ,50.

113 Emm. ,28.

Chr. ,39. Jes. ,43.

ri Jes. ,58.

114 Joh. ,25.

S.H. ,42. T. H.

'2 Chr. ,48. Sid. ,52.

115 S.H..20.Trin.,22.

,53.

'3 Trin. ,39.

,25. Mag.,37. Qu.

160 Jes. ,38. C.C. ,38.

4 S.H. ,36. Jes. ,57.

,39.

161 Jes. ,44.

5 S.H. ,02. Pem. ,32.

116 S. H. ,03.

162 C. C. ,33.

T. H. ,44.

117 Trin. ,20.

163 Pet. ,32.

6 Trin. ,45.

118 Jes. ,64,

164 C. C. ,25. B. S.

7 S. H. ,04. ,59.

119 Cai. ,51.

,28. Mag. ,45.

'8 Pet. ,39. Emm. ,56.

120 Cai. ,37.

165 Cath. ,30.

9 Joh. ,30. Cai. ,36.

121 Cai. ,42.

166 Joh. ,36.

Cla. ,46.

122 Cai. ,36.

167 C. C. ,39.

360

INDEX.

EXERCISES OX BOOK IV, p. 196, &c.

1 S.H.,08.,12. Chr.

,33. Pet. ,34. ,38.

Trin. ,49.

2 Qu. ,20. Emm. ,27.

Cath.,34. Trin. ,44.

Jes. ,46. Ki. 37.

Joh. ,57.

3 Qu. ,20. ,30. ,34.

Trin.,29.Emm.,30.

C.C. ,35. I3.S. ,36.

Pem. ,40. ,48. ,52.

Jes. ,52.

4 Joh. ,16. Pet. ,36.

5 Trin. ,31.

6 Emm. ,24. Qu. ,32.

7 Trin. ,37. Jes. ,47.

8

9 Trin. ,23. Sid. ,39.

,47. Qu. ,41. C.C.

,45.

10 Chr. ,27.

11 S. H. ,16. Qu. ,20.

,27. C.C. ,28. Joh.

39

12 Joh. ,29.

13 S.H. ,13. Trin. ,22.

14 S. H. ,38.

15 Chr. ,45.

16 Cai.,38.

17 Cai. ,35.

18 Joh. ,23.

19 Trin. ,21. Chr. ,30.

,34.

20 Trin. ,44. ,48.

21 Cai. ,42.

22 Cai. ,32.

23 Mag. ,35.

24 Joh. ,22.

25 Trm. ,30. S.H. ,36.

26 Pem. ,29. C.C. ,41.

27 Pem. ,31.

28 Joh. ,42.

29 Jes. ,33.

30 Trin. ,41.

31 Qu. ,20.

32 Joh. ,30.

33 Joh. ,31.

34 Pem. ,29. ,35.

35 S.H.,13. Qu. ,19.

Emm.,21.,33. B.S.

,26. Cai. ,35. Pem.

,36.

36 Jes. ,31.

37 Trin. ,40.

38 Joh. ,18.

39 Joh. ,17. Trin. ,36.

40 Pet. ,25.

41 Qu. ,31.

42 Pet. ,43.

43 Joh. ,25.

44 Trin. ,29.

45 Cai. ,37.

46 Trin. ,26. Qu. ,32.

Chr. ,40. Pem.,49.

47 Trin., 23. Emm.,23.

,32. ,36.

48 Emm.,21.Trin.,36.

Pem. ,42.

49 Chr. ,26. ,42.

50 Emm ,21. ,25. ,40.

,45. Chr. ,39. Pet.

,35. B.S. ,41.

51 Cai. ,38. Jes. 49.

52 Trin. ,21.

53 Emm. ,24.

54 Joh. ,18. Jes. ,49.

55 Pet. ,25.

56 Trin. ,37.

57 Trin. ,23. Qu. ,37.

58 Qu. ,21. ,26. ,36.

59

60 Emm ,25. Mag.,42

61 Qu. ,26.

62 Cai. 33. B.S. ,40.

63 Joh ,14. ,16. ,37.

S. H. ,44.

64 Sid. ,29. Qu. ,43.

65 Trin. ,31.

66 C. C. ,38.

67 Chr. ,32.

68 C. C. ,44.

69 Qu. ,44.

70 Cath.,30. Mag.,33.

,37.

71 Cai. ,40.

72 Sid. ,38. Trin. ,39.

73 Cai. ,41.

74 Trin. ,33.

75 C. C. ,24.

76 Trin. 22. B. S. ,27.

77 Pem. ,36.

78 Trin. ,36.

79 Jes. ,19. Trin. ,22.

,25. ,27. Qu. ,35.

Pem. ,37. Mag. ,45.

80 Qu. ,31. ,40.

Trin. ,42.

81 Jes. ,38.

82 Trin. ,27. Mag. ,43.

83 Cai. ,38.

84 Trin. ,19.

85 Trin. ,24.

86 Joh. ,25.

87 S.H. ,03. Trin. ,24

,30. Qu. ,31.,35

Cai. ,35.

EXERCISES ON BOOK VI, p. 302, &c.

1 Qu. ,38. Jes. ,46.

2 C. C. ,31.

3 Jes. ,19. Trin. ,32.

,44.

4 Qu. ,23. Sid. ,34.

C. C. ,40.

5 Ki. ,45.

6 Pet. ,38.

7 Cath. ,51.

8 S. H. ,50.

9 Pem., 46. T.H.,46.

10 Joh. ,23.

11 Cath., 30. Emm.

,34. Sid. ,44.

12 Trin. ,23. Cai. ,35.

Mag. ,37.

13 Trin. ,30. S..H. ,04.

Mag. .44.

14 Qu. ,20. ,26. ,32.

15 Joh. ,26.

16 Cai. ,31.

17 Trin. â€”

18 Qu. ,38. Chr

Trin. ,33. ,44.

19 Emm. ,23. ,30.

,29.

20 Chr. ,86.

21 Joh. ,20.

22 Joh. ,15.

23 Joh. ,14. Trin.

,4.:

II

INDEX'.

SGI

R,28. ,32. ,34.

.41. 1

,44. Cath.,34. Chr. |

,44.

24 Job. ,19.

25 Qu.,30. C.C.

,40.

26 Joh. ,2S.

27 Qu. ,38.

28 Qu. ,34.

29 Qu. ,24.

30 Pern. ,33.

31 Trin. ,11. ,28.

,43.

Jes. .19. Qu.

,21.

,23. ,26. C. C.

,26.

Pem. ,32. ,34.

,43.

Cai. ,33. Emm.

,21.

32 Joh. ,26.

33 Qu. ,48.

34 Pet. ,28. ,35.

35 Joh. ,19.

36 Cai. ,36.

37 Joh. ,26.

38 Joh. ,15. C.C

,37.

39 Trin. ,25.

40 Joh. ,17.

41 Joh. ,42.

42 ]<:mm. ,47. -

43 Pet. ,25.

44 Trin. ,38.

45 Joh. ,21.

46 Pet. ,32.

47 Joh. ,20.

48 Joh. ,14.

49 Qu. ,36.

60 Qu. ,25.

51 Pet. ,54.

52 Cai. ,44.

63 Joh. ,15.

54 Chr. ,41.

65 S. H. ,50.

56 Mag. ,41.

67 Pet. ,25.

68 Joh. ,17.

69 Qu. ,22.

60 Qu. ,21.

61 Trin. ,26.

62 Pet. ,35.

63 Joh. ,19.

64 Sid. ,30. Emm. ,49.

65 Pem. ,30. S.P. ,42.

66 Qu. ,35. ,36. Pem.

37.

67 Trin. ,21.

68 Joh. ,35.

69 Pet. ,26.

70 S.H. ,18. Qu.,20.

71 Joh. ,18. Cath. ,31.

72 Cai. ,45.

73 Trin. ,35.

74 Pem. ,31. ,43. Qu.

,19. ,25. ,43. Trin.

,22. ,37. Cai. ,43.

Mag. ,32.

75 Chr. ,48.

76 S.H. ,39. Pem. ,43.

77 Qu. ,41.

78 Trin. ,22. Qu. ,39.

Chr. ,42.

79 Qu. ,22. ,38. Trin.

,42. ,44.

80 Qu. ,29. ,35. ,41.

S. P. ,43.

81 Qu. ,40.

82 Qu. ,23. ,36. ,38.

83 Joh. ,13. Trin. ,20.

Emm. ,24. Chr. ,37.

I ,45. Qu., 36., 22. ,44.

THE END.

84 Trin. ,44.

85 Trin. ,32.

86 Qu. ,37.

87 Joh. ,29. Qu. ,43.

88 Joh. ,18.

89 Qu ,21.

80 Trin. ,36.

91 S. H. ,25.

92 Pet. ,33

93 Joh. ,19.

94 Joh. ,22. Emm. ,26.

95 Pem., 34. C. C. ,30.

96 Joh. ,38.

97 Cath. ,31.

98 Emm. ,46.

99 Joh. ,13. ,21.

Trin. ,29. ,34.

Qu. ,43. ,38.

IOOC.C.,28. Pem. ,42.

101 C.C. ,35. S. H.,11.

Pem. 46.T.H. ,46

102 Qu. ,41. ,42.

103 S. H. ,09. B. S.

,30. ,31.

104 S. H. ,36.

105 Sid. ,29.

106 Pet. ,36.

107 Cai. ,39.

108 Trin. ,11. ,20. ,32.

,33. Chr. ,35.

109 Pet. ,37.

110 Cai. ,31.

111 Joh. .31. Qu. ,44.

112 C. C. ,30.

113 Joh. ,20.

114 Emm. ,37.

115 'Jrin. ,20.

116 Cath. ,48.

Ji]ncUd's Elements of Geometry^ with Geometrical

Exercises^ &c. By R. PoTTS, M.A. of Trin. Coll. Camh.

THE UNIVERSITY EDITION. 8vo. price 10s. 2nd. Ed. improved.

THE SCHOOL EDITION, Books I.â€” VI. 12mo. price 4s. 6d-

Books I. -III. 3s. ; Books I., II. Is. 6d. Book I. Is.

SUPPLEMENT to the School Edition, containing portions of Books

XI. and XII. read at Cambridge, with Notes, &c. Is,

THE ENUNCIATIONS OF THE PHOPOSITIONS OF EUCLID,

Books I.-VL, XI. and XIL 9d.

" In addition to its extensive use in the Universities of Oxford and Cambridge, and

the Principal Grammar Schools, Mr. Potts' Euclid is on the Catalogue of Books sup-

plied at the Depositories of the National Society, Westminster, and of the Congregational

Board of Education, Homerton College, &c. ; and the Books may be obtained through

those channels at reduced cost for purposes of National Education."

Â«Â« It may be added that the Council of Eduoation at Calcutta were pleased to order

the iutrodactiou ot tlxese Editions of Euclid's Elements into the Schools and Colleges

under their control in Beugal, in the year 1853.

"In my opinion Mr. Potts has made a valuable addition to Geometrical literature

by his Editions of Euclid's Elements." â€” W. Whewell, D.D., Master of Frinity College,

Cambridge,

"Mr. Potts' Editions of Euclid's 6?eomc^ry are characterized by a due appreciation

of the spirit and exactness of the Greek Geometry, and an acquaintance with its his-

tory, as well as by a knowledge of the modern extensions of the Science. The

Elements are given in such a form as to preserve entirely the spirit of the ancient

reasoning, and having been extensively used in Colleges and Public Schools, cannot

fail to have the effect of keeping up the study of Geometry in its original purity."â€” r

James Chnllis, M.A., Phtminti Professor of Astronomy and Experimental Philosophy i

in the U7iiversity of Cambridge.

"By the publication of these works, Mr. Potts has done very great service to the

<ause of Geometrical Science ; I have adopted Mr. Potts' work as the text-book for my

own Lectures in Geometry, and I believe that it is recommended by all the Mathematical

Tutors and Professors in this University." â€” Robert Walker, M.A., F.R.S., Render in Ex-

perimental Philosophy in the University, and Mathematical Tutor of Wadham Collegey

Oxford.

"When the greater Portion of this Part of the Course was printed, and had for some-

time been in use in the .-academy, a new Edition of Euclid's Elements, by Mr. Robert

Pott's, M.A., of Trinity College, Cambridge, which is likely to supersede most others,

to the extent, at least, of the Six Books, was published. From the manner of arranging

the Demonstrations, this edition has the advantages of the symbolical form, and it is at

the same ti ue free from the manifold objections to which that form is open. The duo-

decimo edition of this work, comprising only the First Six Books of Euclid, with Deduc-

tions from them, having been introduced at this Institution as a text-book, now renders

any other Trealise on Plane Geometry unnecessary in our course of Mathematics." â€”

Preface to a Ireatise on Descriptive Geometry, <$-c., for the Use of the Royal Military

Academy, by S. Hunter Christie, M.A., of Trinity College, Cambridge, Secretary of the

Royal Society, ^-c, and Professor of Mathematics in the Royal Military Academy,

Woohoich.

" Mr. Potts has maintained the text of Simson, and secured the very spirit of Euclid's

Geometry, by means which are simply mechanical. It consists in printing the syllogism

in a separate paragraph, and the members of it in separate subdivisions, each, for the

most part, occupying a single line. The divisions of a proposition are therefore seen at

once without requiring an instant's thought. Were this the only advantage of Mr.

Potts' Edition, the great convenience which it affords in tuition would give it a claim to

become the Geometrical text-book of England. This, however, is not its only merit." â€”

Philosophical Magazine, January, 1848.

" If we may judge from the solutions we have sketched of a few of them [the Geome-

trical Exercises], we should be led to consider them admirably adapted to improve

the taste as well as the skill of the Student. As a series of judicious exercises, indeed,

we do not think there exists one at all comparable to it in our languageâ€” viewed either

the center through the opposite angles of the square to meet the circular ;

arc, will determine two points of the square inscribed in the sector.

100. Let ABCDE be the given pentagon. On AB, AE take equal!

distances AF, AG, join FG, and on FG describe a square FGKH.

Join AH and produce it to meet a side of the pentagon in L. Draw

LM parallel to FH meeting AE in M. Then LM is a side of the

inscribed square.

101. Let ABC be the given triangle. Draw AD making with the

base BC an angle equal to one of the given angles of the parallelogram.

Draw AE parallel to BC and take AD to AE in the given ratio of the

sides. Join BE cutting AC in F.

102. The locus of the intersections of the diagonals of all the

rectangles inscribed in a scalene triangle, is a straight line drawn from the

bisection of the base to the bisection of the shorter side of the triangle.

103. This parallelogram is one half of the square in the circle.

104. Analysis. Let ABCD be the given rectangle, and EFGH that

to be constructed. Then the diagonals of EFGH are equal and bisect

each other in P the center of the given rectangle. About EPF describe

a circle meeting BD in K, and join KE, KF. Then since the rectangle

EFGH is given in species, the angle EPF formed by its diagcmals is

given ; and hence also the opposite angle EKF of the inscribed quadri-

lateral PEKF is given. Also since KP bisects that angle, the angle

PKE is given, and its supplement BKE is given. And in the same way,

KF is parallel to another given line ; and hence EF is parallel to a third

given line. Again, the angle EPF of the isosceles triangle EPF is given ;

and hence the quadrilateral EPFK is given in species.

105. In the figure Euc. in. 30 ; from C draw CE, CF making with

CD, the angles DCE, DCF each equal to the angle CDA or CDB, and

meeting the arc ADB in E and F. Join EF, the segment of the circle

described upon EF and which passes through C, will be similar to ADB.

106. The square inscribed in the circle may be shewn to be equal to

twice the square on the radius ; and five times the square inscribed in

the semicircle to four times the square on the radius.

107. The three triangles formed by three sides of the square with

segments of the sides of the given triangle, may be proved to be similar.

Whence by Euc. vi. 4, the truth of the property.

108. By constructing the figure, it may be shewn that twice the

square inscribed in the quadrant is equal to the square on the radius,

and that five times the square inscribed in the semicircle is equal to four

times the square on the radius. Whence it follows that, &c.

109. By Euc. i. 47, and Euc. vi. 4, it may be shewn, that four times

the square on the radius is equal to fifteen times the square on one of the

equal sides of the triangle.

110. Constructing the figure, the right-angled triangles SCT, ACB

ON BOOK VI. 355

may be proved to have a certain ratio, and the triangles ACB, CPM in

the same way, may be proved to have the same ratio.

111. Let 13 A, AC be the bounding radii, and D a point in the arc of

a quadrant. Bisect BAG by AE, and draw through D, the line HDGP

perpendicular to AE at G, and meeting AB, AC, produced in H, P.

From H draw HM to touch the circle of which BC is a quadrantal arc ;

produce AH, making HL equal to HM, also on HA, take HK equal to

HM. Then K, L, are the points of contact of two circles through D

which touch the bounding radii, AB, AC.

Join DA. Then, since BAC is a right angle, AK is equal to the

radius of the circle which touches BA, BC in K, K' ; and similarly, AL

is the radius of the circle which touches them in L, L'. Also, HAP

being an isosceles triangle, and AD drawn to the base, AD* is shewn

to be equal to AK . KL. Euc. iii. 36 ; ii. 5, Cor.

1 ] 2. Let E, F, G be the centers of the circles inscribed in the triangles

ABC, ADB, ACD. Draw EH, FK, GL perpendiculars on BC, BA, AC

respectively, and join CE, EB ; BF, FA ; CG, GA. Then the relation

between E,, r, r', or EH, FK, GL may be found from the similar triangles,

and the property of right-angled triangles.

113. The two hexagons consist each of six equilateral triangles, and

the ratio of the hexagons is the same as the ratio of their equilateral

triangles.

114. The area of the inscribed equilateral triangle may be proved to

be equal to half of the inscribed hexagon, and the circumscribed triangle

equal to four times the inscribed triangle.

115. The pentagons are similar figures, and can be divided into the

same number of similar triangles. Euc. vi. 19.

1 16. Let the sides AB, BC, CA of the equilateral triangle ABC touch

the circle in the points D, E, F, respectively. Draw AE cutting the

circumference in G ; and take O the center of the circle and draw OD :

draw also HGK touching the circle in G. The property may then be

shewn by the similar triangles AHG, AOD.

INDEX

TO THE

PROBLEMS AND THEOREMS

IX THE

GEOMETRICAL EXERCISES.

ABBREVIATIONS.

Senate House Examination for Degrees.

S. H.

Smith's Mathematical Prizes. S. P.

Bell's University Scholarships. B. S.

St Peter's College. Pet.

Clare College. Cla.

Pembroke College. Pern.

Gonville and Caius College. Cai.

Trinity Hall. T. H.

Corpus Christi College. C. C.

King's College. Ki.

Queen's College. Qu.

St. Catharine's College. Cath.

Jesus College. Jes.

Christ's College. Chr.

St. John's College. Joh.

Magdalene College. Mag.

Trinity College. Trin. -

Emmanuel College. Emm.

Sidney Sussex College. Sid.

Downing College. Down.

In the years the centuries are omitterl,

and the places are supplied by a comma

prefixed, thus ,45 means 1845.

EXERCISES ON BOOK I, p. 69, &c.

1 Emm. ,22. ,35. ,46.

Sid. ,30. Trin. ,37.

2 Trin. ,40. Cai. ,57.

Chr. ,58.

3 Trin. ,32. ,37. ,50.

T.H.,52. Joh. ,54.

S. H. ,54.

4 Sid. ,30., 43. Jes.

,50. ,58. Qu. ,34.

Trin. ,40. Cla. ,47.

Emm. ,56.

5 Emm. ,21. Qu.,23.

,40. ,42. Trin. ,26.

,27. ,29. C. C. ,30.

,55. Pem. ,32. ,38.

6 S. H. ,17. Trin.

,24. ,37. Qu. ,25.

Emm. ,27. ,48.

Cath. ,29.,48.Pem.

,39. ,47. Sid. ,40.

Chr. ,45. Cla. ,56.

7 S. II. ,19. Trin.

,29. Qu.,35. Pem.

,44. Jes. ,49. B. S.

,55.

8 Qu. ,26. ,28. S.H.

,49. ,50. Pet. ,56.

Emm. ,50. C. C.

,57. Cai. ,55.

9 Mag. ,38. Joh. ,58.

10 Emm. ,34.

11 Cai. ,40. Joh. ,50.

12 S H. ,40. ,54.

13 Cath. ,31. S.H. ,50.

14

15 Pet. ,57.

16 Cath.,22.,33. Trin.

,37.

17 Cai. .57.

18 Chr. ..iH.

19 Emm. ,56.

20 T. H. ,51.

21 Jes. ,58.

22 S. H. ,50.

23 Qu. ,19. T. H.,51.

Emm. ,51. Pem.

,57.

24 Jes. ,58.

25 S.H. ,14. Cla. ,55.

26 Cai. ,41.

27 Chr. ,26. ,41. ,52

Jes. ,52. Joh. ,31.

Pet. ,38. Trin. ,39,

,50. Mag. ,51.

28 S. H. ,58.

29 C. C. ,53. S. H.

,59.

30 C, C. ,53. Qu. ,54.

Chr. ,56.

31 Trin. ,31.

32 S.H. ,36. ,48. Mag.

47. Chr. ,54.

33 Emm. ,25.

34 Joh. ,19. Qu. ,25.

35 Chr. ,28. Pem. ,42,

Jes. ,51.

36 Trin. ,26. Sid. ,43.

C. C. ,57.

37 Pem. ,29. B. S.

,48. Qu. ,52.

38 Qu. ,50.

39 Qu. ,31. Cath. ,35.

Emm. ,35. Sid.

,38. B. S. ,40.

Trin. ,27.

I

40 Trin. ,34.

41 S. H. ,55.

42 S. H. .04. C. C.

,23. Chr. ,29. ,5C.

Cath. ,35. Jes. ,52.

Pet. ,36. Qu. ,39.

Trin. ,37. ,49. Cai.

40. Pern. ,48.

43 Trin.,54. Emni.,54.

44 Trin. ,58.

45 Cai. ,55.

46 Pet. ,58.

47 Chr. ,55.

48 Cai. ,49.

49 Jes. ,54.

50 S. H. ,53.

61 Trin., 39., 51. Pern.

,51.

52 Trin. ,43.

53 Joh. ,26. Pem. ,47.

Chr. ,52. ,53.

64 Cai. ,46. Qu. ,48.

65 Cai., 31. Joh. ,30.

66

67 Jes. ,52. Cai. ,56.

68 Jes. ,55.

69 Pet. ,51.

60 Chr. ,39.

61 Pet. ,36.

62 Trin. ,52. ,54. T.II.

.52.

63 Pet. ,51.

64 Trin. ,51.

65 Jes. ,54.

66 Pet. ,51.

67 S. H. ,48.

68

69 T. H. ,54.

70 Trin. ,40.

71

72 Cai. ,33. Qu. ,33.

73 Trin. ,49.

74 Qu. ,31. Chr. ,56.

Sid. ,36. Pet. ,53.

75 Qu. ,19.

76 Qu. ,24.

77 Cla. ,51.

78 Qu. ,32. Jes. ,36.

S. H. ,49. ,50.

79 S.H.,49. Mag. ,52.

80 Qu. ,37.

81 Trin. ,48.

82 Chr. ,58.

8'3 Chr. ,52.

84 Trin. ,52.

85 Cath. ,49.

INDEX.

86 Cla. ,57.

87 Pet. ,46.

88 C. C. ,50. Cai. ,53.

89 Mag. ,51. ,58.

90 Jes. ,54.

91 Cath. ,49. S. H.,54.

92 Jes. ,55.

93 Cai. ,46.

94 Jes. ,41.

95 Chr. ,43.

96 Joh. ,31.

97 Cai. ,36. Cath. ,55.

98 Emm. ,30. Cath.

,57.

99 Trin. ,59.

100 Pet. ,51.

101 Qu. ,29. ,35. ,37.

P.S. ,39.

102

103 Mag. ,52.

104 Chr. ,47. Cla. ,48.

105 Pet. ,51.

106 Sid. ,45. Chr. ,47.

Emm. ,47.

107 S. H. ,52.

108 Emm. ,57.

109 S. H. ,04. Cai.

,34. Emm. ,39.

110 Qu. ,25. Trin.

,25. ,38. Pet. ,39.

Jes.,52. Pem. ,42.

111 S. H. ,03. ,18.

Trin. ,25. ,44. Cla.

,31. ,36.

112 Qu. ,29. ,37. ,26.

Trin. ,27. ,33. ,36.

,40. ,49. ,50. Chr.

,44. Pem. ,45.

Cath. ,58. Emm.

,54. Jes.,52. S.H.

,50. C. C. ,58.

113 Emm. ,32.

114 Qu.,19.,37.Emm.

,25. ,53. Mag. ,29.

,32. Cai., 34. Trin.

,37. ,38. Pet. ,44.

52

115 S. H. ,48.

116 Qu. ,39. Mag. ,54.

S. H. ,59.

117 Trin. ,29.

118 Emm. ,22. C. C.

,58.

119 Pet. ,45.

120 S.H.,35.,48. Joh.

,37.

357

121 Pet. ,38. Chr., 39-

122 S. H. ,53.

123 Joh. ,58.

124 C. C. ,46.

125 Pem. ,46.

126 S. H. ,54.

127 Emm. ,31 Chr.

38

128 Trin.,48. Cath.,46.

129

130 Pem. ,47.

131 Cla.

132 Ki. ,48. S.H. ,53.

Chr. ,55. ,57.

133 Qu. ,30. Chr. ,46.

134 Pet. ,58.

135 Jes. ,57.

136 Mag. ,57.

137 Cai. ,52.

138 Trin. ,37. ,50. ,52.

Joh. ,47. Emm.

,52. ,53. ,56. Chr.

,50. T. II. ,52.

139 Cla. ,36.

140 Mag. ,49.

141 Cla. ,36.

142 Joh. ,58. Chr. ,58.

143 Trin. ,53. ,54.

144 Joh. ,16. Qu.,30.

Pem., 33. ,49. Jes.

,46. Trin., 47. ,58.

C. C. ,58.

145 Pet. ,27.

146 S. H. ,36.

147 Chr. ,54,

148 Cla. ,56.

149 Jes. ,20. Qu. ,32.

,48. Cath. ,35.

S. H. ,59.

150 Trin. ,40.

151 Pet. ,32. ,35.

152 Pet. ,49.

153 S. H. ,55.

154 Jes. ,53.

155 Chr. ,56.

156 T. H. ,52.

157 Joh. ,20. Emm.

,26.

158 Sid. ,46. Mag. ,58.

159 Cai ,37.

160 Emm. ,32. Qu.

,35. ,59. C. C.

,36. ,59. Mag. ,39.

B. S. ,47.

161 Trin. ,21. ,50.

162 Jes. ,35.

358

INDEX.

EXERCISES ON BOOK II, p. 113, &c.

1 S.H. ,U. ,50. Joh.

,18. Trin.,35. Chr.

,55.

2 Joh. ,17.

3 S.H. ,16.,59. Trin.

,27. ,30. ,37. ,47.

,48. Mag. ,31. .43.

Pet. ,29. ,38. Sid.

,34. Emm. ,21, ,27.

,37. ,44. Cai. ,43.

Qu. ,37. T.H. ,55.

4 Emm. ,34. Pem.

,46. Mag. ,51.

5 S.H. ,03. Joh., 18.

Qu. ,21. Trin. ,37.

Sid. ,42. Chr. ,45.

,46. ,48.

6 Pet. ,52.

7 Pet. ,58.

8 Jes. ,54.

9 S. H. ,50.

10 Cai. ,58.

11 Jes. ,53.

12 Pet. ,25.

3 Chr. ,40.

14 Trin. ,42.

15 Pet. ,37.

16 T. H. ,40. ,54.

17 Qu. ,37.

18 S. H. ,38.

19 Chr. ,48. ,54. Jes.

,48. Sid. ,49. Pet.

,55. Pem. ,58.

20 Emm. ,56.

21

22 Qu. ,50.

23 Qu. ,24.

24 Chr. ,49.

25 S.H.,10.,04. Trin.

,29.

26 Pet. ,43.

27 Chr. ,49.

28 Qu. ,55.

29 Qu. ,57.

30 Qu. ,51.

31 Mag. ,57.

32 Cai. ,59.

33 Chr. ,57.

34 Cai. ,44.

35 Joh. ,44.

36 Trin. ,49. Cai. ,57.

37 Joh. ,13. Emm.

,25. ,36. Trin. .32.

Mag. ,33. ,40. Pet.

,52. S. H. ,53.

38 Joh. ,21. S. H.

,50. Pet. ,54.

39 Joh. ,25.

40 Cai. ,42.

41 S H. ,53.

42 T. H. ,58.

43 Joh. ,26. Jes. ,37.

Mag. ,42.

44 Pet. ,44.

45 Emm. ,23. ,26. ,28.

,43. ,51. Trin. ,27.

,44. ,49. ,50. Pet.

,30. Mag. ,33. ,43.

,46. ,52. B. S.,38.

C. C. ,51. Chr.

,41. ,47. ,50.

46 Emm. ,28. Sid.

,33. C. C. ,39.

47 Joh. ,19. Qu. ,29.

,30. ,48.

48 Chr. ,30. Emm.

,36. S. H. ,45.

Cath. ,52.

49 S. H. ,07. T. H.

,44. Pem. ,52. Joh.

,41. Trin. ,53.

Emm. ,52. S. H.

,59.

50 Emm. ,28, ,46.

Trin. 32. Pem. ,47.

51 Chr. ,51.

52 Pet. ,53.

53 Cai. ,28.

54

55

56

57 Jes. ,58.

58 S. H. ,59.

EXERCISES ON BOOK III, p. 160, &c.

1 Chr. ,28. S. H. ,36.

,59. Cai. ,44.

2 Qu.,23. T.H.,54.

Mag. 53.

3 Trin. ,27.

4 Mag. ,53.

5 S. H. ,04. Sid. ,41.

6 Trin. ,19, ,23. Qu.

,21., 22. Pem. ,30.

,39. Sid. ,.36. Pet.

,31. Emm. ,34, ,42.

,44. T. H. 54.

7 Emm. ,22. Pem.

,36. Joh. 57. S. H.

,o3.

8 Pet. ,29. Cla. ,46.

9 Qu. ,56.

10 Mag. ,46.

11 Mag. ,47.

12 S. H. ,43.

13 S. H. ,48.

14 Cath. ,53.

15

16

17 Joh. ,57.

18 Trin. ,19. Sid. ,33.

Cai. ,34. Emm., 34.

Qu. ,36. S.H. ,53.

Chr. ,56. Joh. ,57.

,58.

19 Emm. ,24.

20 C. C. ,42.

21 Joh. ,21.

22 Trin. ,52.

T. H. ,58.

23 Joh. ,17.

24 Joh. ,21.

25 Chr. ,27.

26 S. H. ,48.

27 Pet. ,47.

28 S. H. ,49.

29 Trin. ,39.

SO Emm. ,54.

31 S. H. ,53.

32 S. H. ,59.

33 Qu. ,57.

34 Pet. ,55.

INDEX.

359

35 Trin. ,30. ,39. C. C.

80 Trin. ,35.

123 Pet. ,48. Joh. ,58.

,35. ,45. Emm. ,37.

81 S.H. ,59.

124 Qu. ,54.

Chr. ,39. Pern. ,40.

82 Ki, ,50.

125 Pet. ,52.

36 Sid. ,35.

83 S. H. ,03. Qu. ,22.

126 Trin. ,42.

37 Joh. ,30.

Emm., 27. Sid. ,30.

127

38 Joh. ,20. Emm. ,26.

Cath. ,30. ,35.

128 S.H. ,04. Joh. ,16.

39 Cath. ,31.

Mag. ,34. ,37. ,45.

Qu. ,20. ,35. ,29.

40 Qu. ,36.

B.S.,39.,43. C.C.

Trin. ,22., 23 Pet.

41 Joh. ,28. Qu. ,35.

,57.

,31. B.S. ,30.,34.

42 Emm. ,56.

84 Pet. ,37.

129 Pet. ,43.

43 Trin. ,57.

85 Qu. ,33.

130 Trin. ,33.

44

86 Joh. ,47.

131 Pem. ,44.

45 Qu. ,58.

87 Cai. ,48.

132 Trin. ,20.

46 Pem. ,45.

88

133 Sid. ,35.

47 S. H.,14. Qu. ,20.

89 Joh. ,19. Qu. ,26.

134 T. H. ,58.

,32. Joh. ,25.

90 S. H. ,58.

135 Qu. ,49.

Emm., 32. Chr. ,45.

91 Qu. ,52.

136 Qu. ,54.

Cai. ,44.

92 Qu. ,39. Pem. ,43.

137 Joh. ,58.

48 Pet. ,56.

93 Joh. ,30.

138 Emm. ,47.

49 Trin. ,57.

94 Trin. ,24.

139 Jes. ,49.

50 Trin. ,34.

95 Qu. ,54.

140 Joh. ,41. ,42. ,49.

51 Cai. ,32. ,41.

96 Joh. ,17.

141 Qu. ,33.

52 Emm. ,21. Pem.

97 Sid. ,35. Pem. ,42.

142 Joh. ,20.

,32. Cla. ,36. Cai.

98 Qu. ,38.

143 Joh. ,25. T. H.

,45.

99 Cai. ,31.

,55.

63 S. H. ,53.

100 S.H. ,48. Qu.,57.

144 T. H. ,58.

54 Cla. ,56.

101 S. H. ,50. Qu.

145 S. H. ,48.

55 S. H. ,55.

,54. Pem. ,50.

146 Cath. ,58.

56 Cla. ,56.

102 Cai. ,47.

147 T. H. ,54.

57 Emm. ,57.

103 Cai. ,40.

148 Cla.

68 Trin. ,43.

104 Emm. ,56. ,57.

149

69

105 T. H. ,58.

150 Jes. ,56.

60 Trin. ,11,

106 Pet. ,52.

151 Mag. ,49.

161 Qu. ,36.

107 Cai. ,39. Jes. ,26.

152 Joh. ,18. ,19. Qu.

62 Cai. ,44.

C. C. ,38.

,26., 39. Mag. ,29.

63 Jes. ,33.

108 Pet.,39.Pem.,45.

Emm. ,30. Pem.

64 Joh. ,22.

109 Chr. ,40.

,44.

65 S. H. ,29.

110 Trin. ,29. ,32. ,38.

153 Mag. ,35.

66 Joh. ,42. Chr. ,53.

S. H. ,08. Pet.

154 Cath. ,30.

B7 S. H.,25

,19. ,20. ,21. Qu.

155 Joh. ,34.

B8 Cai. ,43. Emm. 44.

,20. ,28. Mag. ,30.

156 Trin.,26. Pem.,34.

59 Joh. ,14. Chr. ,26.

B.S.,39. Chr.,51.

157 C. C. ,46.

C. C. ,55.

Ill S. H. ,49.

158 Joh. ,35.

JO Trin. ,29. Sid. ,45.

112 Joh. ,31.

159 Trin. ,38. Joh. ,19.

S. H. ,50.

113 Emm. ,28.

Chr. ,39. Jes. ,43.

ri Jes. ,58.

114 Joh. ,25.

S.H. ,42. T. H.

'2 Chr. ,48. Sid. ,52.

115 S.H..20.Trin.,22.

,53.

'3 Trin. ,39.

,25. Mag.,37. Qu.

160 Jes. ,38. C.C. ,38.

4 S.H. ,36. Jes. ,57.

,39.

161 Jes. ,44.

5 S.H. ,02. Pem. ,32.

116 S. H. ,03.

162 C. C. ,33.

T. H. ,44.

117 Trin. ,20.

163 Pet. ,32.

6 Trin. ,45.

118 Jes. ,64,

164 C. C. ,25. B. S.

7 S. H. ,04. ,59.

119 Cai. ,51.

,28. Mag. ,45.

'8 Pet. ,39. Emm. ,56.

120 Cai. ,37.

165 Cath. ,30.

9 Joh. ,30. Cai. ,36.

121 Cai. ,42.

166 Joh. ,36.

Cla. ,46.

122 Cai. ,36.

167 C. C. ,39.

360

INDEX.

EXERCISES OX BOOK IV, p. 196, &c.

1 S.H.,08.,12. Chr.

,33. Pet. ,34. ,38.

Trin. ,49.

2 Qu. ,20. Emm. ,27.

Cath.,34. Trin. ,44.

Jes. ,46. Ki. 37.

Joh. ,57.

3 Qu. ,20. ,30. ,34.

Trin.,29.Emm.,30.

C.C. ,35. I3.S. ,36.

Pem. ,40. ,48. ,52.

Jes. ,52.

4 Joh. ,16. Pet. ,36.

5 Trin. ,31.

6 Emm. ,24. Qu. ,32.

7 Trin. ,37. Jes. ,47.

8

9 Trin. ,23. Sid. ,39.

,47. Qu. ,41. C.C.

,45.

10 Chr. ,27.

11 S. H. ,16. Qu. ,20.

,27. C.C. ,28. Joh.

39

12 Joh. ,29.

13 S.H. ,13. Trin. ,22.

14 S. H. ,38.

15 Chr. ,45.

16 Cai.,38.

17 Cai. ,35.

18 Joh. ,23.

19 Trin. ,21. Chr. ,30.

,34.

20 Trin. ,44. ,48.

21 Cai. ,42.

22 Cai. ,32.

23 Mag. ,35.

24 Joh. ,22.

25 Trm. ,30. S.H. ,36.

26 Pem. ,29. C.C. ,41.

27 Pem. ,31.

28 Joh. ,42.

29 Jes. ,33.

30 Trin. ,41.

31 Qu. ,20.

32 Joh. ,30.

33 Joh. ,31.

34 Pem. ,29. ,35.

35 S.H.,13. Qu. ,19.

Emm.,21.,33. B.S.

,26. Cai. ,35. Pem.

,36.

36 Jes. ,31.

37 Trin. ,40.

38 Joh. ,18.

39 Joh. ,17. Trin. ,36.

40 Pet. ,25.

41 Qu. ,31.

42 Pet. ,43.

43 Joh. ,25.

44 Trin. ,29.

45 Cai. ,37.

46 Trin. ,26. Qu. ,32.

Chr. ,40. Pem.,49.

47 Trin., 23. Emm.,23.

,32. ,36.

48 Emm.,21.Trin.,36.

Pem. ,42.

49 Chr. ,26. ,42.

50 Emm ,21. ,25. ,40.

,45. Chr. ,39. Pet.

,35. B.S. ,41.

51 Cai. ,38. Jes. 49.

52 Trin. ,21.

53 Emm. ,24.

54 Joh. ,18. Jes. ,49.

55 Pet. ,25.

56 Trin. ,37.

57 Trin. ,23. Qu. ,37.

58 Qu. ,21. ,26. ,36.

59

60 Emm ,25. Mag.,42

61 Qu. ,26.

62 Cai. 33. B.S. ,40.

63 Joh ,14. ,16. ,37.

S. H. ,44.

64 Sid. ,29. Qu. ,43.

65 Trin. ,31.

66 C. C. ,38.

67 Chr. ,32.

68 C. C. ,44.

69 Qu. ,44.

70 Cath.,30. Mag.,33.

,37.

71 Cai. ,40.

72 Sid. ,38. Trin. ,39.

73 Cai. ,41.

74 Trin. ,33.

75 C. C. ,24.

76 Trin. 22. B. S. ,27.

77 Pem. ,36.

78 Trin. ,36.

79 Jes. ,19. Trin. ,22.

,25. ,27. Qu. ,35.

Pem. ,37. Mag. ,45.

80 Qu. ,31. ,40.

Trin. ,42.

81 Jes. ,38.

82 Trin. ,27. Mag. ,43.

83 Cai. ,38.

84 Trin. ,19.

85 Trin. ,24.

86 Joh. ,25.

87 S.H. ,03. Trin. ,24

,30. Qu. ,31.,35

Cai. ,35.

EXERCISES ON BOOK VI, p. 302, &c.

1 Qu. ,38. Jes. ,46.

2 C. C. ,31.

3 Jes. ,19. Trin. ,32.

,44.

4 Qu. ,23. Sid. ,34.

C. C. ,40.

5 Ki. ,45.

6 Pet. ,38.

7 Cath. ,51.

8 S. H. ,50.

9 Pem., 46. T.H.,46.

10 Joh. ,23.

11 Cath., 30. Emm.

,34. Sid. ,44.

12 Trin. ,23. Cai. ,35.

Mag. ,37.

13 Trin. ,30. S..H. ,04.

Mag. .44.

14 Qu. ,20. ,26. ,32.

15 Joh. ,26.

16 Cai. ,31.

17 Trin. â€”

18 Qu. ,38. Chr

Trin. ,33. ,44.

19 Emm. ,23. ,30.

,29.

20 Chr. ,86.

21 Joh. ,20.

22 Joh. ,15.

23 Joh. ,14. Trin.

,4.:

II

INDEX'.

SGI

R,28. ,32. ,34.

.41. 1

,44. Cath.,34. Chr. |

,44.

24 Job. ,19.

25 Qu.,30. C.C.

,40.

26 Joh. ,2S.

27 Qu. ,38.

28 Qu. ,34.

29 Qu. ,24.

30 Pern. ,33.

31 Trin. ,11. ,28.

,43.

Jes. .19. Qu.

,21.

,23. ,26. C. C.

,26.

Pem. ,32. ,34.

,43.

Cai. ,33. Emm.

,21.

32 Joh. ,26.

33 Qu. ,48.

34 Pet. ,28. ,35.

35 Joh. ,19.

36 Cai. ,36.

37 Joh. ,26.

38 Joh. ,15. C.C

,37.

39 Trin. ,25.

40 Joh. ,17.

41 Joh. ,42.

42 ]<:mm. ,47. -

43 Pet. ,25.

44 Trin. ,38.

45 Joh. ,21.

46 Pet. ,32.

47 Joh. ,20.

48 Joh. ,14.

49 Qu. ,36.

60 Qu. ,25.

51 Pet. ,54.

52 Cai. ,44.

63 Joh. ,15.

54 Chr. ,41.

65 S. H. ,50.

56 Mag. ,41.

67 Pet. ,25.

68 Joh. ,17.

69 Qu. ,22.

60 Qu. ,21.

61 Trin. ,26.

62 Pet. ,35.

63 Joh. ,19.

64 Sid. ,30. Emm. ,49.

65 Pem. ,30. S.P. ,42.

66 Qu. ,35. ,36. Pem.

37.

67 Trin. ,21.

68 Joh. ,35.

69 Pet. ,26.

70 S.H. ,18. Qu.,20.

71 Joh. ,18. Cath. ,31.

72 Cai. ,45.

73 Trin. ,35.

74 Pem. ,31. ,43. Qu.

,19. ,25. ,43. Trin.

,22. ,37. Cai. ,43.

Mag. ,32.

75 Chr. ,48.

76 S.H. ,39. Pem. ,43.

77 Qu. ,41.

78 Trin. ,22. Qu. ,39.

Chr. ,42.

79 Qu. ,22. ,38. Trin.

,42. ,44.

80 Qu. ,29. ,35. ,41.

S. P. ,43.

81 Qu. ,40.

82 Qu. ,23. ,36. ,38.

83 Joh. ,13. Trin. ,20.

Emm. ,24. Chr. ,37.

I ,45. Qu., 36., 22. ,44.

THE END.

84 Trin. ,44.

85 Trin. ,32.

86 Qu. ,37.

87 Joh. ,29. Qu. ,43.

88 Joh. ,18.

89 Qu ,21.

80 Trin. ,36.

91 S. H. ,25.

92 Pet. ,33

93 Joh. ,19.

94 Joh. ,22. Emm. ,26.

95 Pem., 34. C. C. ,30.

96 Joh. ,38.

97 Cath. ,31.

98 Emm. ,46.

99 Joh. ,13. ,21.

Trin. ,29. ,34.

Qu. ,43. ,38.

IOOC.C.,28. Pem. ,42.

101 C.C. ,35. S. H.,11.

Pem. 46.T.H. ,46

102 Qu. ,41. ,42.

103 S. H. ,09. B. S.

,30. ,31.

104 S. H. ,36.

105 Sid. ,29.

106 Pet. ,36.

107 Cai. ,39.

108 Trin. ,11. ,20. ,32.

,33. Chr. ,35.

109 Pet. ,37.

110 Cai. ,31.

111 Joh. .31. Qu. ,44.

112 C. C. ,30.

113 Joh. ,20.

114 Emm. ,37.

115 'Jrin. ,20.

116 Cath. ,48.

Ji]ncUd's Elements of Geometry^ with Geometrical

Exercises^ &c. By R. PoTTS, M.A. of Trin. Coll. Camh.

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tions from them, having been introduced at this Institution as a text-book, now renders

any other Trealise on Plane Geometry unnecessary in our course of Mathematics." â€”

Preface to a Ireatise on Descriptive Geometry, <$-c., for the Use of the Royal Military

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