Copyright
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

. (page 37 of 38)
Online LibraryEuclidEuclid'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)
Font size
QR-code for this ebook


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. —

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.— 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."

«« 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." — 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."— 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." — 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." —
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." —
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 language— viewed either



Online LibraryEuclidEuclid'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)