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ERRÅTÀ for the first fix Books.
B. II. pr. 3: 1. 5. for AC, CD, r. AF, CE; pr. 10. 1. 15. for DEFr. DFE.
B. HII. pr. 23. note, for def. 11. r. def. 10, pr. 28. for def.14.1 r. def. 4.1.

pr. 37. cor. 1. 1 2 for point A. r. point D.
B IV. pr. 15 p. 64. 1. 8. for CG, GFr. CG, GD.
B. V. pr. 9. 1. 5. for it has to C, r. A has to C; the same pr. 10. 1.6.
B. VI. pr. 12. p. 88. 1. 1. for EF r. DF. pr. 29. I. 17. for KL r. EL.

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Τ Η Ε

E L E M E N T S

F

E U C L I I D.

BOOK XI.

DEFINITION S.

1.

Book XI. ness.

II.
The term of a solid, is a superficies.

III.
A right line is perpendicular to a plain, when it makes right

angles with all the lines that touch it, and are drawn in the
fame plain.

IV.
A plain is perpendicular to a plain, when all the right lines in

one plain, drawn at right angles to the common section of the
two plains, are at right angles to the other plain.

V.
The inclination of a right line to a plain, is the acute angle

contained under that line, and another right one drawn in
the plain, from that end of the inclining line, which is in
the plain, to the point where a right line falls from the other
end of the inclining line, perpendicular to the plain.

VI,

Book XI.

VI.
The inclination of a plain to a plain, is the acute angle con-

tained by the right lines drawn in both plains, to the same
point of their common section, and making right angles with
it.

VII.
Plains are inclined similarly, when their angles of inclination
are equal.

VIII.
Parallel plains are such, which being produced, never meet.

IX.
Similar folid figures are such as are contained under an en
qual number of similar plains.

X. Equal and similar solid figures are such as are contained by an equal number of similar and equal plains,

XI.
A solid angle is the inclination of more than two right lines
that meet in one point, but are not in the fame superficies.

XII.
A pyramid is a solid figure, contained by more than two

plains set upon one plain, and meeting at one point in the

vertex.

XIII.
A prism is a solid figure contained by plains, whereof the two

opposite are equal, similar, and parallel ; and the other pa-
rallelograms.

XIV,
A sphere is a solid figure, described by a semicircle revolving

about its diameter, which remains fixed in the same pofi-
tion.

XV. The axis of a sphere is that fixed right line about which the semicircle revolves.

XVI.
The centre of a sphere is the same with that of the femi,
circle.

XVII.
The diameter of a sphere is a right line drawn through the

centre, and terminated on either lide by the superficies of the
sphere.

XVIII.
A cone is a solid figurc described by a right angled triangle

revolving about one of the sides, containing the right angle,
remaining fixed. If the fixed right line be equal to the o-
ther fide containing the right angle, then it is a rectangular

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