Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

1

ERRATA for the first fix Books.

B. II. pr. 3, 1. 5. for AC, CD, r. AF, CE; pr. 10. 1. 15. for DEF r. DFE. B. HI. pr. 23. note, for def. 11. r. def. 10; pr. 28. for def.14.1 r. def. 4.1. pr. 37. cor. 1. 12. for point A. r. point D.

BIV. pr. 15 p. 64. 1. 8. for CG, GF r. CG, GD.

B. V. pr. 9. 1. 5. for it has to C, r. A has to C; the fame pr. 10. 1. 6.

B. VI. pr. 12. p. 88. 1. 1. for EF r. DF. pr. 29. l. 17. for KL r. EL.

H

R

H

.30.

THÉ

ELEMENT S

O F

EUCLI D.

воок XI.

DEFINITION S.

A

I.

Solid, is that which hath length, breadth, and thick-Book XI.

nefs.

II.

The term of a folid, is a fuperficies.

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 fection 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,

[blocks in formation]

The inclination of a plain to a plain, is the acute angle contained by the right lines drawn in both plains, to the fame point of their common section, and making right angles with it.

VII.

Plains are inclined fimilarly, when their angles of inclination are equal.

VIII.

Parallel plains are fuch, which being produced, never meet.

IX.

Similar folid figures are fuch as are contained under an equal number of fimilar plains.

X.

Equal and fimilar folid figures are fuch as are contained by an equal number of fimilar and equal plains.

XI.

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

XII.

A pyramid is a folid figure, contained by more than two plains fet upon one plain, and meeting at one point in the

vertex.

XIII.

A prifm is a folid figure contained by plains, whereof the two oppofite are equal, fimilar, and parallel; and the other parallelograms.

XIV.

A fphere is a folid figure, defcribed by a femicircle revolving about its diameter, which remains fixed in the same pofition.

XV.

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

XVI.

The centre of a fphere is the fame with that of the femicircle.

XVII.

The diameter of a fphere is a right line drawn through the centre, and terminated on either fide by the fuperficies of the sphere.

XVIII.

A cone is a folid figure defcribed by a right angled triangle revolving about one of the fides, containing the right angle, remaining fixed. If the fixed right line be equal to the other fide containing the right angle, then it is a rectangular

« ΠροηγούμενηΣυνέχεια »