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paring for that University. It contains all that is required for the examination at Responsions. If the student does not intend to pursue the subject further, he may

omit the Deductions. The additional matter by the present Editor has been included in brackets, that the student may be able to distinguish what is absolutely required of him, from what is only intended to help him in acquiring that knowledge. It is

very desirable that every student entering at Oxford should have read over these books at least once.

5. Lower Crescent, Clifton,

May, 1852.

DIRECTIONS TO THE LEARNER.

First. Procure a case of instruments.

Secondly. Draw each figure correctly as the construction in the Proposition directs.

Thirdly. In subsequent cases of having to draw the same figure, use the shorter method (if any) pointed out in the Note which follows the Proposition.

Fourthly. If possible, go over the first five Propositions of the First Book, vivâ voce, with a teacher.

Fifthly. Read the First Book twice before proceeding to the Second

TUE

ELEMENTS OF EUCLID.

BOOK I.

DEFINITIONS.

I.

A POINT is that which hath no parts, or which hath no BOOK I. magnitude.

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A straight line is that which lies evenly between its extreme

points.

[A, B, C, above, are straight lines ; D, E are not straight lines, but curves.]

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A superficies is that which hath only length and breadth.

Fig. 1.

B

D

Fig. 2.

E

G

VI.
The extremities of a superficies are lines.

[The superficies, fig. 1., is bounded by four straight lines ; that in fig. 2. by one straight line and two lines which are not straight lines, but curves. ]

VII.
A plane superficies is that in which any two points being

taken, the straight line between them lies wholly in that
superficies.

VIII.

Fig. 1.

“A plane angle is the inclination of A

two lines to one another in a plane,
which meet together, but are not
in the same direction.”

[Fig. 1., plane rectilineal angle;
fig. 2., plane angle, not rectilineal.]

Fig. 2.

B

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