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THE

ELEMENTS OF GEOMETRY,

SYMBOLICALLY ARRANGED.

PUBLISHED BY COMMAND OF THE LORDS COMMISSIONERS

OF THE ADMIRALTY,

FOR THE USE OF THE BOYS OF THE ROYAL HOSPITAL SCHOOLS,

GREENWICH.

SECOND EDITION.

L O N D ON:

JOHN MURRAY, ALBEMARLE STREET.

1846.

916.

GEOMETRY is divided into Plane and Solid Geometry. The former is confined to the consideration of the properties of Space within the same plane, and the latter to the relations that exist between different Planes or Surfaces, or of the Solids which these describe or terminate. In this book, the points, lines, and surfaces are all considered to be in the same plane; and the text of the first books of Euclid has been adhered to as closely in this little work as its symbolical form, and the object for which it is intended, will admit of.

The Learner is earnestly recommended to repeat distinctly to himself, each step in the demonstrations of the propositions; and moreover to refer to the propositions upon which the proofs depend. He will thus acquire a facility of not only writing down the propositions with neatness and accuracy; but also, when called upon to demonstrate them by word of mouth, of expressing himself in clear and intelligible language.

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THE

ELEMENTS OF GEOMETRY.

ABBREVIATIONS.

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adj. signifies adjacent.

axiom.
circumfer.

ence. cr.

centre. const. construction. def.

definition. descr. describe. diam. diameter. dist.

distance. ea. to ea. »

each to each. equilat. equilateral ext.

exterior. fig. hyp.

hypothesis. int.

interior.

i. e. signifies that is.
isosc.

isosceles.
oppo. opposite.
post.

postulate. prod.

Sproduce.

produced.
prop. proposition.
pt.
rect.

rectangle.
rectilin. rectilineal.
rem.

remainder.

right. seg.

segment. sq.

square. str.

straight. viz.

namely.

» point.

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rt.

» figure.

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+ signifies {plus, the sign

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SYMBOLS.

* signifies not less than. Tof addition

Sperpendicu

I (minus, the

lar to. sign of sub

parallel to. traction.

M

not parallel to. equal to.

because. not equal to.

therefore. greater than.

circle. (not greater

triangle. (than.

parallelogram. less than.

angle.

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G E O M E TRY.

DEFINITIONS.

I. A point is that which has position, but not magnitude.

II.
A line is length without breadth.

III.
The extremities of a line are points.

IV.

A straight line is that which lies evenly between its extreme points.

V. A superficies is that which has only length and

breadth.

VI.
The extremities of a superficies are lines.

VII.
A plane superficies is that in which any two

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

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