Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

lid, having the common base, ABC ; then, if the folld EABC is not equal to the folid FABC, let it be equal to some solid as GA BC, either greater or less than EABC, which cannot be; for the one would contain the other, and if the solid angle is conG

tained by more than three plane angles, equal and similar to one

another, then it can EL

be divided into angles which are contained by three equal and fi. milar plane angles,

by Prop. 20. Book Vi. D

and parts have the

fame proportion B

C their like multiples,

by Prop. 15. Book V. wherefore universally, figures bounded by

an equal number of equal and similar planes are equal and fimilar.

N. B. In the references, when the proposition referred to is in the fame book with the proposition to be proved, the book is Bot named, but only the number of the proposition, but, if in any

other book, both are named.

as

[merged small][merged small][merged small][ocr errors][ocr errors][merged small][merged small][merged small][merged small]

Book I.

A

I.
Point is that which hath no parts or magnitude.

II.
A line is length without breadth.

III.
The bounds of a line are points.

IV.
A right line is that which lieth evenly between its points.

V.
A superficies is that which hath only length and breadth.

VI.
The bounds of a superficies are lines.

VII.
A plain superficies is that which lieth evenly between its lines.

VIII.
A plain angle is the inclination of two lines to one another in

the same plain, which touch each other, but do not lie in the
same right line.

IX.
If the lines containing the angle be right ones, then the angle is
called a right-lined angle.

X.
When one right line standing on another right line makes the

angles on each side thereof equal to one another, each of these
angles is a right one, and that line which stands

upon ther is called a perpendicular to that whereon it stands.

А

XI. An

the O

Book 1.

XI.

An obtuse angle is that which is greater than a right one.

XII.
An acute angle is that which is less than a right one.

XIII.
A term, or bound, is the extreme of

any thing.

XIV.
A figure is that which is contained under one or more terms.

XV.
A circle is a plain figure bounded by one line, called the circum-

ference, to which all right lines drawn from a certain point
within the same are equal.

XVI.
That point is called the center of the circle.

XVII.
The diameter of a circle is a right line drawn through the cen-

ter, and terminated on both ends by the circumference, and
divides the circle into two equal parts.

XVIII. A semicircle is a figure contained under any diameter, and the circumference cut off by that diameter.

XIX.
A segment of a circle is a figure contained under a right line,
and circumference cut off by that right line.

XX.
Right-lined figures are such as are contained by right lines.

XXI.
Three sided figures are such as are contained by three lines.

XXII.
Four sided figures are such as are contained by four lines.

XXIII.
Many fided figures are such as are contained by more than four
lines.

XXIV.
An equilateral triangle is that which hath three equal fides.

XXV.
An isosceles triangle, that which hath two fides equal.

XXVI.
A scalene triangle, that which hath all the three sides unequal.

XXVII.
A right angled triangle is that which hath one right angle in it.

XXVIII.
An obtufe angled one, that which hath one obtuse angle in it.

XXIX.
An acute angled triangle is that which hath all the angles les
than right ones.

XXX.

Воок І.
A fquare is that which hath four equal fides, and its angles all
right ones.

XXXI.
An oblong, or rectangle, is lònger than broad, its opposite fides
are equal, and its angles all right ones.

XXXII.
A rhombus, that which hath four equal sides, but not right
angles.

XXXIII.
A rhomboides, whose opposite sides and angles are equal.

XXXIV.
All quadrilateral figures beside these are called trapezia.

XXXV.
Parallel right lines are such as, being produced both ways in
the same plain, never meet.

XXXVI.
A parallelogram is a figure whose opposite sides are parallel.

[merged small][ocr errors]

G

I.
RANT that a right line may be drawn from any one
point to another :

II.
That a finite right line may be continued directly forwards: And,

III.
That a circle may be described about any center, with any

distance.

A X I OM S.

I

[ocr errors]

1.
HINGS equal to one and the same thing are equal to
one another.

II.
If equal things are added to equal things, the wholes will be e-
qual.

III.
If from equal things equal things be taken, the remainders will

be equal.

IV:
If to unequal things equal things are added, the whole will be
unequal.

V. If

1

V. Book I.

If from unequal things equal parts are taken, the remainders will be unequal.

VI. Things which are double one and the same thing are equal between themselves.

VII.
Things which are half one and the same thing are equal between
themselves.

VIII.
Things which mutually agree together are equal to one another.

IX,
Any whole is greater than its part.

X.
Two right lines do not bound a figure.

XI.
All right angles are equal to one another.

XII.
If a right line fall upon two right lines, making the inward

angles on the same side less than two right angles, these right
lines continually produced will at last meeț one another on
that side where the angles are less than right ones.
N. B. Any angle is expressed by three letters, of which

that at the vertex is named betwixt the other two..

PRO

« ΠροηγούμενηΣυνέχεια »