## Euclid's Elements of geometry, books i. ii. iii. iv |

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Side 7

If two triangles have two

each , and have also the angles contained by those

1 . ) they shall have their bases , or third

If two triangles have two

**sides**of the one equal to two**sides**of the other , each toeach , and have also the angles contained by those

**sides**equal to one another : (1 . ) they shall have their bases , or third

**sides**, equal ; ( 2 . ) the two triangles ... Side 21

Q . E . D . PROPOSITION 21 . — THEOREM . If from the ends of the

triangle there be drawn tro straight lines to a point within the triangle , these shall

be less than the other two

Q . E . D . PROPOSITION 21 . — THEOREM . If from the ends of the

**side**of atriangle there be drawn tro straight lines to a point within the triangle , these shall

be less than the other two

**sides**of the triangle , but shull contain a greater angle . Side 24

Euclides. 1 . The two

namely , AB to DE , and AC to DF , 2 . But the angle BAC greater than the angle

EDF . Sequence . - - The base BC shall be greater than the base EF .

Construction .

Euclides. 1 . The two

**sides**AB , AC , equal to the two DE , DF , each to each ,namely , AB to DE , and AC to DF , 2 . But the angle BAC greater than the angle

EDF . Sequence . - - The base BC shall be greater than the base EF .

Construction .

Side 46

And because the two

each ( def . 30 ) , and the angle DBA equal to the angle FBC ; 8 . Therefore the

base AD is equal to the base FC , and the triangle ABD to the triangle FBC . ( I . 4

. ) ...

And because the two

**sides**AB , BD , are equal to the two**sides**FB , BC , each toeach ( def . 30 ) , and the angle DBA equal to the angle FBC ; 8 . Therefore the

base AD is equal to the base FC , and the triangle ABD to the triangle FBC . ( I . 4

. ) ...

Side 50

to the base , and terminated by the

, any line so bisected is parallel to the base . 40 . To describe a triangle equal to a

given quadrilateral figure . 41 . If two triangles have two

to the base , and terminated by the

**sides**, or the**sides**produced . And conversely, any line so bisected is parallel to the base . 40 . To describe a triangle equal to a

given quadrilateral figure . 41 . If two triangles have two

**sides**of the one equal ...### Hva folk mener - Skriv en omtale

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### Vanlige uttrykk og setninger

ABCD angle ABC angle BAC angle BCD angle equal assumed base base BC BC is equal bisected BOOK centre circle ABC circumference coincide common Conclusion Conclusion.—Therefore const Construction Construction.-1 Demonstration Demonstration.-1 describe diameter distance divided double draw drawn equilateral exterior angle extremities fall figure four given circle given point given rectilineal given straight line greater half Hypothesis.—Let inscribed join less manner meet opposite angle parallel parallelogram pass pentagon perpendicular produced Prop proved Q. E. D. PROPOSITION reason rectangle contained rectilineal figure References—Prop regular right angles segment semicircle shown sides Sought.-It is required square on AC Take third touches the circle triangle ABC twice the rectangle whole

### Populære avsnitt

Side 25 - If two triangles have two angles of the one equal to two angles of the other, each to each ; and one side equal to one side, viz.

Side 2 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.

Side 99 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.

Side 4 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...

Side 66 - ... the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse...

Side 65 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.

Side 32 - F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 58 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced...

Side 88 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...

Side 33 - The straight lines which join the extremities of two equal and parallel straight lines towards the same parts, are also themselves equal and parallel.