## Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |

### Inni boken

Side 30

...

one fide of the one equal to one side of the other , either that fide which is

between tbe equal angles , or that which is opposite to one of them , then will the

...

...

**have two angles of the one equal to two angles of the other**, each to each , andone fide of the one equal to one side of the other , either that fide which is

between tbe equal angles , or that which is opposite to one of them , then will the

...

Side 32

... BAC equal to the remaining angle e DF . If therefore two triangles

the one equal to one side of the other , either that which is between the equal ...

... BAC equal to the remaining angle e DF . If therefore two triangles

**have two****angles of the one equal to two angles of the other**, each to each ; and one side ofthe one equal to one side of the other , either that which is between the equal ...

Side 113

equal to the angle E B F. But the right angle Are is equal to the right angle BFE :

therefore , the two triangles E AF , EBF

...

equal to the angle E B F. But the right angle Are is equal to the right angle BFE :

therefore , the two triangles E AF , EBF

**have two angles of the one equal to two****angles of the other**, and the side E F of the one equal to the side E F of the other...

Side 184

... two triangles F H C , FK Ç , will

common fide Fc , which is opposite to one of the equal angles : Therefore [ by 26.

1. ) ...

... two triangles F H C , FK Ç , will

**have two angles of the one equal to two angles****of the other**, and one side of the one equal to one side of the other , viz . thecommon fide Fc , which is opposite to one of the equal angles : Therefore [ by 26.

1. ) ...

Side 317

the angle A E G is equal to the angle ' Beh : Therefore B the two triangles AGE ,

EBM

and one fide A E of the one equal to one fide E B of the other , which lies between

...

the angle A E G is equal to the angle ' Beh : Therefore B the two triangles AGE ,

EBM

**have two angles of the one equal to two angles of the other**, each to each ,and one fide A E of the one equal to one fide E B of the other , which lies between

...

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### Vanlige uttrykk og setninger

A B C ABCD added alſo altitude baſe becauſe centre circle circumference common cone cylinder definition demonſtrated deſcribed diameter difference divided double draw drawn equal equal angles equiangular equimultiples Euclid exceeds fall fame fides figure firſt folid fore four fourth given right line greater half inſcribed join leſs magnitudes manner meet multiple oppoſite parallel parallelogram perpendicular plane polygon priſms PROP proportional propoſition proved pyramid ratio rectangle remaining angle right angles right line A B right lined figure ſame ſay ſecond ſegment ſhall ſides ſimilar ſince ſolid ſome ſphere ſquare ſtand ſum taken THEOR theſe third thoſe thro touch triangle triangle ABC twice vertex Wherefore whole whoſe baſe

### Populære avsnitt

Side 247 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Side 30 - 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. either the sides adjacent to the equal...

Side 248 - But it was proved that the angle AGB is equal to the angle at F ; therefore the angle at F is greater than a right angle : But by the hypothesis, it is less than a right angle ; which is absurd.

Side 18 - When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.

Side 32 - Let the straight line EF, which falls upon the two straight lines AB, CD, make the alternate angles AEF, EFD equal to one another; AB is parallel to CD.

Side 56 - 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 391 - KL: but the cylinder CM is equal to the cylinder EB, and the axis LN to the axis GH; therefore as the cylinder EB to...

Side 110 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.

Side 130 - When you have proved that the three angles of every triangle are equal to two right angles...

Side 183 - FK : in the same manner it may be demonstrated, that FL, FM, FG are each of them equal to FH, or FK : therefore the five straight lines FG, FH, FK, FL, FM are equal to one another : wherefore the circle described from the centre F, at the distance of...