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

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Side x

**Prop**. vii . at page 64. the Scholium at page 97. the Scholium at page 100.**Prop**: viii . at page 204 .**Prop**. ix . at page 205. the Scholium at påge 106 . and the proposition .**Prop**. ix . at page 158.**Prop**. x . at page 160. Side 6

... were less than both the angles A E F , CFE on the left ; and since two different right lines cannot be drawn from the same point out of a given right line parallel to that given right line ; and since it is demonfrated at

... were less than both the angles A E F , CFE on the left ; and since two different right lines cannot be drawn from the same point out of a given right line parallel to that given right line ; and since it is demonfrated at

**prop**. Side 8

**PROP**. III . PROBL . Two unequal right lines being given , to take a right line from the greater equal to the lefjer . ' . Let the two unequal right lines given be A B and c , whereof let A B be the greater ; it is required to take a ... Side 11

For in the right line BD , let there be taken any point as F ; and from the greater line A E , let be taken AG equal to AF the less [ by

For in the right line BD , let there be taken any point as F ; and from the greater line A E , let be taken AG equal to AF the less [ by

**prop**. 3. ) and draw the right lines FC , G B. В " Therefore because AF is equal to AG , and the ... Side 12

**PROP**. VI . THEOR . If two angles of a triangle be equal to one another , then mail the sides opposite to the equal angles be equal to one another . Let the triangle A B C have the angle A b c equal to the angle A C3 .### Hva folk mener - Skriv en omtale

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Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Ingen forhåndsvisning tilgjengelig - 2016 |

### 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 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...