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

### From inside the book

Results 1-5 of 100

Page 6

gles , those right lines , being infinitely produced , do meet on that fide where the angles are

gles , those right lines , being infinitely produced , do meet on that fide where the angles are

**less**than two right angles ; 12. Page 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

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. ) ... Page 12

If it should be asked , Why then he did not set it down first ? I answer , Because the latter part was the

If it should be asked , Why then he did not set it down first ? I answer , Because the latter part was the

**less**important and useful part of ... Page 20

... to the remaining angle ABD , the

... to the remaining angle ABD , the

**less**equal to the greater ; which is impoffible : therefore , the right lines B E , B C are not both in one direction . Page 23

Any two angles of every triangle taken together , are

Any two angles of every triangle taken together , are

**less**than two right angles . Let there be a triangle ABC : I say , any two angles of the triangle ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Common terms and phrases

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

### Popular passages

Page 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.

Page 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...

Page 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.

Page 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.

Page 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.

Page 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.

Page 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...

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

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

Page 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...