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

### From inside the book

Page 10

If therefore two triangles have two sides of the one equal to two sides of the other , each to each ; and

If therefore two triangles have two sides of the one equal to two sides of the other , each to each ; and

**have one angle of the one equal to one angle of the**other , viz . that which is contained under the equal lines ; then shall the ... Page 248

If two triangles

If two triangles

**have one angle of the one equal to one angle of the**other , and the sides about the equal angles proportional : these triangles will be equiangular , baving those angles equal which are opposite to the homologous fides ... Page 249

Therefore if two triangles

Therefore if two triangles

**have one angle of the one equal to one angle of the**other , and the fides about the equal angles proportional ; these triangles will be equiangular , having those angles ... Page 251

If therefore two triangles

If therefore two triangles

**have one angle of the one equal to one angle of the**other , and the sides about two other angles proportional , and have also each of the remaining angles either less or greater than a right angle : these ... Page 258

Therefore if equal parallelograms

Therefore if equal parallelograms

**have one angle of the one equal to one angle of the**other ; the sides about the equal angles will be reciprocally proportional . And if parallelograms**have one angle of the one equal to one angle of the**...### What people are saying - Write a review

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### Common terms and phrases

A B C ABCD added alſo altitude baſe becauſe centre circle circumference common cone continue 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 245 - 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 28 - 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 246 - 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 16 - 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 30 - 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 54 - 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 389 - 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 108 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.

Page 128 - When you have proved that the three angles of every triangle are equal to two right angles...

Page 181 - 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...