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

### From inside the book

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Page 276

If a parallelogram be taken away from a parallelogram similar to the whole , alike

fituate , and both having one

same

A ...

If a parallelogram be taken away from a parallelogram similar to the whole , alike

fituate , and both having one

**common**angle : I say they will also both have thesame

**common**diameter . For from the parallelogram Abcd let the parallelogramA ...

Page 277

Therefore the parallelograms ABCD , KG have not both the fame

diameter . Wherefore the parallelograms A BCD , A EFG have both the same

allelogram ...

Therefore the parallelograms ABCD , KG have not both the fame

**common**diameter . Wherefore the parallelograms A BCD , A EFG have both the same

**common**diameter . If therefore a parallelogram be taken away from a par .allelogram ...

Page 300

Let the right line A c be the

, and let the right line ECD cutting the circle , make the angle ACD equal to the

angle ABC in the segment ABC , or the angle ACE equal to the angle Arc in the ...

Let the right line A c be the

**common**base of the segments A B C , A FC of a circle, and let the right line ECD cutting the circle , make the angle ACD equal to the

angle ABC in the segment ABC , or the angle ACE equal to the angle Arc in the ...

Page 330

Hi For let the plane de pass thro ' the right line A B , and let the right line ce be the

and from the same draw Fg in the plane G A H De at right angles to CE .

Hi For let the plane de pass thro ' the right line A B , and let the right line ce be the

**common**fection of the plane DE and the given plane : Take any point F in c E ,and from the same draw Fg in the plane G A H De at right angles to CE .

Page 457

33. where he first uses the word Side of a parallelepipedon , he calls the side of

the parallelogram , which is the base of that solid , the side of the

parallelepipedon . As this is somewhat contrary to

might not be ...

33. where he first uses the word Side of a parallelepipedon , he calls the side of

the parallelogram , which is the base of that solid , the side of the

parallelepipedon . As this is somewhat contrary to

**common**conception , I think itmight not be ...

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### 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...