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

### From inside the book

Results 1-5 of 61

Page 16

... D F or er equal to Hence it appears , how any given angle may be

... D F or er equal to Hence it appears , how any given angle may be

**divided**into 4 , 8 , 16 , 32 , & c . equal parts , viz . by bisecting each part again . Page 55

For any right - lined figure , by drawing diagonals , may be resolved or

For any right - lined figure , by drawing diagonals , may be resolved or

**divided**into as many triangles as the figure has fides , wanting two . Page 69

... nd GI be

... nd GI be

**divided**at k into two cq a ' ra ts ; this half GK will be gr . ater tan the perp ndicular drawi . f.om. D to AM : th refore bitect [ by 9. Page 73

Therefore a given trapezium is

Therefore a given trapezium is

**divided**into two equal parts , by a right line drawn from a given point in the middle of its side . Which was to be done . Page 74

If there be two right lines , and one of them is cut or

If there be two right lines , and one of them is cut or

**divided**into any parts whatsoever , the reEtangle contained under the two right lines is equal to ...### 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...