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

### From inside the book

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Page 56

as many right angles as there are triangles ; that is , equal to twice as many right

angles , wanting the angles of two triangles ; that is , wanting four right angles , as

the

as many right angles as there are triangles ; that is , equal to twice as many right

angles , wanting the angles of two triangles ; that is , wanting four right angles , as

the

**figure**has sides . Therefore all the angles of any right - lined**figure**, when ... Page 67

parallel to the diagonal ca , cutting the continuation of AF in the point G , and

draw the right line cG , which let cut the side A B of the

, draw a second diagonal CF of the

...

parallel to the diagonal ca , cutting the continuation of AF in the point G , and

draw the right line cG , which let cut the side A B of the

**figure**in the point K. Again, draw a second diagonal CF of the

**figure**; and continuing out the next fide F e of...

Page 169

I , A Right lined

angle of the

inscribed . 2. A right lined

every ...

I , A Right lined

**figure**is faid to be inscribed in a right lined**figure**, when everyangle of the

**figure**inscribed touches every side of the**figure**in which it isinscribed . 2. A right lined

**figure**is said to circumscribe a right lined**figure**, whenevery ...

Page 270

x ] N S LCD . and alike situate be described ; but upon e i , GH , let the right lined

right ...

x ] N S LCD . and alike situate be described ; but upon e i , GH , let the right lined

**figures**MF , NH fimilar and alike fituate , be defcribed : I say as the fight lined**figure**KAB is to the right lined**figure**1 c D ; To is the right lined**figure**MF to theright ...

Page 284

In right angled triangles the

angle is equal to both the

angle , which are similar to it , and have the same situation ? Let the right angled

...

In right angled triangles the

**figure**described upon the side opposite to the rightangle is equal to both the

**figures**described upon the sides containing the rightangle , which are similar to it , and have the same situation ? Let the right angled

...

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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...