## The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The first six books, together with the eleventh and twelfth |

### Inni boken

Side 31

I. gles , each to each , to which the equal fides are

the angle ACB is equal to the angle CBD . and because the straight line BC

meets the ' two straight lines AC , BD and makes , the alternate angles ACB ,

CBD ...

I. gles , each to each , to which the equal fides are

**opposite**. there- Book I. forethe angle ACB is equal to the angle CBD . and because the straight line BC

meets the ' two straight lines AC , BD and makes , the alternate angles ACB ,

CBD ...

Side 222

First , Let the parallelograms DG , HN which are

common side HG . then because the folid AH is i cut by the plane AGHC passing

thro ' the diagonals AG , CH of the

First , Let the parallelograms DG , HN which are

**opposite**to the base AB have acommon side HG . then because the folid AH is i cut by the plane AGHC passing

thro ' the diagonals AG , CH of the

**opposite**planes ALGF , CBHD , AH is cut into ... Side 251

II .

the triangle HKL

between the parallel m planes ABC , m . 15. 11 . HKL . and it is manifest that ...

II .

**opposite**to it , is equal to the prism having the triangle GFC for its base , andthe triangle HKL

**opposite**to it ; for they are of the fame altitude , because they arebetween the parallel m planes ABC , m . 15. 11 . HKL . and it is manifest that ...

Side 253

ABC to the triangle DEF , fo is the prism having the triangle LXC for its base , and

OMN the triangle

, and the

ABC to the triangle DEF , fo is the prism having the triangle LXC for its base , and

OMN the triangle

**opposite**to it , to the prism of which the base is the triangle RVF, and the

**opposite**triangle STY . and because the two prisms in the pyramid ... Side 4

5 : PROP . I. Na right angled plain triangle , if the hypothenuse be made radius ,

the sides become the fines of the angles

made radius , the remaining fide is the tangent of the angle

...

5 : PROP . I. Na right angled plain triangle , if the hypothenuse be made radius ,

the sides become the fines of the angles

**opposite**to them ; and if either side bemade radius , the remaining fide is the tangent of the angle

**opposite**to it , and the...

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### Vanlige uttrykk og setninger

added alſo altitude angle ABC angle BAC baſe becauſe Book Book XI caſe circle circle ABCD circumference common cone cylinder Definition demonſtrated deſcribed diameter divided double draw drawn equal equal angles equiangular equimultiples exceſs fame fides firſt folid fore four fourth given angle given in poſition given in ſpecies given magnitude given ratio given ſtraight line greater Greek half join leſs likewiſe magnitude manner meet muſt oppoſite parallel parallelogram perpendicular plane priſm produced PROP proportionals Propoſition pyramid radius reaſon rectangle rectangle contained remaining right angles ſame ſecond ſegment ſhall ſhewn ſides ſimilar ſolid ſphere ſquare ſquare of AC taken THEOR theſe third thro triangle ABC wherefore whole

### Populære avsnitt

Side 157 - D ; wherefore the remaining angle at C is equal to the remaining angle at F ; Therefore the triangle ABC is equiangular to the triangle DEF. Next, let each of the angles at C, F be not less than a right angle ; the triangle ABC is also, in this case, equiangular to the triangle DEF.

Side 24 - ... be equal, each to each ; and also the third angle of the one to the third angle of the other. Let ABC, DEF be two triangles which have the angles ABC, ECA equal to the angles DEF, EFD, viz.

Side 45 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.

Side 73 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...

Side 163 - 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.

Side 81 - ELF. Join BC, EF ; and because the circles ABC, DEF are equal, the straight lines drawn from their centres are equal: therefore the two sides BG, GC, are equal to the two EH, HF ; and the angle at G is equal to the angle at H ; therefore the base BC is equal (4.

Side 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Side 80 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.

Side 36 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.