## 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

Resultat 1-5 av 6

Side 71

3 . than one point . for , if it be possible , let the

C are in the circumference of the

them ...

3 . than one point . for , if it be possible , let the

**circle**ACK touch the Book III .**circle**ABC in the points A , C , and join AC . therefore because the two points A ,C are in the circumference of the

**circle**ACK , the straight line AC K which joinsthem ...

Side 92

If from any point without a Α .

as AB , AC , the rectangles contained by the whole lines EN and the parts of them

without the

If from any point without a Α .

**circle**, there be drawn two straight lines cutting it ,as AB , AC , the rectangles contained by the whole lines EN and the parts of them

without the

**circle**, are equal to one another , viz . the rectangle BA , AE to the ... Side 95

A

of the

described . VII . A straight line is faid to be placed in a

extremities of ...

A

**circle**is said to be described about a rectilineal figure , when the circumferenceof the

**circle**passes thro ' all the angular points of the figure about which it isdescribed . VII . A straight line is faid to be placed in a

**circle**, when theextremities of ...

Side 248

Book XII . is to the space S. therefore as the

the polygon AXBOCPDR to the polygon EKFLGMHN . but the

greater than the polygon contained in it ; whered . 14. 5. fore the space S is

greater ...

Book XII . is to the space S. therefore as the

**circle**ABCD is to the space S , lo is ethe polygon AXBOCPDR to the polygon EKFLGMHN . but the

**circle**ABCD isgreater than the polygon contained in it ; whered . 14. 5. fore the space S is

greater ...

Side 267

to any not to the

than the cone EN . In the same manner it may be demonstrated that the

EFGH is not to the

to any not to the

**circle**EFGH , as the cone AL to any solid which is less Book XII .than the cone EN . In the same manner it may be demonstrated that the

**circle**EFGH is not to the

**circle**ABCD , as the cone EN solid less than the cone AL .### Hva folk mener - Skriv en omtale

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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.