## 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 8

Side 20

AB . therefore AC is

See N. A 8. 3. 1 . PROP . XX . THEOR . NY two sides of a triangle are together

...

AB . therefore AC is

**greater**than AB . wherefore the**greater**angle , & c . Q. E. D.See N. A 8. 3. 1 . PROP . XX . THEOR . NY two sides of a triangle are together

**greater**than the third fide . Let ABC be a triangle ; any two sides of it together are...

Side 23

AB equal to DE , Book 1 . and AC to DF ; but the angle BAC

angle EDF . the base BC is also

DF , let DE be the side which is not

the ...

AB equal to DE , Book 1 . and AC to DF ; but the angle BAC

**greater**than theangle EDF . the base BC is also

**greater**than the base EF . Of the two sides DE ,DF , let DE be the side which is not

**greater**than the other , and at the point D inthe ...

Side 127

THA HAT magnitude which has a

same magnitude is the

has a

THA HAT magnitude which has a

**greater**ratio than See N. -another has unto thesame magnitude is the

**greater**of the two . and that magnitude to which the samehas a

**greater**ratio than it has unto another magnitude is the lesser of the two . Side 130

Book V. B and D , N and K are equimultiples ; if M be

than K ; and if equal , equal ; and if less , less b ; but b . 5. Def . 5 . G is

than K , therefore M is

Book V. B and D , N and K are equimultiples ; if M be

**greater**than N , G is**greater**than K ; and if equal , equal ; and if less , less b ; but b . 5. Def . 5 . G is

**greater**than K , therefore M is

**greater**than N. but H is not**greater**than L ; and M , H are ... Side 285

therefore c also the sphere GHK is

in the sphere DEF . but it is also less , because it is contained c . 14. So within it ,

which is impossible . therefore the sphere ABC has not to any sphere less than ...

therefore c also the sphere GHK is

**greater**than the solid polyhe- Book XII . dronin the sphere DEF . but it is also less , because it is contained c . 14. So within it ,

which is impossible . therefore the sphere ABC has not to any sphere less than ...

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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.