## 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 7

Side 68

F a point be

straight lines to the circumference , that point is the center of the circle . Let the

point D be

more ...

F a point be

**taken**within a circle , from which there fall more than two equalstraight lines to the circumference , that point is the center of the circle . Let the

point D be

**taken**within the circle ABC , from which to the circumference there fallmore ...

Side 119

V. THEOR . IF F one magnitude be the same multiple of another , See N. which a

magnitude

remainder shall be the same multiple of the remainder , that the whole is of the

whole .

V. THEOR . IF F one magnitude be the same multiple of another , See N. which a

magnitude

**taken**from the first is of a magnitude**taken**from the other ; theremainder shall be the same multiple of the remainder , that the whole is of the

whole .

Side 135

A. So But let HO , MP be equimultiples of EB , FD ; and because AE is to EB , as

CF to FD , and that of AE , CF are

the equimultiples HO , MP ; if GK be greater than HO , LN is greater than MP ; and

...

A. So But let HO , MP be equimultiples of EB , FD ; and because AE is to EB , as

CF to FD , and that of AE , CF are

**taken**equimultiples GK , LN ; and of EB , FD ,the equimultiples HO , MP ; if GK be greater than HO , LN is greater than MP ; and

...

Side 136

A and because if magnitudes

also proportionals 6 when C

DF to FC ; and alternately , as BE is to DF , so is EA to FC . but as AE to CF , so ,

by ...

A and because if magnitudes

**taken**jointly be proR 17. 5. portionals , they arealso proportionals 6 when C

**taken**separately ; therefore aş BE is to EA , fo E isDF to FC ; and alternately , as BE is to DF , so is EA to FC . but as AE to CF , so ,

by ...

Side 308

Book . it seems to have been

appeared evident enough to him , and others who substitute the confused and

indistinct idea the vulgar have of proportionals , in place of that accurate idea

which is ...

Book . it seems to have been

**taken**out of the Elements by Theon , because itappeared evident enough to him , and others who substitute the confused and

indistinct idea the vulgar have of proportionals , in place of that accurate idea

which is ...

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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.