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

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Resultat 1-5 av 5

Side 336

Book XI . quired that B , C , D together be greater than A , from each of these

taking away B , C , the remaining one D must be greater than the

above B and C. take therefore any magnitude D which is less than A , B , C

together , but ...

Book XI . quired that B , C , D together be greater than A , from each of these

taking away B , C , the remaining one D must be greater than the

**excess**of Aabove B and C. take therefore any magnitude D which is less than A , B , C

together , but ...

Side 369

Let the

to the magnitude BC ; the

magnitude , has a given ratio to BC . Let AD be the given magnitude the

of ...

Let the

**excess**of the magnitude AB above a given magnitude , have a given ratioto the magnitude BC ; the

**excess**of AC , both of them together , above a givenmagnitude , has a given ratio to BC . Let AD be the given magnitude the

**excess**of ...

Side 375

5 . of EG to FD is given . and GB is given , therefore EG the

the given magnitude GB , has a given ratio to FD . the other case is thewn in the

same way . F D 1 PROP . XXIV . 13 . IF F there be three magnitudes , the first of ...

5 . of EG to FD is given . and GB is given , therefore EG the

**excess**of EB abovethe given magnitude GB , has a given ratio to FD . the other case is thewn in the

same way . F D 1 PROP . XXIV . 13 . IF F there be three magnitudes , the first of ...

Side 376

Also if the first has a given ratio to the second , and the

a given magnitude has also a given ratio to the second , the same

have a given ratio to the first ; as is evident from the oth Dat . 17 . PROP . XXV .

Also if the first has a given ratio to the second , and the

**excess**of the third abovea given magnitude has also a given ratio to the second , the same

**excess**shallhave a given ratio to the first ; as is evident from the oth Dat . 17 . PROP . XXV .

Side 378

IF F there be three magnitudes the

magnitude has a given ratio to the second : and the

a given magnitude has also a given ratio to the third . the

a ...

IF F there be three magnitudes the

**excess**of the first of which above a givenmagnitude has a given ratio to the second : and the

**excess**of the second abovea given magnitude has also a given ratio to the third . the

**excess**of the first abovea ...

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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.