## 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 118

See N. TF the first of four magnitudes has the same ratio to the second which the

third has to the fourth ; then any

have the same ratio to any

See N. TF the first of four magnitudes has the same ratio to the second which the

third has to the fourth ; then any

**equimultiples**whatever of the first and third fhallhave the same ratio to any

**equimultiples**of the second and fourth , viz . the ... Side 119

Book V. and in like manner the first and the third have the same ratio to any

second , the same ratio which the third C has to the fourth D , and of A and C let E

and F ...

Book V. and in like manner the first and the third have the same ratio to any

**equimultiples**whatever of the second and fourth . Let A the first have to B thesecond , the same ratio which the third C has to the fourth D , and of A and C let E

and F ...

Side 127

Let A have to C a greater ratio than B has to C ; A is greater than B. for because A

has a greater ratio to C , than B has to C , there are a fome

B , and some multiple of a . 7.Def . 5 . C fuch , that the multiple of A is greater ...

Let A have to C a greater ratio than B has to C ; A is greater than B. for because A

has a greater ratio to C , than B has to C , there are a fome

**equimultiples**of A andB , and some multiple of a . 7.Def . 5 . C fuch , that the multiple of A is greater ...

Side 129

The first six books, together with the eleventh and twelfth Robert Simson. of A , C ,

E , and L , M , N

greater than M , and K greater than N ; and if equal , equal ; aid if less , less a .

The first six books, together with the eleventh and twelfth Robert Simson. of A , C ,

E , and L , M , N

**equimultiples**of B , D , F ; if Ġ be greater Book V. than L , H isgreater than M , and K greater than N ; and if equal , equal ; aid if less , less a .

Side 133

LM is the same multiple : of CF , that LN is of CD . but LM was fhewn to be the

same multiple of CF , that GK is of AB ; GK therefore is the same multiple of AB ,

that LN is of CD ; that is , GK , LN are

HK is ...

LM is the same multiple : of CF , that LN is of CD . but LM was fhewn to be the

same multiple of CF , that GK is of AB ; GK therefore is the same multiple of AB ,

that LN is of CD ; that is , GK , LN are

**equimultiples**of AB , CD . Next , becauseHK is ...

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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.