## 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 5

Side 7

BCD . and from the center B , at the distance BA describe the circle D A . B E ACE

; and from the point C in which the circles cut one another

b CA , CB to the points A , B. ABC shall be an equilateral triangle . Because the ...

BCD . and from the center B , at the distance BA describe the circle D A . B E ACE

; and from the point C in which the circles cut one another

**draw**the straight linesb CA , CB to the points A , B. ABC shall be an equilateral triangle . Because the ...

Side 75

is required to

Find a the center E of the circle , and join . AE ; and from the a . 1. 3 . center E , at

the distance EA describe the circle AFG ; from the point D

angles ...

is required to

**draw**a straight line from A which shall touch the Book IIL circle .Find a the center E of the circle , and join . AE ; and from the a . 1. 3 . center E , at

the distance EA describe the circle AFG ; from the point D

**draw**6 DF at rightangles ...

Side 159

From the point A

take any point D , and take AC which is the fame multiple of AD that AB is of the

part A which is to be cut off from it ; join BC , and

...

From the point A

**draw**a straight line AC making any angle with AB ; and in ACtake any point D , and take AC which is the fame multiple of AD that AB is of the

part A which is to be cut off from it ; join BC , and

**draw**DE parallel to it . then AE is...

Side 198

I. AC to the base DF ; the angle ABC is equal d to the angle DEF . Therefore if two

straight lines , & c . Q. E. D. PROP . XI . PROB . To a 10

perpendicular to a plane , from a given point above it . Let A be the given point

above ...

I. AC to the base DF ; the angle ABC is equal d to the angle DEF . Therefore if two

straight lines , & c . Q. E. D. PROP . XI . PROB . To a 10

**draw**a straight lineperpendicular to a plane , from a given point above it . Let A be the given point

above ...

Side 422

ment of a circle EGF containing an angle equal to the given angle BAC ;

bisecting EF at right angles , and join EG , GF . then fince the angle EGF is equal

to the angle BAC , and that EGF is an Ifofceles triangle and ABC is not , the ...

ment of a circle EGF containing an angle equal to the given angle BAC ;

**draw**GHbisecting EF at right angles , and join EG , GF . then fince the angle EGF is equal

to the angle BAC , and that EGF is an Ifofceles triangle and ABC is not , the ...

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### 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.