## 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 104

It is also

circumference DE , if to each be added BCD , the whole F B E ABCD is equal to

the whole EDCB . and the angle AED stands on the circumference ABCD , and

the angle ...

It is also

**equiangular**; because the А. circumference AB is equal to thecircumference DE , if to each be added BCD , the whole F B E ABCD is equal to

the whole EDCB . and the angle AED stands on the circumference ABCD , and

the angle ...

Side 109

Let ABCD be the given circle ; it is required to inscribe an equilateral and

equilateral triangle inscribed a in the e . 3. 4 . circle , and AB the side of an

equilateral and ...

Let ABCD be the given circle ; it is required to inscribe an equilateral and

**equiangular**quindecagon in the circle ABCD . Let AC be the side of anequilateral triangle inscribed a in the e . 3. 4 . circle , and AB the side of an

equilateral and ...

Side 157

VI . they are equal . and the angle at A is equal to the angle at D ; wherefore the

remaining angle at Cis equal to the remaining angle at F. therefore the triangle

ABC is

VI . they are equal . and the angle at A is equal to the angle at D ; wherefore the

remaining angle at Cis 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 ... Side 166

I. remaining angle AGB 6. wherefore the triangle FCD is

triangle GAB . again , at the points G , B in the straight line GB , make a the angle

BGH equal to the anF gle DFE , and the angle K к GBH equal to FDE ; therefore

the ...

I. remaining angle AGB 6. wherefore the triangle FCD is

**equiangular**to thetriangle GAB . again , at the points G , B in the straight line GB , make a the angle

BGH equal to the anF gle DFE , and the angle K к GBH equal to FDE ; therefore

the ...

Side 269

... NSE , having the sides about all their angles proportionals , are

and fimilar to one another . and therefore the pyramid of which e . 5. 6 . the base

is the triangle AKQ , and vertex L , is similar to the pyramid the base of which is

the ...

... NSE , having the sides about all their angles proportionals , are

**equiangular**and fimilar to one another . and therefore the pyramid of which e . 5. 6 . the base

is the triangle AKQ , and vertex L , is similar to the pyramid the base of which is

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.