## 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 45

F a straight line be

whole and one of the parts , is equal to the rectangle contained by the two parts ,

together with the square of the foresaid part . Let the straight line AB be

into ...

F a straight line be

**divided**into any two parts , the rectangle contained by thewhole and one of the parts , is equal to the rectangle contained by the two parts ,

together with the square of the foresaid part . Let the straight line AB be

**divided**into ...

Side 159

O

parts that shall have the same ratios to one another which the parts of the

given straight line have . Let AB be the straight line given to be

O

**divide**a given straight line similarly to a given**divided**straight line , that is , intoparts that shall have the same ratios to one another which the parts of the

**divided**given straight line have . Let AB be the straight line given to be

**divided**, and ... Side 252

See N. I. F there be two pyramids of the same altitude , upon triangular bases ,

and each of them be

, and also into two equal prisms ; and if each of these pyramids be

...

See N. I. F there be two pyramids of the same altitude , upon triangular bases ,

and each of them be

**divided**into two equal pyramids fimilar to the whole pyramid, and also into two equal prisms ; and if each of these pyramids be

**divided**in the...

Side 257

THEOR VERY prism having a triangular base may be

that have triangular bases , and are equal to one another . E Let there be a prism

of which the base is the triangle ABC , and let DEF be the triangle opposite to it ...

THEOR VERY prism having a triangular base may be

**divided**into three pyramidsthat have triangular bases , and are equal to one another . E Let there be a prism

of which the base is the triangle ABC , and let DEF be the triangle opposite to it ...

Side 397

47 ECTILINEAL figures gizen in species , are

given in species . . Let the rectilineal figure ABCDE be given in fpecies ; ABCDE

may be

ABCDE ...

47 ECTILINEAL figures gizen in species , are

**divided**into triangles which aregiven in species . . Let the rectilineal figure ABCDE be given in fpecies ; ABCDE

may be

**divided**into triangles given in species . Join BE , BD , and becauseABCDE ...

### 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.