## 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 25

DE , EF , each to each ; and the

and the other

are ...

**equal**t ) DE , and BC to EF , the two sides GB , BC are**equal**to Book I. the twoDE , EF , each to each ; and the

**angle**... I. the triangle GBC to the triangle DEF ,and the other

**angles**to the othe**angles**, each to each , to which the**equal**fidesare ...

Side 154

IF ( F the fides of two triangles , about each of their angles , be proportionals , the

triangles shall be equiangular , and have their

homologous fides . a . 23. I. Let the triangles ABC , DEF have their fides

proportionals ...

IF ( F the fides of two triangles , about each of their angles , be proportionals , the

triangles shall be equiangular , and have their

**equal angles**opposite to thehomologous fides . a . 23. I. Let the triangles ABC , DEF have their fides

proportionals ...

Side 213

I F each of two solid

one another , each to each ; the ... Let there be two solid

; and let the

...

I F each of two solid

**angles**be contained by three See N. plane**angles equal**toone another , each to each ; the ... Let there be two solid

**angles**at the points A , B; and let the

**angle**at A be contained by the three plane**angles**CAD , CAE , EAD...

Side 219

II . to DG , and from the point K erect « KH at right

BAL ; and make KH

contained by the three plane

at ...

II . to DG , and from the point K erect « KH at right

**angles**to the Book XI . planeBAL ; and make KH

**equal**to GF , and join AH . then the solid**angle**at A which iscontained by the three plane

**angles**BAL , BAH , HAL is**equal**to the solid**angle**at ...

Side 236

Def.11 .

in that plane ; therefore ABH is a right

Def.11 .

**angles**d with every straight line meeting it in that plane . but BH meets itin that plane ; therefore ABH is a right

**angle**. for the same reason , DEM is a right**angle**, and is therefore**equal**to the**angle**ABH . and the**angle**HAB is**equal**to ...### Hva folk mener - Skriv en omtale

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### 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.