## 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

Side 153

outward , & c . Q. E. D.

equiangular

as BC to CE . f .

CE ; 8.

**is**equal to the outward**angle**EAD , and the**angle**ACF to the Book**VI**. alternate**angle**CAD ; therefore also EAD**is**equal to the**angle**CAD . Wherefore**if**theoutward , & c . Q. E. D.

**PROP**. IV .**THEOR**. T HE fides about the equal angles ofequiangular

**triangles**... 34. I.**one**of the sides of the**triangle**T'EX , BA**is**to AF ,as BC to CE . f .

**2**.**6**. but AF**is**equal to CD , therefore $ as BA to CD , fo**is**BC toCE ; 8.

Side 154

154 Book

equal ...

154 Book

**VI**.**PROP**. V.**THEOR**.**IF**( F the fides of**two triangles**, about**each**of**their**angles , be proportionals , the ...**is**equiangular to the triangle DEF , and**their**equal angles are opposite to the homologous fides , viz . the**angle**ABCequal ...

Side 155

Book VI . yok

equal to

proportionals , the triangles shall be equi .

equal which ...

Book VI . yok

**PROP**.**VI**.**THEOR**.**IF**F**two triangles have one angle**of the**one**equal to

**one angle**of the other , and the sides about the equal anglesproportionals , the triangles shall be equi .

**angular**, and fhall**have**those anglesequal which ...

Side 156

Book

proportionals ; then

than a right ...

Book

**VI**.**PROP**. VII .**THEOR**. See N.**IF**F**two triangles have one angle**of the**one**equal to**one angle**of the other , and the sides about two other anglesproportionals ; then

**if each**of the remaining angles be either less , or not lessthan a right ...

Side 331

same straight line . but there seems to

Demonstration of these cases , to which this 32. ...

which

**Prop**.**is**not general enough ; because not only two similar parallelograms that**have an angle**common to both , are about the ...**have their**diameters in thesame straight line . but there seems to

**have**been another , and that a directDemonstration of these cases , to which this 32. ...

**PROP**. XXXII . B.**VI**.**If two****triangles**which**have**two sides of the**one**, & c . Let GAF , HFC be**two triangles**which

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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.