## 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 9

Side 51

I. to CE , and thro ' F draw FG parallel to AB ; and join AF . then

equal to CE , the angle EAC is equal o to the angle C. 5. I. AEC ; and

angle ACE is a right angle , the two others AEC , EAC together make one right ...

I. to CE , and thro ' F draw FG parallel to AB ; and join AF . then

**because**AC isequal to CE , the angle EAC is equal o to the angle C. 5. I. AEC ; and

**because**theangle ACE is a right angle , the two others AEC , EAC together make one right ...

Side 269

5 . are about equal angles AKQ , EMS ,

each of them , the fame part of four right angles at the centers K , M ; therefore the

triangle AKQ is similar to the triangle EMS . c . 6.6 . and

shewn ...

5 . are about equal angles AKQ , EMS ,

**because**these angles are , Book XII .each of them , the fame part of four right angles at the centers K , M ; therefore the

triangle AKQ is similar to the triangle EMS . c . 6.6 . and

**because**it has beenshewn ...

Side 285

therefore c also the sphere GHK is greater than the solid polyhe- Book XII . dron

in the sphere DEF . but it is also less ,

which is impossible . therefore the sphere ABC has not to any sphere less than ...

therefore c also the sphere GHK is greater than the solid polyhe- Book XII . dron

in the sphere DEF . but it is also less ,

**because**it is contained c . 14. So within it ,which is impossible . therefore the sphere ABC has not to any sphere less than ...

Side 308

Book . it seems to have been taken out of the Elements by Theon ,

appeared evident enough to him , and others who substitute the confused and

indistinct idea the vulgar have of proportionals , in place of that accurate idea

which is ...

Book . it seems to have been taken out of the Elements by Theon ,

**because**itappeared evident enough to him , and others who substitute the confused and

indistinct idea the vulgar have of proportionals , in place of that accurate idea

which is ...

Side 316

Proposition ,

other , PROP . XIX . B. V. A Corollary is added to this , which is as frequently used

as the Proposition itself . the Corollary which is subjoined to it in the Greek ...

Proposition ,

**because**it depends upon the fame insufficient foundation with theother , PROP . XIX . B. V. A Corollary is added to this , which is as frequently used

as the Proposition itself . the Corollary which is subjoined to it in the Greek ...

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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.