## 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 7

Side 292

Because by

together equal to four right angles , and the two angles BAD , ADC are toA gether

equal to the two angles BCD , ABC . wherefore BAD , ADC are the half of all the ...

Because by

**Prop**. 32. B. 1. all the angles of the quadrilateral figure ABCD aretogether equal to four right angles , and the two angles BAD , ADC are toA gether

equal to the two angles BCD , ABC . wherefore BAD , ADC are the half of all the ...

Side 308

and simplest is demonstrated in the Greek . and it is probable Theon thought it

was sufficient to give this one , since he was to make use of neither of them in his

...

**PROP**. VI . B. V. There are two cases of this Proposition , of which only the firstand simplest is demonstrated in the Greek . and it is probable Theon thought it

was sufficient to give this one , since he was to make use of neither of them in his

...

Side 316

... same objection holds good against the Demonstration which some give of the

1.

because it depends upon the fame insufficient foundation with the other ,

... same objection holds good against the Demonstration which some give of the

1.

**Prop**. of the 6. Book , which we have made against this of the 18. Proposition ,because it depends upon the fame insufficient foundation with the other ,

**PROP**. Side 457

14. and for a like reason

will make the thing clear ; suppose it were to be demonstrated , That if a

magnitude A together with a given magnitude has a given ratio to another

magnitude B ...

14. and for a like reason

**Prop**. 15. has been added to the Data . one examplewill make the thing clear ; suppose it were to be demonstrated , That if a

magnitude A together with a given magnitude has a given ratio to another

magnitude B ...

Side 458

immediately placed , as being of the same kind , it is now put into its proper place

. but

text , which is here

...

immediately placed , as being of the same kind , it is now put into its proper place

. but

**Prop**. 21. in the Greek is left out , as being the fame with**Prop**. 14. in thattext , which is here

**Prop**. 18 .**PROP**. XXIV . This , which is**Prop**. 13. in the Greek...

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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.