## 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 46

I. and opposite angle ADB ; but ADB is equal d to the angle ABD , because BA is

equal to AD , being sides of a square ;

angle GBC , A CB e . 6. 1 . and therefore the fide BC is equal e to f . 34 . the fide ...

I. and opposite angle ADB ; but ADB is equal d to the angle ABD , because BA is

equal to AD , being sides of a square ;

**wherefore**the angle CGB is equal to theangle GBC , A CB e . 6. 1 . and therefore the fide BC is equal e to f . 34 . the fide ...

Side 155

T. FDG equal to either of the angles BAC , EDF ; and the angle DFG equal to the

angle ACB .

at Gb , and consequently the triGb . b . 32. I. angle ABC is equiangular to the ...

T. FDG equal to either of the angles BAC , EDF ; and the angle DFG equal to the

angle ACB .

**wherefore**the remaining angle at B is А. equal to the remaining oneat Gb , and consequently the triGb . b . 32. I. angle ABC is equiangular to the ...

Side 236

... one equal to two angles in the other , each to each , and one side equal to one

side , oppofite to one of the equal angles in each , viz . HA equal to DM ; therefore

the remaining fides are equal è , each to each .

... one equal to two angles in the other , each to each , and one side equal to one

side , oppofite to one of the equal angles in each , viz . HA equal to DM ; therefore

the remaining fides are equal è , each to each .

**wherefore**AB is equal to DE . Side 269

... to EN ; therefore , again , ex aequali , as QL to LA , fo is SN to NE .

the triangles LQA , NSE , having the sides about all their angles proportionals ,

are equiangular and fimilar to one another . and therefore the pyramid of which e

.

... to EN ; therefore , again , ex aequali , as QL to LA , fo is SN to NE .

**wherefore**the triangles LQA , NSE , having the sides about all their angles proportionals ,

are equiangular and fimilar to one another . and therefore the pyramid of which e

.

Side 316

Propositions are shorter than those Euclid gives of easier Propositions , either in

the preceding , or following Books .

explicit . and the 22. and 23. Propofitions are , as they ought to be , extended to ...

Propositions are shorter than those Euclid gives of easier Propositions , either in

the preceding , or following Books .

**wherefore**it was proper to make them moreexplicit . and the 22. and 23. Propofitions are , as they ought to be , extended to ...

### 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.