## The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The first six books, together with the eleventh and twelfth |

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Resultat 1-5 av 5

Side 328

Book VI . tangle AH is equal to the given square upon the straight line C.

wherefore the rectangle AH equal to the given square upon C , has been applied

to the

2.

Book VI . tangle AH is equal to the given square upon the straight line C.

wherefore the rectangle AH equal to the given square upon C , has been applied

to the

**given straight line**AB , deficient by the square GK . Which was to be done .2.

Side 381

IF F a straight line be drawn to a given point in a

given angle with it . that straight line is given in position . Let AB be a straight line

given in position , and C a given point in it , the straight line drawn to C which ...

IF F a straight line be drawn to a given point in a

**given straight line**, and makes agiven angle with it . that straight line is given in position . Let AB be a straight line

given in position , and C a given point in it , the straight line drawn to C which ...

Side 434

with LD . let CBG be the diameter , and construct the figure . therefore because

the G F H figure EF given in fpecies is described upon the

EF is given B Ć . 56. Dat in magnitude c . and the and the gnomon ELH is A D d .

with LD . let CBG be the diameter , and construct the figure . therefore because

the G F H figure EF given in fpecies is described upon the

**given straight line**EB ,EF is given B Ć . 56. Dat in magnitude c . and the and the gnomon ELH is A D d .

Side 464

10 find three straight lines such , that the ratio of the first to the second is given ;

and if a

the third is given ; also the rectangle con . tained by the first and third is given .

10 find three straight lines such , that the ratio of the first to the second is given ;

and if a

**given straight line**be taken from the second , the ratio of the remainder tothe third is given ; also the rectangle con . tained by the first and third is given .

Side 465

1 by making as KM to KL , so GD to HB . to the

rectangle equal to LK , KO exceeding by a square , e . 29. 6 . and let BA , AH be

its fides . then is AB the first of the straight lines required to be found . and by ...

1 by making as KM to KL , so GD to HB . to the

**given straight line**BH apply e arectangle equal to LK , KO exceeding by a square , e . 29. 6 . and let BA , AH be

its fides . then is AB the first of the straight lines required to be found . and by ...

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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.