## 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 5

Side 44

Let A and BC be two straight lines ; and let BC be divided into any parts in the

points D , E ; the

also to ...

Let A and BC be two straight lines ; and let BC be divided into any parts in the

points D , E ; the

**rectangle contained**by the straight lines A , BC is equal to the**rectangle contained**by A , BD ; B Di E.C and to that contained by A , DE ; andalso to ...

Side 45

is the

which AD is equal to AB ; and CE is contained by AB , BC , for BE is equal to AB .

therefore the

...

is the

**rectangle contained**by BA , AC ; for it is contained by Book II . DA , AC , ofwhich AD is equal to AB ; and CE is contained by AB , BC , for BE is equal to AB .

therefore the

**rectangle contained**by AB , AC together with the rectangle AB , BC...

Side 164

IF F four straight lines be proportionals , the

is equal to the

by the extremes be equal to the

IF F four straight lines be proportionals , the

**rectangle contained**by the extremesis equal to the

**rectangle contained**by the means , and if the**rectangle contained**by the extremes be equal to the

**rectangle contained**by the means , the four ... Side 165

F three straight lines be proportionals , the

equal to the square of the mean : and if the

be equal to the square of the mean , the three straight lines are proportionals .

F three straight lines be proportionals , the

**rectangle contained**by the extremes isequal to the square of the mean : and if the

**rectangle contained**by the extremesbe equal to the square of the mean , the three straight lines are proportionals .

Side 35

Wherefore by 16. 6. the proposition is manifest . PROP . XXXI . FIG . .25 . IN Na

spherical triangle , the re & angle contained by the fines of the two fides , is to the

square of the radius , as the

Wherefore by 16. 6. the proposition is manifest . PROP . XXXI . FIG . .25 . IN Na

spherical triangle , the re & angle contained by the fines of the two fides , is to the

square of the radius , as the

**rectangle contained**by the fine of the arch which is ...### Hva folk mener - Skriv en omtale

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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.