## 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 6

Side 188

A straight line is perpendicular , or at right angles , to a

right angles with every straight line meeting ... A

, when the straight lines drawn in one of the

common ...

A straight line is perpendicular , or at right angles , to a

**plane**, when it makesright angles with every straight line meeting ... A

**plane**is perpendicular to a**plane**, when the straight lines drawn in one of the

**planes**perpendicularly to thecommon ...

Side 191

ON NE part of a straight line cannot be in a

it . If it be possible , " let AB part of the straight line ABC be in the

part BC above it and since the straight line AB is in the

...

ON NE part of a straight line cannot be in a

**plane**and See N. another part aboveit . If it be possible , " let AB part of the straight line ABC be in the

**plane**, and thepart BC above it and since the straight line AB is in the

**plane**, it can be produced...

Side 199

10 ere & a straight line at right angles to a given

from the point A at right an . D B gles to the

10 ere & a straight line at right angles to a given

**plane**, from a point given in the**plane**. 1 Let A be the point given in the**plane**; it is required to erect a straight linefrom the point A at right an . D B gles to the

**plane**. From any point B above the ... Side 204

Book XI . to their common section , are also at right angles to the other

and any straight line FG in the

CE the common section of the

the ...

Book XI . to their common section , are also at right angles to the other

**plane**d ;and any straight line FG in the

**plane**DE , which is at 4.4.Def.11 . right angles toCE the common section of the

**planes**, has been proved to be perpendicular tothe ...

Side 214

Book XI . and the angle GMN is the inclination of the

, which

and in the same manner it may be demonstrated , that the other

Book XI . and the angle GMN is the inclination of the

**plane**FBG to the**plane**FBH, which

**planes**have therefore the same inclination to e.7.Def.nn. one another .and in the same manner it may be demonstrated , that the other

**planes**in which ...### 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.