## 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

But , indeed , this Propofition , which makes the roth Definition of the IIth Book , is

not truc universally , except in the

figures is concained by no more than three plane angles ; for in other

...

But , indeed , this Propofition , which makes the roth Definition of the IIth Book , is

not truc universally , except in the

**case**in which each of the folid angles of thefigures is concained by no more than three plane angles ; for in other

**cases**, two...

Side 157

Next , Let each of the angles at C , F be not less than a right angle . the triangle

ABC is also in this

being A made , it may be proved in like manner that BC is equal to BG , and the ...

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 . The same constructionbeing A made , it may be proved in like manner that BC is equal to BG , and the ...

Side 292

B. I. There are two

but is as neceffary as the other , and ... text appears plainly from this , that the

second part of Prop 5. which is necessary to the Demonftration of this

B. I. There are two

**cases**of this Proposition , one of which is not in the Greek text ,but is as neceffary as the other , and ... text appears plainly from this , that the

second part of Prop 5. which is necessary to the Demonftration of this

**case**, can ... Side 302

There are two

angles are in a fegment not greater than a ... fimple Demonstration is given than

that which is in Commandine , as being derived only from the first

the ...

There are two

**cases**of this Propofition , the second of which , viz . when theangles are in a fegment not greater than a ... fimple Demonstration is given than

that which is in Commandine , as being derived only from the first

**case**, withoutthe ...

Side 308

B. V. There are two

is demonstrated in the Greek . and it ... Proposition for the same reason . the

demonstration of the other

5.

B. V. There are two

**cases**of this Proposition , of which only the first and simplestis demonstrated in the Greek . and it ... Proposition for the same reason . the

demonstration of the other

**case**is now added , becaufe both of them , as also the5.

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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.