## 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 263

Book XII . fore the rest of the cylinder , that is the prism of which the base is the

polygon AEBFCGDH , and of which the altitude is the same with that of the

cylinder , is greater than the triple of the

pyramid ...

Book XII . fore the rest of the cylinder , that is the prism of which the base is the

polygon AEBFCGDH , and of which the altitude is the same with that of the

cylinder , is greater than the triple of the

**cone**. but this prism is triple d of thepyramid ...

Side 264

... and upon the triangles erecting pyramids hav . bapo ing their vertices the same

with that of the

the

...

... and upon the triangles erecting pyramids hav . bapo ing their vertices the same

with that of the

**cone**, and so on , there must at length remain some fegments ofthe

**cone**which together shall be less than the excess of the**cone**above the third...

Side 267

to any not to the circle EFGH , as the

than the

EFGH is not to the circle ABCD , as the

to any not to the circle EFGH , as the

**cone**AL to any solid which is less Book XII .than the

**cone**EN . In the same manner it may be demonstrated that the circleEFGH is not to the circle ABCD , as the

**cone**EN solid less than the**cone**AL . Side 269

... the fame vertices with the

the first

triplicate ratio of that which the side AK has to the side EM ; that is , which AC has

to EG ...

... the fame vertices with the

**cones**, it may be demonstrated that each pyramid inthe first

**cone**has to each in the other , taking them in the same order , thetriplicate ratio of that which the side AK has to the side EM ; that is , which AC has

to EG ...

Side 270

Book XII . ratio of that which AC has to EG ; therefore as the

base is the circle ABCD , and vertex L , is to the folid X , so is the pyramid the

base of which is the polygon DQATBYCV , and vertex L to the pyramid the base

of ...

Book XII . ratio of that which AC has to EG ; therefore as the

**cone**of which thebase is the circle ABCD , and vertex L , is to the folid X , so is the pyramid the

base of which is the polygon DQATBYCV , and vertex L to the pyramid the base

of ...

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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.