## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With Notes and Illus., and an Appendix in Five Books |

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Side 219

are less than the excess of the cylinder above the triple of the

those upon the segments of the circle AE, EB, BF, &c. Therefore the rest of the

cylinder, that is, the prism of which the base is the polygon AEBFCGDH, and of ...

are less than the excess of the cylinder above the triple of the

**cone**. Let them bethose upon the segments of the circle AE, EB, BF, &c. Therefore the rest of the

cylinder, that is, the prism of which the base is the polygon AEBFCGDH, and of ...

Side 220

Therefore the rest of the

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

greater than the third part of the cylinder. But this pyramid is the third part of the

prism ...

Therefore the rest of the

**cone**, that is, the pyramid, of which the base is thepolygon AEBFCGDH, and of which the vertex is the same with that of the

**cone**, isgreater than the third part of the cylinder. But this pyramid is the third part of the

prism ...

Side 221

Upon each of these triangles form a pyramid having the same vertex with the

in which it is: and thus dividing each of these arcs into two equal parts, and from

the ...

Upon each of these triangles form a pyramid having the same vertex with the

**cone**; each of these pyramids is greater than the half of the segment of the**cone**in which it is: and thus dividing each of these arcs into two equal parts, and from

the ...

Side 223

But, by the hypothesis, the

AC has to EG ; therefore, as the

DQATBYCWL, to the pyramid HSEOFPGRN. But the same

the ...

But, by the hypothesis, the

**cone**ABCDL has to X, the triplicate ratio of that whichAC has to EG ; therefore, as the

**cone**ABCDL is to X, so is the pyramidDQATBYCWL, to the pyramid HSEOFPGRN. But the same

**cone**is greater thanthe ...

Side 225

PROP. XIV. THEOR.

as their altitudes. ... Therefore also GH is to KL, as the

, and the cylinder EB to the cylinder FD. Wherefore

PROP. XIV. THEOR.

**CoNEs**and cylinders upon equal bases are to one anotheras their altitudes. ... Therefore also GH is to KL, as the

**cone**ABG to the**cone**CDK, and the cylinder EB to the cylinder FD. Wherefore

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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... Euclid Ingen forhåndsvisning tilgjengelig - 2016 |

### Vanlige uttrykk og setninger

ABCD altitude angle ABC angle BAC angle equal BC is equal bisected centre chord circle ABC circumference cone const contained cylinder describe a circle diagonal diameter divided draw equal angles equal to AC equiangular equilateral Euclid exterior angle fore fourth given circle given point given ratio given straight line greater half Hence hypotenuse inscribed join less Let ABC magnitudes manner multiple opposite parallel parallelepiped parallelogram perpendicular polygon polyhedron prism PROB produced PROP proportional proposition pyramid radius rectangle rectilineal figure right angles Schol segments semicircle sides similar similar triangles solid angles square of AC straight lines drawn tangent THEOR third triangle ABC triplicate ratio vertex vertical angle wherefore

### Populære avsnitt

Side 94 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.

Side 53 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.

Side 143 - 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 4 - A rhombus is that which has all its sides equal, but its angles are not right angles.

Side 57 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.

Side 138 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...

Side 43 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.

Side 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 40 - 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.

Side 36 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...