## 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 210

Let there be a pyramid of which the base is the triangle ABC, and the

the pyramid ABCD may be divided into two equal and similar triangular pyramids,

which are similar to the whole; and into two equal prisms which together are ...

Let there be a pyramid of which the base is the triangle ABC, and the

**vertex**D :the pyramid ABCD may be divided into two equal and similar triangular pyramids,

which are similar to the whole; and into two equal prisms which together are ...

Side 215

the pyramid of which the base is ABD, and

which the base is EBD and

pyramid, and D as its

ECF ...

the pyramid of which the base is ABD, and

**vertex**C, is equal to the pyramid ofwhich the base is EBD and

**vertex**C. But EBC may be taken as the base of thispyramid, and D as its

**vertex**. It is therefore equal (XII. 5.) to the pyramid of whichECF ...

Side 219

this prism is triple of the pyramid upon the same base, of which the

same with the

AEBFCGDH, having the same

which the ...

this prism is triple of the pyramid upon the same base, of which the

**vertex**is thesame with the

**vertex**of the cone; therefore the pyramid upon the baseAEBFCGDH, having the same

**vertex**with the cone, is greater than the cone, ofwhich the ...

Side 221

Upon each of these triangles form a pyramid having the same

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 ...

Upon each of these triangles form a pyramid having the same

**vertex**with thecone; 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 230

... straight lines be drawn to the centre A, there will be formed a polyhedron

between the arcs BX, KX, composed of pyramids, the bases of which are the

quadrilaterals KBOS, SOPT, TPRY, and the triangle YRX, and of which the

common

... straight lines be drawn to the centre A, there will be formed a polyhedron

between the arcs BX, KX, composed of pyramids, the bases of which are the

quadrilaterals KBOS, SOPT, TPRY, and the triangle YRX, and of which the

common

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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...