## 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 161

Therefore the sides of the parallelograms BD, EG about the equal angles are

proportionals: the parallelograms are, therefore, (VI. def. 1.)

another. In the same manner, it would be shown that the parallelogram BD is

Therefore the sides of the parallelograms BD, EG about the equal angles are

proportionals: the parallelograms are, therefore, (VI. def. 1.)

**similar**to oneanother. In the same manner, it would be shown that the parallelogram BD is

**similar**to HK. Side 207

If, therefore, &c. k | h F PROP. I. THEOR.

are to. * This, which is the first proposition of the tenth book, is necessary for

some of the propositions of this book. . * This proposition is merely a lemma to the

17th ...

If, therefore, &c. k | h F PROP. I. THEOR.

**SIMILAR**polygons inscribed in circles,are to. * This, which is the first proposition of the tenth book, is necessary for

some of the propositions of this book. . * This proposition is merely a lemma to the

17th ...

Side 210

A TRIANGULAR pyramid may be divided into two equal and

pyramids, which are

which together are greater than half of the whole pyramid. Let there be a pyramid

of ...

A TRIANGULAR pyramid may be divided into two equal and

**similar**triangularpyramids, which are

**similar**to the whole pyramid; and into two equal prisms,which together are greater than half of the whole pyramid. Let there be a pyramid

of ...

Side 216

the vertices, be

the triplicate ratio of that which the side BC has to the homologous side EF.

Complete the parallelograms BM, BN, BK, and the parallelepiped BGML

contained by ...

the vertices, be

**similar**, and similarly situated; the pyramid ABCG has to DEFH,the triplicate ratio of that which the side BC has to the homologous side EF.

Complete the parallelograms BM, BN, BK, and the parallelepiped BGML

contained by ...

Side 346

TRIANGULAR pyramids are

faces in the other, each to each, and their inclinations equal. Let ABC, abc be the

bases, and D, d the vertices of two triangular pyramids, in which ABC, DBC are ...

TRIANGULAR pyramids are

**similar**, if two faces in one of them be**similar**to twofaces in the other, each to each, and their inclinations equal. Let ABC, abc be the

bases, and D, d the vertices of two triangular pyramids, in which ABC, DBC are ...

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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...