## 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 156

because the

22.) EB : BC : : LG : GH; that is, the sides about the equal angles EBC, LG H are

proportionals; therefore (VI. 6.) the triangles EBC, LGH are equiangular, and (VI.4

.

because the

**polygons**are similar, A B : BC : : FG : GH ; therefore, ex æquo, (W.22.) EB : BC : : LG : GH; that is, the sides about the equal angles EBC, LG H are

proportionals; therefore (VI. 6.) the triangles EBC, LGH are equiangular, and (VI.4

.

Side 208

SIMILAR

diameters. ... ABCDE, FGH KL ; and let BM, GN be the diameters of the circles:

the square of BM is to the square of GN as the

SIMILAR

**polygons**inscribed in circles, are to one another as the squares of thediameters. ... ABCDE, FGH KL ; and let BM, GN be the diameters of the circles:

the square of BM is to the square of GN as the

**polygon**AC is to the**polygon**FH. Side 221

I.) the square of AC is to the square of EG, as the

L, to the pyramid of which the base is the other

therefore, ...

I.) the square of AC is to the square of EG, as the

**polygon**ATBYCVDQ to the**polygon**EOFPGRHS; and (XII. 2.) ... base is the first of these**polygons**, and vertexL, to the pyramid of which the base is the other

**polygon**, and its vertex N :therefore, ...

Side 264

D to be the area of a circle EF, of which the radius AE is greater than AB, and let

GHK be a regular

not meet the circumference of EF. Then, by dividing this

...

D to be the area of a circle EF, of which the radius AE is greater than AB, and let

GHK be a regular

**polygon**described about the circle BC, such that its sides donot meet the circumference of EF. Then, by dividing this

**polygon**into triangles by...

Side 290

OF isoperimetrical

one which is equilateral. . For, if possible, let ABCDE be the maximum

and yet the side AE greater than AB. On BE describe the isosceles triangle BFE ...

OF isoperimetrical

**polygons**, having a given number of sides, the maximum is theone which is equilateral. . For, if possible, let ABCDE be the maximum

**polygon**,and yet the side AE greater than AB. On BE describe the isosceles triangle BFE ...

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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...