## 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 40

If through any point in either

parallel to the sides; of the four parallelograms thus formed, those through which

the

If through any point in either

**diagonal**of a parallelogram, straight lines be drawnparallel to the sides; of the four parallelograms thus formed, those through which

the

**diagonal**does not pass, and which are called the complements of the other ... Side 162

If two similar parallelograms have a common angle, and be similarly situated ;

they are about the same

similarly situated, and have the angle DAB common : they are about the same ...

If two similar parallelograms have a common angle, and be similarly situated ;

they are about the same

**diagonal**. Let the parallelograms BD, EG be similar andsimilarly situated, and have the angle DAB common : they are about the same ...

Side 271

which is evidently the

FG equal to FE, and join GE. Then it would be shown as before, that BG is less

than BE; and therefore BE, the difference between the side and

which is evidently the

**diagonal**of a square of which FE or EB is the side, cut offFG equal to FE, and join GE. Then it would be shown as before, that BG is less

than BE; and therefore BE, the difference between the side and

**diagonal**of the ... Side 273

To find DA, take the

triangle, and for its hypotenuse take the side of a square equal to the given sum

of the squares of AB, AC : then the

To find DA, take the

**diagonal**of the square of BD as one leg of a right-angledtriangle, and for its hypotenuse take the side of a square equal to the given sum

of the squares of AB, AC : then the

**diagonal**of the square described on half the ... Side 327

On one of the diagonals describe a segment of a circle containing an angle equal

to the given angle at either extremity of the other; from the middle point of this

...

On one of the diagonals describe a segment of a circle containing an angle equal

to the given angle at either extremity of the other; from the middle point of this

**diagonal**as centre, with half the other**diagonal**as radius, describe an arc cutting...

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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...