## 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 47

A RecTANGLE is said to be

any of the right angles. T 2. In every parallelogram, the figure which is composed

of either of the parallelograms about a diagonal, and of the two complements, ...

A RecTANGLE is said to be

**contained**by the two straight lines which are aboutany of the right angles. T 2. In every parallelogram, the figure which is composed

of either of the parallelograms about a diagonal, and of the two complements, ...

Side 48

into any parts in the points D, E: the rectangle

the rectangles

11.) BF at right angles to BC, and (I. 3.) make BG equal to A : through G draw (I.

into any parts in the points D, E: the rectangle

**contained**by A and BC is equal tothe rectangles

**contained**by A and BD, A and DE, and A and EC. From B draw (I.11.) BF at right angles to BC, and (I. 3.) make BG equal to A : through G draw (I.

Side 174

The inclination of two planes which meet one another, is the angle

two straight lines drawn from any point of their common section at right angles to

it, one upon each plane.* 3. If that angle be a right angle, the planes are ...

The inclination of two planes which meet one another, is the angle

**contained**bytwo straight lines drawn from any point of their common section at right angles to

it, one upon each plane.* 3. If that angle be a right angle, the planes are ...

Side 188

It is required to make a solid angle

each to each. From the lines

HK, all equal to one another; and join AC, DF, GK: then (XI. 22.) a triangle may be

...

It is required to make a solid angle

**contained**by plane angles equal to B, E, H,each to each. From the lines

**containing**the angles, cut off BA, BC, ED, EF, HG,HK, all equal to one another; and join AC, DF, GK: then (XI. 22.) a triangle may be

...

Side 369

This definition readily arises from the supposition, that when four magnitudes are

proportional, the first term is

are ...

This definition readily arises from the supposition, that when four magnitudes are

proportional, the first term is

**contained**in the second as often as the third is**contained**in the fourth, which, with the exception of the order in which the termsare ...

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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...