## 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 32

the straight line CD, which meets the two straight lines AB, EF, makes the

alternate angles ECD, CDB equal to one ... to the interior and remote angle ABC :

but the angle ACE was shown to be equal to the

...

the straight line CD, which meets the two straight lines AB, EF, makes the

alternate angles ECD, CDB equal to one ... to the interior and remote angle ABC :

but the angle ACE was shown to be equal to the

**angle BAC**; therefore the whole...

Side 75

THE

upon the same base, that is, upon the same part of the circumference. In the

circle ABC, let BEC be an

circumference, ...

THE

**angle**at the centre of a circle is double of the**angle**at the circumference,upon the same base, that is, upon the same part of the circumference. In the

circle ABC, let BEC be an

**angle**at the centre, and**BAC**an**angle**at thecircumference, ...

Side 81

these are together equal to two right angles; therefore BAC is a right angle, and it

is an angle in a semicircle. But (I. ax. 9.) the angle BAD is less, and BAE greater

than the right

these are together equal to two right angles; therefore BAC is a right angle, and it

is an angle in a semicircle. But (I. ax. 9.) the angle BAD is less, and BAE greater

than the right

**angle BAC**: therefore an angle in a segment greater than a ... Side 167

Let ABC, DEF be equal circles; and let BGC, EHF be angles at their centres, and

BAC, EDF, be angles at their circumferences; as the arc BC to the arc EF, so is

the angle BGC to EHF, and the

...

Let ABC, DEF be equal circles; and let BGC, EHF be angles at their centres, and

BAC, EDF, be angles at their circumferences; as the arc BC to the arc EF, so is

the angle BGC to EHF, and the

**angle BAC**to EDF; and also the sector BGC to the...

Side 355

From this it follows, that if two angles of one triangle be equal to two angles of

another, their third angles are also equal. Let now ABC be a triangle having the

ABC, ...

From this it follows, that if two angles of one triangle be equal to two angles of

another, their third angles are also equal. Let now ABC be a triangle having the

**angle BAC**a right angle, and draw the perpendicular AD. Then, in the trianglesABC, ...

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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...