## 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 3

Quadrilateral figures, by four straight lines: 16. Polygons, by more than four

straight lines.” 17. Of three-sided figures,f an equilateral triangle is that which has

its three

19.

Quadrilateral figures, by four straight lines: 16. Polygons, by more than four

straight lines.” 17. Of three-sided figures,f an equilateral triangle is that which has

its three

**sides**equal : 18. An isosceles triangle is that which has two**sides**equal :19.

Side 10

If two triangles have two

each ;t and have also the angles contained by those

1.) they have likewise their bases, or third

If two triangles have two

**sides**of the one equal to two**sides**of the other, each toeach ;t and have also the angles contained by those

**sides**equal to one another: (1.) they have likewise their bases, or third

**sides**,f equal; (2) the two triangles are ... Side 15

The case in which the vertex of one triangle is upon a

demonstration. Therefore on the same base, and on the same

cannot be two triangles that have their

extremity ...

The case in which the vertex of one triangle is upon a

**side**of the other, needs nodemonstration. Therefore on the same base, and on the same

**side**of it, therecannot be two triangles that have their

**sides**which are terminated in oneextremity ...

Side 23

the angle B would be less than , the angle C, but it is not; therefore the

not * * less than AB; and it has been shown that it is not equal ^ to AB: ... Let ABC

be a triangle; any two

the angle B would be less than , the angle C, but it is not; therefore the

**side**AC isnot * * less than AB; and it has been shown that it is not equal ^ to AB: ... Let ABC

be a triangle; any two

**sides**of it are together greater than the third**side**. Side 28

If the proposition be taken in this order, the enunciation may be as follows:– If two

triangles be equiangular to one another, and if a

other, which are opposite to equal angles, be equal : then (1.) the remaining ...

If the proposition be taken in this order, the enunciation may be as follows:– If two

triangles be equiangular to one another, and if a

**side**of the one and a**side**of theother, which are opposite to equal angles, be equal : then (1.) the remaining ...

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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...