## 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 5

The

the chord, and made to depend on it. In like manner the definition of a segment of

a circle is placed before that of its species, the semicircle. The following, which ...

The

**diameter**being merely a particular chord, its definition is placed after that ofthe chord, and made to depend on it. In like manner the definition of a segment of

a circle is placed before that of its species, the semicircle. The following, which ...

Side 72

Let A BCD be a circle, of which the

be nearer to the centre than FG ; A D is greater than BC, and BC than FG. 1. From

the centre draw (I. 12.) EH, EK perpendiculars to BC, FG, and join EB, EC, EF.

Let A BCD be a circle, of which the

**diameter**is AD, and the centre E : and let BCbe nearer to the centre than FG ; A D is greater than BC, and BC than FG. 1. From

the centre draw (I. 12.) EH, EK perpendiculars to BC, FG, and join EB, EC, EF.

Side 229

Draw the

circle BCDE, meeting the surface of the sphere in X. Let planes pass through AX

and each of the straight lines BD, KN : these, from what has been said, will ...

Draw the

**diameter**KAN, and through A draw AX perpendicular to the plane of thecircle BCDE, meeting the surface of the sphere in X. Let planes pass through AX

and each of the straight lines BD, KN : these, from what has been said, will ...

Side 232

... this other polyhedron the triplicate ratio of that which the

sphere has to the

same number of pyramids, and in the same order; the pyramids will be similar, ...

... this other polyhedron the triplicate ratio of that which the

**diameter**of the greatersphere has to the

**diameter**of the less. For, if these two solids be divided into thesame number of pyramids, and in the same order; the pyramids will be similar, ...

Side 258

If through any point in the

drawn making equal angles with the

four points, the straight lines joining the opposite points intersect one another in

the ...

If through any point in the

**diameter**of a circle produced, two straight lines bedrawn making equal angles with the

**diameter**, and cutting the circumference infour points, the straight lines joining the opposite points intersect one another in

the ...

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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...