## 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 285

drawn meeting one another, such that the square of one of them is to the

difference between the square of the other and a given space, in a

inequality, the locus of their point of intersection is the circumference of a given

circle.

drawn meeting one another, such that the square of one of them is to the

difference between the square of the other and a given space, in a

**given ratio**ofinequality, the locus of their point of intersection is the circumference of a given

circle.

Side 286

Then CD” o —AD* + S: CE*:: m”: n”: that is, the difference between the square of

CD and the given space AD”—S, has to the square of CE a

therefore, if m, n be unequal, the...locus of C is a given circle;—if they be equal, it

is a ...

Then CD” o —AD* + S: CE*:: m”: n”: that is, the difference between the square of

CD and the given space AD”—S, has to the square of CE a

**given ratio**: andtherefore, if m, n be unequal, the...locus of C is a given circle;—if they be equal, it

is a ...

Side 325

is required to divide ABC into parts in a

Divide AB in E, so that AE, EB may be in the

D; take BG a mean proportional between BF and BC, and draw GH parallel to ...

is required to divide ABC into parts in a

**given ratio**, by a straight line parallel to D.Divide AB in E, so that AE, EB may be in the

**given ratio**, and draw EF parallel toD; take BG a mean proportional between BF and BC, and draw GH parallel to ...

Side 369

the first and second terms be nearly in the

third and fourth. The illustration here

proposition I., page 127. Elrington, Leslie, and others, instead of Euclid's

definition, have ...

the first and second terms be nearly in the

**ratio**of equality, so will those of thethird and fourth. The illustration here

**given**is the same in substance asproposition I., page 127. Elrington, Leslie, and others, instead of Euclid's

definition, have ...

Side 385

In a given rhombus to inscribe a rectangle having its sides in a

through the vertex and the extremities of the base of a triangle, two circles be

described intersecting one another in the base or its continuation, their diameters

...

In a given rhombus to inscribe a rectangle having its sides in a

**given ratio**. 61. If,through the vertex and the extremities of the base of a triangle, two circles be

described intersecting one another in the base or its continuation, their diameters

...

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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...