## 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 46

For, as was seen in the preceding corollary, the squares of BC, CA are equal to

the squares of EF, FD; from which, if the unequal squares of BC, EF be taken, the

remaining

For, as was seen in the preceding corollary, the squares of BC, CA are equal to

the squares of EF, FD; from which, if the unequal squares of BC, EF be taken, the

remaining

**square of AC**is less than the remaining square of DF, and therefore ... Side 53

BC, together with the

construct the figure as in the preceding propositions. Then, because (I. 43. the

complements AG, GE are equal, add to each of them CK; the whole AK is ...

BC, together with the

**square of A.C.**Upon AB describe (I. 46.) the square AE, andconstruct the figure as in the preceding propositions. Then, because (I. 43. the

complements AG, GE are equal, add to each of them CK; the whole AK is ...

Side 55

In like manner, the square of EF is equal to twice the square of GF or CD. Now, (I.

47.) the squares of AD and DF, or of AD and DB, are equal to the square of AF;

and the squares of AE, EF, that is, twice the

...

In like manner, the square of EF is equal to twice the square of GF or CD. Now, (I.

47.) the squares of AD and DF, or of AD and DB, are equal to the square of AF;

and the squares of AE, EF, that is, twice the

**square of AC**and twice the square of...

Side 59

be any triangle, having the angle B acute; and let AD be perpendicular to BC,

one of the sides containing that angle: the

of CB, BA, by twice the rectangle CB.B.D. The squares of CB, BD are equal (II.7.)

...

be any triangle, having the angle B acute; and let AD be perpendicular to BC,

one of the sides containing that angle: the

**square of AC**is less than the squaresof CB, BA, by twice the rectangle CB.B.D. The squares of CB, BD are equal (II.7.)

...

Side 285

Let A, B be the given points, and let C be another point such that AC, BC being

drawn, the difference between the

square of BC a given ratio of inequality: the locus of C is a given circle.

Let A, B be the given points, and let C be another point such that AC, BC being

drawn, the difference between the

**square of AC**and a given space, has to thesquare of BC a given ratio of inequality: the locus of C is a given circle.

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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...