## 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 49

If a straight line be divided into any two parts, the

whole and one of the parts, is equal to the square of that part, together with the

parts ...

If a straight line be divided into any two parts, the

**rectangle**contained by thewhole and one of the parts, is equal to the square of that part, together with the

**rectangle**contained by the two parts. Let the straight line AB be divided into twoparts ...

Side 51

But the gnomon CMG, and LG make up the figure CEFB, which is the square of

CB: also AH is the

to DH, and LG is the square of CD. Therefore the

...

But the gnomon CMG, and LG make up the figure CEFB, which is the square of

CB: also AH is the

**rectangle**under AD and DB, because DB is equal (II. 4. cor. 1.)to DH, and LG is the square of CD. Therefore the

**rectangle**AD.DB, together with...

Side 84

EC, BE, ED, being all equal, the

B.E.E.D. But let one of them B D pass through the centre, and cut the other AB

which does not pass through the centre, at right angles, in the point E. Then if BD

be ...

EC, BE, ED, being all equal, the

**rectangle**AE.EC is equal to the**rectangle**B.E.E.D. But let one of them B D pass through the centre, and cut the other AB

which does not pass through the centre, at right angles, in the point E. Then if BD

be ...

Side 85

away the common square of EF, and the remaining

the remaining

through the centre. Take the centre F, and through E draw the diameter GEFH.

Then ...

away the common square of EF, and the remaining

**rectangle**AE.EC is equal tothe remaining

**rectangle**BE.E.D.” Lastly, let neither of the lines AC, BD passthrough the centre. Take the centre F, and through E draw the diameter GEFH.

Then ...

Side 152

Now the parallelogram BG is contained by AB and F, because AG is equal to F;

and DH is contained by CD and E, because CH is equal to E. Therefore the

to 9 ...

Now the parallelogram BG is contained by AB and F, because AG is equal to F;

and DH is contained by CD and E, because CH is equal to E. Therefore the

**rectangle**AB.F is equal to the**rectangle**CD.E. h 2. If the**rectangle**AB.F be equalto 9 ...

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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...