## 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 13

the remaining angles are equal, each to each, to which the equal ; }; sides are

exterior angles DBF, ECF, are also equal.” PROP. vi. TheOR.f If two angles of a ...

the remaining angles are equal, each to each, to which the equal ; }; sides are

**opposite**; therefore, the angle ABF is equal to the angle ACF, and (I. 4. schol.) theexterior angles DBF, ECF, are also equal.” PROP. vi. TheOR.f If two angles of a ...

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 side of the one and a side of the

other, which are

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 the

other, which are

**opposite**to equal angles, be equal : then (1.) the remaining ... Side 142

B c le OTHERWISE. Let the triangles be ABC and A DE; and, the angles BAC,

DAE being equal, let the triangles be placed so that the sides AB, AD, which are

contiguous, ...

B c le OTHERWISE. Let the triangles be ABC and A DE; and, the angles BAC,

DAE being equal, let the triangles be placed so that the sides AB, AD, which are

**opposite**to equal angles C and E, may be in the same straight line, andcontiguous, ...

Side 195

First, let the parallelograms DG, HN, which are

common side HG. I. H Then because AHis cut by the plane AGHC K passing

through the diagonals AG, CH, of vo n the

20 ...

First, let the parallelograms DG, HN, which are

**opposite**to the base AB, have acommon side HG. I. H Then because AHis cut by the plane AGHC K passing

through the diagonals AG, CH, of vo n the

**opposite**planes ALGF, CBHD.AH is , ^20 ...

Side 298

R b = c sin B = c cos A; that is, the product of either leg and the radius is equal to

the product of the hypotenuse and the sine of the angle

the hypotenuse and the cosine of the adjacent angle. When R = 1, this becomes

...

R b = c sin B = c cos A; that is, the product of either leg and the radius is equal to

the product of the hypotenuse and the sine of the angle

**opposite**to that leg, or ofthe hypotenuse and the cosine of the adjacent angle. When R = 1, this becomes

...

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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...