## The Elements of Euclid |

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Side 26

Let the straight line EF, which falls upon the two straight lines AB, CD make the

alternate angles AEF, EFD equal to one another; AB is parallel to CD. For, if it be

not parallel, AB and CD being produced shall

Let the straight line EF, which falls upon the two straight lines AB, CD make the

alternate angles AEF, EFD equal to one another; AB is parallel to CD. For, if it be

not parallel, AB and CD being produced shall

**meet**either towards B, D, ... Side 36

Ax.) if produced far enough: therefore HB, FE shall

the points LM : then HLKF is a parallelogram, of which the diameter is HK, and

AG, ...

Ax.) if produced far enough: therefore HB, FE shall

**meet**, if produced; let them**meet**in K, and through K, draw KL parallel to EA or FH, and produce HA, GB tothe points LM : then HLKF is a parallelogram, of which the diameter is HK, and

AG, ...

Side 86

... the rectangle AB, BC is equal to the square of BD; and because from the point

E B without the circle ACD two straight lines BCA, BD are drawn to the

circumference, one of which cuts, and the other

rectangle AB, ...

... the rectangle AB, BC is equal to the square of BD; and because from the point

E B without the circle ACD two straight lines BCA, BD are drawn to the

circumference, one of which cuts, and the other

**meets**the circle, and that therectangle AB, ...

Side 89

the angles BCD, CDE by the straight lines CF, DF, and from the point F, in which

they

and CF common to the triangles BCF, DCF, the two sides BC, CF, are equal to ...

the angles BCD, CDE by the straight lines CF, DF, and from the point F, in which

they

**meet**, draw the straight lines FB, FA, FE; therefore, since BC is equal to CD,and CF common to the triangles BCF, DCF, the two sides BC, CF, are equal to ...

Side 160

with every straight line meeting it in that plane; but BF, which is in that plane,

points B, D, and draw the straight line B, D, to which draw DE at right angles, in

the ...

with every straight line meeting it in that plane; but BF, which is in that plane,

**meets**it: there- A - fore the angle ABF is a right ... Let them**meet**the plane in thepoints B, D, and draw the straight line B, D, to which draw DE at right angles, in

the ...

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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1834 |

The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Robert Simson Ingen forhåndsvisning tilgjengelig - 2017 |

The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Robert Simson Ingen forhåndsvisning tilgjengelig - 2017 |

### Vanlige uttrykk og setninger

altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given point given ratio given straight line gles gnomon join less Let ABC meet multiple parallel parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third three plane angles triangle ABC triplicate ratio vertex wherefore

### Populære avsnitt

Side 45 - Ir a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Side 41 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.

Side 54 - Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle.

Side 18 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC.

Side 10 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line: it is required to draw from the point A a straight line equal to BC.

Side 8 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 256 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.

Side 129 - 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 23 - At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...

Side 20 - ANY two angles of a triangle are together less than two right angles.