## The Elements of Euclid |

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Resultat 1-5 av 10

Side 55

the

the point F: it cuts it also at right angles. Take (1.3.) E the

join EA, EB. Then, because AF is equal to FB, and FE common to the two ...

the

**centre**, bisect any straight line AB, which does not pass through the**centre**, inthe point F: it cuts it also at right angles. Take (1.3.) E the

**centre**of the circle, andjoin EA, EB. Then, because AF is equal to FB, and FE common to the two ...

Side 56

If two circles cut one another, they shall not have the same

circles ABC, CDG cut one another in the points B, C; they have not the same

line ...

If two circles cut one another, they shall not have the same

**Centre**. Let the twocircles ABC, CDG cut one another in the points B, C; they have not the same

**centre**. For, if it be possible, let E be their**centre**: join EC, and draw any straightline ...

Side 59

THEOR. lf a point be taken within a circle, from which there fall more than two

equal straight lines to the circumference, that point is the

the point D be taken within the circle ABC, from which to the circumference there

fall ...

THEOR. lf a point be taken within a circle, from which there fall more than two

equal straight lines to the circumference, that point is the

**centre**of the circle. Letthe point D be taken within the circle ABC, from which to the circumference there

fall ...

Side 62

Let the straight lines AB, CD, in the circle ABDC, be equal to one another: they

are equally distant from the

from it draw EF, EG perpendiculars to AB, CD; then, because the straight line EF,

...

Let the straight lines AB, CD, in the circle ABDC, be equal to one another: they

are equally distant from the

**centre**. Take E the**centre**of the circle ABDC, andfrom it draw EF, EG perpendiculars to AB, CD; then, because the straight line EF,

...

Side 66

If a straight line touch a circle, and from the point of contact a straight line be

drawn at right angles to the touching line, the

line. Let the straight line DE touch the circle ABC in C, and from C let CA be

drawn at ...

If a straight line touch a circle, and from the point of contact a straight line be

drawn at right angles to the touching line, the

**centre**of the circle shall be in thatline. Let the straight line DE touch the circle ABC in C, and from C let CA be

drawn at ...

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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.