## The Elements of Euclid |

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Side 43

THEOR. lf a straight line be

contained by the whole line thus produced, and the part of it produced, together

with the square of half the line

...

THEOR. lf a straight line be

**bisected**, and produced to any point; the rectanglecontained by the whole line thus produced, and the part of it produced, together

with the square of half the line

**bisected**, is equal to the square of the straight line...

Side 72

Let ADB be the given circumference, it is required to

(10. 1.) it in C; from the point C draw CD at right angles to AB, and join AD, DB:

the circumference ADB is

and ...

Let ADB be the given circumference, it is required to

**bisect**it. Join AB, and**bisect**(10. 1.) it in C; from the point C draw CD at right angles to AB, and join AD, DB:

the circumference ADB is

**bisected**in the point D. Because AC is equal to CB,and ...

Side 86

to the angle BAC, and the angle DAB is

same manner, it may be demonstrated that the angles ABC, BCD, CDA are

severally

is ...

to the angle BAC, and the angle DAB is

**bisected**by the straight line AC: in thesame manner, it may be demonstrated that the angles ABC, BCD, CDA are

severally

**bisected**by the straight lines BD, AC; therefore, because the angle DABis ...

Side 89

point F, in which they meet, draw the ... G to the angle CBF ; wherefore the angle

ABC is

demonstrated, ...

**Bisect**(9. 1.) the angles BCD, CDE by the straight lines CF, DF, and from thepoint F, in which they meet, draw the ... G to the angle CBF ; wherefore the angle

ABC is

**bisected**by the straight line BF: in the same manner it may bedemonstrated, ...

Side 153

If an angle of a triangle be

base; the rectangle contained by the sides ... to the rectangle contained by the

segments of the base, together with the square of the straight line

angle.

If an angle of a triangle be

**bisected**by a straight line, which likewise cuts thebase; the rectangle contained by the sides ... to the rectangle contained by the

segments of the base, together with the square of the straight line

**bisecting**theangle.

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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.