## The Elements of Euclid |

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Resultat 1-5 av 9

Side 68

to the D angle CDB, because they are in the same

ACB is equal to the angle ADB, because they are in the same

therefore the whole angle ADC is equal to the angles CAB, ACB : to each of

these ...

to the D angle CDB, because they are in the same

**segment**BADC, and the angleACB is equal to the angle ADB, because they are in the same

**segment**ADCB:therefore the whole angle ADC is equal to the angles CAB, ACB : to each of

these ...

Side 69

For, if the

point A be on C, and the - —— straight line AB upon A B C D CD, the point B

shall coincide with the point D, because AB is equal to CD: therefore the straight

...

For, if the

**segment**E F AEB be applied to the Tos**segment**CFD, so as the o N /~ -point A be on C, and the - —— straight line AB upon A B C D CD, the point B

shall coincide with the point D, because AB is equal to CD: therefore the straight

...

Side 70

other points; and the circle of which ABC is a

evident, that if the angle ABD be greater than the angle BAD, the centre E falls

without the

angle ABD ...

other points; and the circle of which ABC is a

**segment**is described: and it isevident, that if the angle ABD be greater than the angle BAD, the centre E falls

without the

**segment**ABC, which therefore is less than a semicircle; but if theangle ABD ...

Side 73

In a circle, the angle in a semicircle is a right angle; but the angle in a

greater than a semicircle is less than a right angle; and the angle in a

less than a semicircle is greater than a right angle. Let ABCD be a circle, of which

...

In a circle, the angle in a semicircle is a right angle; but the angle in a

**segment**greater than a semicircle is less than a right angle; and the angle in a

**segment**less than a semicircle is greater than a right angle. Let ABCD be a circle, of which

...

Side 74

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

drawn cutting the circle, the angles made by this line with the line touching the

circle, shall be equal to the angles which are in the alternate

circle.

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

drawn cutting the circle, the angles made by this line with the line touching the

circle, shall be equal to the angles which are in the alternate

**segments**of thecircle.

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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Ingen forhåndsvisning tilgjengelig - 2016 |

The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Euclid Ingen forhåndsvisning tilgjengelig - 2016 |

### 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.