## The Elements of Euclid |

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Resultat 1-5 av 14

Side 25

o to equal angles in each; then shall the other sides be equal, each to each; and

also the

triangles which have the angles ABC, BCA equal to the angles DEF, EFD, viz.

o to equal angles in each; then shall the other sides be equal, each to each; and

also the

**third**angle of the one to the**third**angle of the other. Let ABC, DEF be twotriangles which have the angles ABC, BCA equal to the angles DEF, EFD, viz.

Side 86

To describe an isosceles triangle, having each of the angles at the base double

of the

that the rectangle AB, BC be equal to the square of CA; and from the centre A, ...

To describe an isosceles triangle, having each of the angles at the base double

of the

**third**angle. Take any straight line AB, and divide (11. 2.) it in the point C, sothat the rectangle AB, BC be equal to the square of CA; and from the centre A, ...

Side 94

N. B. “When four magnitudes are proportionals, it is usually expressed by saying,

the first is to the second, as the

of four magnitudes (taken as in the fifth definition) the multiple of the first is ...

N. B. “When four magnitudes are proportionals, it is usually expressed by saying,

the first is to the second, as the

**third**to the fourth.' VII. When of the equimultiplesof four magnitudes (taken as in the fifth definition) the multiple of the first is ...

Side 99

If the first of four magnitudes has the same ratio to the second which the

to the fourth, then any equimultiples whatever of the first and

same ratio to any equimultiples of the second and fourth, viz. 'the equimultiple of

...

If the first of four magnitudes has the same ratio to the second which the

**third**hasto the fourth, then any equimultiples whatever of the first and

**third**shall have thesame ratio to any equimultiples of the second and fourth, viz. 'the equimultiple of

...

Side 168

PROP. XIX. THEOR. If two planes cutting one another be each of them perpendi.

cular to a

plane. Let the two planes AB, BC be each of them perpendicular to a

...

PROP. XIX. THEOR. If two planes cutting one another be each of them perpendi.

cular to a

**third**plane; their common section shall be perpendi. cular to the sameplane. Let the two planes AB, BC be each of them perpendicular to a

**third**plane,...

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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.