## The Elements of Euclid |

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Resultat 1-5 av 7

Side 42

therefore the

square of BC. If therefore a straight line, &c. Q. E. D. PROP. IV. THEOR. If a

straight line be divided into any two parts, the square of the whole line is equal to

the ...

therefore the

**rectangle**AB, BC, is equal to the**rectangle**AC,**CB**, together with thesquare of BC. If therefore a straight line, &c. Q. E. D. PROP. IV. THEOR. If a

straight line be divided into any two parts, the square of the whole line is equal to

the ...

Side 50

First, let AD fall within the triangle ABC; and because the straight line CD is

divided into two parts in A the point D, the squares of

twice the

...

First, let AD fall within the triangle ABC; and because the straight line CD is

divided into two parts in A the point D, the squares of

**CB**, BD are equal (7. 2.) totwice the

**rectangle**contained by**CB**, BD, and the square of DC: to each of these...

Side 341

... have a given ratio to the triangle. - Let the triangle ABC have a given obtuse

angle ABC; and produce the straight line

contained by DB, BC, has a given ratio to the triangle ABC. - Because the angle

ABC is ...

... have a given ratio to the triangle. - Let the triangle ABC have a given obtuse

angle ABC; and produce the straight line

**CB**, ... the double of the**rectangle**contained by DB, BC, has a given ratio to the triangle ABC. - Because the angle

ABC is ...

Side 342

the rectangle AB, BC to its half the triangle ABC; therefore, ex æquali, as twice

BD is to the half of DA, that is, as quadruple of BD ... the ratio of twice the B D C

13.

the rectangle AB, BC to its half the triangle ABC; therefore, ex æquali, as twice

BD is to the half of DA, that is, as quadruple of BD ... the ratio of twice the B D C

**rectangle CB**, BD to the triangle ABC is given; and twice the**rectangle CB**, BD is (13.

Side 357

therefore the square of BC, and the straight line BC, is given : and the ratio of BC

to BD, as also of BD to BA, has been shown to be given; therefore (9. dat) the

ratio of ...

**rectangle CB**, BD is given, being the given excess of the square of BC, BA;therefore the square of BC, and the straight line BC, is given : and the ratio of BC

to BD, as also of BD to BA, has been shown to be given; therefore (9. dat) the

ratio of ...

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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.