## The Elements of Euclid |

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Resultat 1-5 av 7

Side 300

Let the magnitude AB together with the given magnitude BE, that is, AE, have a

given ratio to the magnitude CD; the excess of CD above a given magnitude has

a given ratio to AB. Because the

...

Let the magnitude AB together with the given magnitude BE, that is, AE, have a

given ratio to the magnitude CD; the excess of CD above a given magnitude has

a given ratio to AB. Because the

**ratio of AE**to CD is given, as AE to CD, so make...

Side 303

5) to CF, as AB to CD : but the

AG to CF is given; and because BE, BG are each of them given, GE is given:

therefore AG, the excess of

CF.

5) to CF, as AB to CD : but the

**ratio**of AB to CD is given, where. fore the**ratio**ofAG to CF is given; and because BE, BG are each of them given, GE is given:

therefore AG, the excess of

**AE**above a given magnitude GE, has a given**ratio**toCF.

Side 305

given, because GE is given; therefore the sum

remainder FC has a given

15. PROP. xxii. D. If two magnitudes have a given

...

given, because GE is given; therefore the sum

**AE**together with GA, to which theremainder FC has a given

**ratio**, is given. The second part is manifest from prop.15. PROP. xxii. D. If two magnitudes have a given

**ratio**to one another, if from one...

Side 306

But if the ratio of AB to CD be not the same with the

greater than it, or, by inversion, the ratio of CD to AB is greater than the ratio of CF

to AE: first, let the ratio of AB to CD be greater than the

But if the ratio of AB to CD be not the same with the

**ratio of AE**to CF, it is eithergreater than it, or, by inversion, the ratio of CD to AB is greater than the ratio of CF

to AE: first, let the ratio of AB to CD be greater than the

**ratio of AE**to CF; and as ... Side 334

cond EF be made to a straight line M ; if the ratio of the triangles be given, the

ratio of the other side of the first to the ... Let this straight line be EG ; therefore the

cond EF be made to a straight line M ; if the ratio of the triangles be given, the

ratio of the other side of the first to the ... Let this straight line be EG ; therefore the

**ratio of AE**A C to EG is given; and EB is to - FD, as FC to EG, therefore the F- D ...### Hva folk mener - Skriv en omtale

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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.