## The Elements of Euclid |

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Side 249

Analogy is the similitude of

purpose in mathematics, but only to

and confused notions of analogy: but the whole of the doctrine of

whole ...

Analogy is the similitude of

**ratios**, is of the same kind, and can serve for nopurpose in mathematics, but only to

**give**beginners some general, though grossand confused notions of analogy: but the whole of the doctrine of

**ratios**, and thewhole ...

Side 257

... we have

the Greek and other editions, which very ... I say the

fourth D, is either equal to, or greater, or less than the

second ...

... we have

**given**a legitimate demonstration of this proposition instead of that inthe Greek and other editions, which very ... I say the

**ratio**of the third C to thefourth D, is either equal to, or greater, or less than the

**ratio**of the first A to thesecond ...

Side 265

pression by which the

the same time, is shown that there are ... demonstration is not Euclid's: these

superfluous things are now left out, and a more simple demonstration is

from ...

pression by which the

**ratio**of the first A to the third C is signified, and by which, atthe same time, is shown that there are ... demonstration is not Euclid's: these

superfluous things are now left out, and a more simple demonstration is

**given**from ...

Side 297

found to the sum of the two magnitudes by which the

of them, and the given magnitude; each of the parts is given.” Let the given

magnitude AB be divided into the parts AC, CB. which have a

found to the sum of the two magnitudes by which the

**given ratio**is exhibited, oneof them, and the given magnitude; each of the parts is given.” Let the given

magnitude AB be divided into the parts AC, CB. which have a

**given ratio**to one ... Side 301

If the excess of a magnitude, above a given magnitude, has a

another magnitude; the excess of both together above a given magnitude shall

have to that other a

above a ...

If the excess of a magnitude, above a given magnitude, has a

**given ratio**toanother magnitude; the excess of both together above a given magnitude shall

have to that other a

**given ratio**: and if the excess of two magnitudes togetherabove a ...

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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.