## The Elements of Euclid |

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Resultat 1-5 av 6

Side 215

than the excess of the cylinder above the triple of the

upon the segments of the circle AE, EB, BF, FC, CG, GD, DH, HA. Therefore the

rest of the cylinder, that is, the prism of which the base is the polygon AEBFCGDH

, ...

than the excess of the cylinder above the triple of the

**cone**. , Let them be thoseupon the segments of the circle AE, EB, BF, FC, CG, GD, DH, HA. Therefore the

rest of the cylinder, that is, the prism of which the base is the polygon AEBFCGDH

, ...

Side 216

part of the cylinder. Let these be the segments upon AE, EB, BF, FC, CG, GD, DH,

HA. Therefore the rest of the

...

**cone**, which together shall be less than the excess of the**cone**above the thirdpart of the cylinder. Let these be the segments upon AE, EB, BF, FC, CG, GD, DH,

HA. Therefore the rest of the

**cone**, that is, the pyramid, of which the base is the H...

Side 217

than the solid Z: let these be the segments upon EO, OF, FP, PG, GR, RH, HS, SE

: therefore the remainder of the

polygon EOFPGRHS, and its vertex the same with that of the

...

than the solid Z: let these be the segments upon EO, OF, FP, PG, GR, RH, HS, SE

: therefore the remainder of the

**cone**, viz. the pyramid of which the base is thepolygon EOFPGRHS, and its vertex the same with that of the

**cone**, is greater than...

Side 218

N: therefore, as the

the polygon ATBYCVDQ, and vertex L, to the pyramid the base of which is the

polygon EOFPGRHS, and vertex N. : but the

...

N: therefore, as the

**cone**AL to the solid X, so is the pyramid of which the base isthe polygon ATBYCVDQ, and vertex L, to the pyramid the base of which is the

polygon EOFPGRHS, and vertex N. : but the

**cone**AL is greater than the pyramid...

Side 221

But by the hypothesis, the

L., has to the solid X, the triplicate ratio of that which AC has to EG: therefore as

the

...

But by the hypothesis, the

**cone**of which the base is the circle ABCD, and vertexL., has to the solid X, the triplicate ratio of that which AC has to EG: therefore as

the

**cone**of which the base is the circle ABCD, and vertex L, is to the solid X, so is...

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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.