## The Elements of Euclid |

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Side 181

and similar to the opposite D t H one BE; and the parallelogram GE to CH: Z

therefore the

parallel- E ograms CA, GE, EC, is equal (C. 11.) to the

...

and similar to the opposite D t H one BE; and the parallelogram GE to CH: Z

therefore the

**prism**contained by the two A triangles CGF, DAE, and the threeparallel- E ograms CA, GE, EC, is equal (C. 11.) to the

**prism**contained by the two...

Side 199

If there be two triangular

parallelogram, and the base of the other a ... and the other a triangle GHK for its

base; if the parallelogram AF, be double of the triangle GHK, the

If there be two triangular

**prisms**of the same altitude, the base of one of which is aparallelogram, and the base of the other a ... and the other a triangle GHK for its

base; if the parallelogram AF, be double of the triangle GHK, the

**prism**ABCDEF ... Side 205

of the triangle GFC: but when there are two

one has a parallelogram for its base, and the other a triangle that is half of the

parallelogram, these

of the triangle GFC: but when there are two

**prisms**of the same altitude, of whichone has a parallelogram for its base, and the other a triangle that is half of the

parallelogram, these

**prisms**are equal (40. 11.) to one another; therefore the**prism**... Side 207

parts in the points N, Y by the same planes: therefore the

RVFSTY are of the same altitude; and therefore as the base LXC to the base RVF

; that is, as the triangle ABC to the triangle DEF, so (Cor. 32. 11.) is the

having ...

parts in the points N, Y by the same planes: therefore the

**prisms**LXCOMN,RVFSTY are of the same altitude; and therefore as the base LXC to the base RVF

; that is, as the triangle ABC to the triangle DEF, so (Cor. 32. 11.) is the

**prism**having ...

Side 209

the solid Q is greater than the

which is impossible. Therefore the base ABC is not to the base DEF, as the

pyramid ABCG to any solid which is less than the pyramid DEFH. In the same

manner it ...

the solid Q is greater than the

**prisms**in the pyramid DEFH. But it is also less,which is impossible. Therefore the base ABC is not to the base DEF, as the

pyramid ABCG to any solid which is less than the pyramid DEFH. In the same

manner it ...

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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.