## The Elements of Euclid |

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Resultat 1-5 av 6

Side 208

Let the

vertices are the points G, H, be of the same altitude; as the base ABC, to the base

DEF, so is the

Let the

**pyramids**of which the triangles ABC, DEF are the bases, and of which thevertices are the points G, H, be of the same altitude; as the base ABC, to the base

DEF, so is the

**pyramid**ABCG to the**pyramid**DEFH. For, if it be not so, the base ... Side 209

the solid Q is greater than the prisms in the

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

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 samemanner it ...

Side 210

the

FGH, as the

the triangle FGH, as the

the

**pyramid**ABCM to the**pyramid**FGHN; and the triangle ACD to the triangleFGH, as the

**pyramid**ACDM to the**pyramid**FGHN; and also the triangle ADE tothe triangle FGH, as the

**pyramid**ADEM to the**pyramid**FGHN; as all the first ... Side 212

ratio of that which their homologous sides have: therefore the solid BGML has to

the solid EHPO the triplicate ratio of that which the side BC has to the

homologous side EF: but as the solid BGML is to the solid EHPO, so is (15. 5.) the

ratio of that which their homologous sides have: therefore the solid BGML has to

the solid EHPO the triplicate ratio of that which the side BC has to the

homologous side EF: but as the solid BGML is to the solid EHPO, so is (15. 5.) the

**pyramid**... Side 213

t the solid 'parallelopipeds BGML, EHPO contained by these planes and those

opposite to them: and because the

and that the solid BGML is sectuple of the

t the solid 'parallelopipeds BGML, EHPO contained by these planes and those

opposite to them: and because the

**pyramid**ABCG is equal to the**pyramid**DEFH,and that the solid BGML is sectuple of the

**pyramid**ABCG, and the solid EHPO ...### 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.