## The Elements of Euclid |

### Inni boken

Resultat 1-5 av 9

Side 184

SoLID parallelopipeds which are upon equal bases and of the same

equal to one another.” Let the solid parallelopipeds AE, CF be upon equal bases

AB, CD, and be of the same

SoLID parallelopipeds which are upon equal bases and of the same

**altitude**, areequal to one another.” Let the solid parallelopipeds AE, CF be upon equal bases

AB, CD, and be of the same

**altitude**; the solid AE is equal to the solid CF. First ... Side 185

But let the solid parallelopipeds SE, CF be upon equal bases SB, CD, and be of

the same

bases; and place the bases SB, CD in the same plane, so that CL, LB be in a

straight ...

But let the solid parallelopipeds SE, CF be upon equal bases SB, CD, and be of

the same

**altitude**, and let their insisting straight lines be at right angles to thebases; and place the bases SB, CD in the same plane, so that CL, LB be in a

straight ...

Side 189

Let AB, CD be equal solid parallelopipeds; their bases are reciprocally

proportional to their

straight lines, ...

Let AB, CD be equal solid parallelopipeds; their bases are reciprocally

proportional to their

**altitudes**; that is, as the base EH is to the base NP, so is the**altitude**of the solid CD to the**altitude**of the solid AB. - First, let the insistingstraight lines, ...

Side 190

Make then CT equal to AG, and | G complete the solid parallelopiped CV of which

the base is NP, and the

solid CD, therefore the A E C N solid AB is to the solid CV, as (7. 5.) the solid CD

...

Make then CT equal to AG, and | G complete the solid parallelopiped CV of which

the base is NP, and the

**altitude**CT. H. Because the solid AB is equal --- to thesolid CD, therefore the A E C N solid AB is to the solid CV, as (7. 5.) the solid CD

...

Side 191

is the solid AB to the solid CV ; for the solids AB, CV are of the same

as MC to CT, so is the base MP to the base PT, and the solid GD to the solid (25.

11.) CV: and therefore as the solid AB to the solid CV, so is the solid CD to the ...

is the solid AB to the solid CV ; for the solids AB, CV are of the same

**altitude**; andas MC to CT, so is the base MP to the base PT, and the solid GD to the solid (25.

11.) CV: and therefore as the solid AB to the solid CV, so is the solid CD to the ...

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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.