## The Elements of Euclid |

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Resultat 1-5 av 5

Side 214

Let a cone have the same base with a

same altitude. The cone is the third part of the

triple of the cone. If the

than the ...

Let a cone have the same base with a

**cylinder**, viz. the circle ABCD, and thesame altitude. The cone is the third part of the

**cylinder**; that is, the**cylinder**istriple of the cone. If the

**cylinder**be not triple of the cone, it must either be greaterthan the ...

Side 222

the

same base, and of the same altitude: therefore also the

&c.

the

**cylinder**to the**cylinder**; for every cone is the third part of the**cylinder**upon thesame base, and of the same altitude: therefore also the

**cylinder**has to the**cylinder**the triplicate ratio of that which AC has to EG. Wherefore similar cones,&c.

Side 223

it is to be shown, that the

axis KF. Produce the axis EF both ways; and take any number of straight lines EN

, NL, each equal to EK; and any number FX, XM each equal to FK; and let planes

...

it is to be shown, that the

**cylinder**AH is to the**cylinder**HC, as the axis EK to theaxis KF. Produce the axis EF both ways; and take any number of straight lines EN

, NL, each equal to EK; and any number FX, XM each equal to FK; and let planes

...

Side 224

therefore also the

cut by the plane CD parallel to its opposite planes, as the F

to ...

therefore also the

**cylinders**EB, CM are equal. And because the**cylinder**FM iscut by the plane CD parallel to its opposite planes, as the F

**cylinder**CM to the**cylinder**FD, so is (13. 12.) the axis LN to the axis KL. But the**cylinder**CM is equalto ...

Side 225

consequently ES is a

MP: and because the

EFGH; for the

the ...

consequently ES is a

**cylinder**, the base of which is the circle EFHG, and altitudeMP: and because the

**cylinder**AX is equal to ... is the base ABCD to the baseEFGH; for the

**cylinders**AX, ES are of the same altitude; and as the**cylinder**EO tothe ...

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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.