## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With Notes and Illus., and an Appendix in Five Books |

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Side 218

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 ...

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 ...

Side 219

of the

straight lines be drawn from the points of division to the extremities of the arcs,

and upon the triangles thus made, prisms be formed of the same altitude with the

...

of the

**cylinder**in which they are. If, therefore, each of the arcs be bisected, andstraight lines be drawn from the points of division to the extremities of the arcs,

and upon the triangles thus made, prisms be formed of the same altitude with the

...

Side 224

every cone is a third part of the

altitude. Therefore also the

which AC has to EG : wherefore similar cones, &c. PROP. XIII. THEOR. If a

every cone is a third part of the

**cylinder**upon the same base, and of the samealtitude. Therefore also the

**cylinder**has to the**cylinder**, the triplicate ratio of thatwhich AC has to EG : wherefore similar cones, &c. PROP. XIII. THEOR. If a

**cylinder**... Side 225

as

multiple is the

multiple the axis MK is of the axis KF, the same multiple is the

as

**cylinders**; therefore, whatever multiple the axis KL is of the axis KE, the samemultiple is the

**cylinder**PG of the**cylinder**GB. For the same reason, whatevermultiple the axis MK is of the axis KF, the same multiple is the

**cylinder**QG of the ... Side 226

them be equal; and the

altitudes KL, MN be unequal, and MN the greater; from MN take MP equal to KL,

and through P cut the

them be equal; and the

**cylinders**AX, EO being also equal, and (XII. ... But let thealtitudes KL, MN be unequal, and MN the greater; from MN take MP equal to KL,

and through P cut the

**cylinder**EO by the plane YS parallel to the planes of the ...### Hva folk mener - Skriv en omtale

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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... Euclid Ingen forhåndsvisning tilgjengelig - 2016 |

### Vanlige uttrykk og setninger

ABCD altitude angle ABC angle BAC angle equal BC is equal bisected centre chord circle ABC circumference cone const contained cylinder describe a circle diagonal diameter divided draw equal angles equal to AC equiangular equilateral Euclid exterior angle fore fourth given circle given point given ratio given straight line greater half Hence hypotenuse inscribed join less Let ABC magnitudes manner multiple opposite parallel parallelepiped parallelogram perpendicular polygon polyhedron prism PROB produced PROP proportional proposition pyramid radius rectangle rectilineal figure right angles Schol segments semicircle sides similar similar triangles solid angles square of AC straight lines drawn tangent THEOR third triangle ABC triplicate ratio vertex vertical angle wherefore

### Populære avsnitt

Side 94 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.

Side 53 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.

Side 143 - 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 4 - A rhombus is that which has all its sides equal, but its angles are not right angles.

Side 57 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.

Side 138 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...

Side 43 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.

Side 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 40 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Side 36 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...