## 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 199

Wherefore the solid AB has to the solid KO, the

has to EK; and the solid KO is equal to CD, and the straight line EK to CF.

Therefore the solid A B has to CD the

to the ...

Wherefore the solid AB has to the solid KO, the

**triplicate ratio**of that which AEhas to EK; and the solid KO is equal to CD, and the straight line EK to CF.

Therefore the solid A B has to CD the

**triplicate ratio**of that which the side AE hasto the ...

Side 216

the vertices, be similar, and similarly situated; the pyramid ABCG has to DEFH,

the

Complete the parallelograms BM, BN, BK, and the parallelepiped BGML

contained by ...

the vertices, be similar, and similarly situated; the pyramid ABCG has to DEFH,

the

**triplicate ratio**of that which the side BC has to the homologous side EF.Complete the parallelograms BM, BN, BK, and the parallelepiped BGML

contained by ...

Side 223

B.) their solid angles are equal to one another, and they are contained b the

same number of similar planes: and (XII. 8.) AKQL has to EMSN the

of that which AK has to EM. In the same manner, if straight lines be drawn from D,

V, ...

B.) their solid angles are equal to one another, and they are contained b the

same number of similar planes: and (XII. 8.) AKQL has to EMSN the

**triplicate ratio**of that which AK has to EM. In the same manner, if straight lines be drawn from D,

V, ...

Side 232

similar pyramids have to one another the

. Therefore the pyramid, of which the base is the quadrilateral KBOS, and the

vertex A, has to the pyramid in the other sphere of the same order, the triplicate ...

similar pyramids have to one another the

**triplicate ratio**of their homologous sides. Therefore the pyramid, of which the base is the quadrilateral KBOS, and the

vertex A, has to the pyramid in the other sphere of the same order, the triplicate ...

Side 233

BC, EF: the sphere ABC has to the sphere DEF the

BC has to EF. For, if not, the sphere ABC will have to a sphere either less or

greater than DEF, the

that ratio ...

BC, EF: the sphere ABC has to the sphere DEF the

**triplicate ratio**of that whichBC has to EF. For, if not, the sphere ABC will have to a sphere either less or

greater than DEF, the

**triplicate ratio**of that which BC has to EF. First, let it havethat ratio ...

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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...