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

### Inni boken

Resultat 1-5 av 5

Side 201

THE bases and

and (1.) ... their bases are reciprocally proportional to their

base EH is to the base NP, so is the

THE bases and

**altitudes**of equal parallelepipeds are reciprocally proportional:and (1.) ... their bases are reciprocally proportional to their

**altitudes**; that is, as thebase EH is to the base NP, so is the

**altitude**of CD to the**altitude**of AB. First, let ... Side 217

THE bases and

proportional: and (2.) ... be equal: their bases and

proportional, viz., ABC is to DEF, as the

THE bases and

**altitudes**of equal triangular pyramids are reciprocallyproportional: and (2.) ... be equal: their bases and

**altitudes**are reciprocallyproportional, viz., ABC is to DEF, as the

**altitude**of the pyramid DEFH to the**altitude**of ABCG. Side 218

Let a cone have the same base with a cylinder, viz., the circle ABCD, and the

same

triple of the cone. If the cylinder be not triple of the cone, it must either be greater

than ...

Let a cone have the same base with a cylinder, viz., the circle ABCD, and the

same

**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 greater

than ...

Side 289

Draw DAE parallel and AF perpendicular to BC: the

, having its perimeter equal to that of ABC, and not being isosceles, is less than

AF. For through any other point G in the parallel draw GB, GC. Then the angles ...

Draw DAE parallel and AF perpendicular to BC: the

**altitude**of any triangle on BC, having its perimeter equal to that of ABC, and not being isosceles, is less than

AF. For through any other point G in the parallel draw GB, GC. Then the angles ...

Side 344

Draw AML perpendicular to CE, and consequently to GK: the

straight lines AB, AC, AD, AE are cut proportionally by GK. Join CL, GM; these (XI.

2. and 16.) are in the same plane, and are parallel to one another. Hence (VI.

Draw AML perpendicular to CE, and consequently to GK: the

**altitude**AL, and thestraight lines AB, AC, AD, AE are cut proportionally by GK. Join CL, GM; these (XI.

2. and 16.) are in the same plane, and are parallel to one another. Hence (VI.

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### Andre utgaver - Vis alle

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...