## 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 7

straight line.f Let AB be the given straight line; it is required to describe an

equilateral triangle upon it. Let A B be perpendicular to CD, and EF to G.H. then

the ...

**PROPOSITION**I. PROBLEM.f To describe an equilateral triangle on a given finitestraight line.f Let AB be the given straight line; it is required to describe an

equilateral triangle upon it. Let A B be perpendicular to CD, and EF to G.H. then

the ...

Side 28

This

may be demonstrated in a single case, the same as either the first or second in

Euclid's method, given above: and it may be so postponed without impropriety, ...

This

**proposition**, therefore, if it be postponed till the student has learned the 32d,may be demonstrated in a single case, the same as either the first or second in

Euclid's method, given above: and it may be so postponed without impropriety, ...

Side 163

all parallelograms having one angle coinciding with BCL, and their diagonals

with CA, are similar, it follows from this

given straight line BC, two parallelograms of the same altitude be described, one

of ...

all parallelograms having one angle coinciding with BCL, and their diagonals

with CA, are similar, it follows from this

**proposition**, that if, on the segments of agiven straight line BC, two parallelograms of the same altitude be described, one

of ...

Side 207

If, therefore, &c. k | h F PROP. I. THEOR. SIMILAR polygons inscribed in circles,

are to. * This, which is the first

some of the

17th ...

If, therefore, &c. k | h F PROP. I. THEOR. SIMILAR polygons inscribed in circles,

are to. * This, which is the first

**proposition**of the tenth book, is necessary forsome of the

**propositions**of this book. . * This**proposition**is merely a lemma to the17th ...

Side 272

A porism is a

render a certain problem indeterminate, or capable of innumerable solutions. 3.

Isoperimetrical figures are such as have their perimeters, or bounding lines, ...

A porism is a

**proposition**affirming the possibility of finding such conditions as willrender a certain problem indeterminate, or capable of innumerable solutions. 3.

Isoperimetrical figures are such as have their perimeters, or bounding lines, ...

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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...