## 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 145

IN a right-angled triangle, if a perpendicular be drawn from the right angle to the

to one another. Let ABC be a right-angled triangle, having the right angle BAC; ...

IN a right-angled triangle, if a perpendicular be drawn from the right angle to the

**hypotenuse**, the triangles on each side of it are similar to the whole triangle, andto one another. Let ABC be a right-angled triangle, having the right angle BAC; ...

Side 256

If on the

described, and straight lines be drawn from the right angle to the remote angles

of the rectangle, dividing the

extreme ...

If on the

**hypotenuse**of a right-angled triangle, a rectangle of any altitude bedescribed, and straight lines be drawn from the right angle to the remote angles

of the rectangle, dividing the

**hypotenuse**into three parts; the rectangle of theextreme ...

Side 297

In like manner it would be proved, by means of the triangles CDQ, CDK, that DQ,

the cotangent of AM, is equal to DK, the cotangent of AF, and that their cosecants

CQ, CK are equal. PROP. I. THEOR. IN a right-angled triangle, the

In like manner it would be proved, by means of the triangles CDQ, CDK, that DQ,

the cotangent of AM, is equal to DK, the cotangent of AF, and that their cosecants

CQ, CK are equal. PROP. I. THEOR. IN a right-angled triangle, the

**hypotenuse**... Side 384

Given one leg of a right-angled triangle, and the remote segment of the

triangle. - 45. Given the base of a triangle, the vertical angle, and the side of the

inscribed ...

Given one leg of a right-angled triangle, and the remote segment of the

**hypotenuse**, made by a perpendicular from the right angle; to construct thetriangle. - 45. Given the base of a triangle, the vertical angle, and the side of the

inscribed ...

Side 385

If the

inscribed square, standing on the

To divide a given semicircle into two parts by a perpendicular to the diameter, ...

If the

**hypotenuse**of a right-angled triangle be given, the side of the greatestinscribed square, standing on the

**hypotenuse**, is one-third of the**hypotenuse**. 67.To divide a given semicircle into two parts by a perpendicular to the diameter, ...

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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...