## 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 313

GIVEN one of the angles at the base of a triangle, the difference of the sides, and

the difference of the segments into which the base is divided by the line bisecting

the

GIVEN one of the angles at the base of a triangle, the difference of the sides, and

the difference of the segments into which the base is divided by the line bisecting

the

**vertical angle**; to construct the triangle. Construct the triangle DBG, having ... Side 314

to half the

arc meeting DC in C; * and make the angle DCA equal to D : ABC is the required

triangle. For (I. 6.) AD is equal to AC, and therefore BA, AC are equal to BD, the ...

to half the

**vertical angle**; from B as centre, with the base as radius, describe anarc meeting DC in C; * and make the angle DCA equal to D : ABC is the required

triangle. For (I. 6.) AD is equal to AC, and therefore BA, AC are equal to BD, the ...

Side 317

Hence to solve the problem in which the base and the

construct the triangle, so that the inscribed circle may be a maximum, describe

the segment as before, and to find D bisect the arc of the segment. The rest of the

...

Hence to solve the problem in which the base and the

**vertical angle**are given, toconstruct the triangle, so that the inscribed circle may be a maximum, describe

the segment as before, and to find D bisect the arc of the segment. The rest of the

...

Side 318

Hence, if GB were drawn, it and GF being known, BF, and the angle BGF, or BAC,

can be computed. The rest is easy; DAE, half the difference of B and C, being

known. PROP. X. PROB. Given the base of a triangle, the

Hence, if GB were drawn, it and GF being known, BF, and the angle BGF, or BAC,

can be computed. The rest is easy; DAE, half the difference of B and C, being

known. PROP. X. PROB. Given the base of a triangle, the

**vertical angle**, and the ... Side 387

Given the base and

bisecting the

double of one of the angles at the base, the rectangle under the sides is equal to

the ...

Given the base and

**vertical angle**of a triangle, to construct it, so that the linebisecting the

**vertical angle**may be a mean ... If the**vertical angle**of a triangle bedouble of one of the angles at the base, the rectangle under the sides is equal to

the ...

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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...