## The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth Books : with Notes, an Appendix, and Exercises |

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Side 3

[ A

18 . A semicircle is the figure contained by a diameter and the part of the

circumference cut off by the diameter . 19 . A segment of a circle is the figure

contained ...

[ A

**radius**of a circle is a straight line drawn from the centre to the circumference . ]18 . A semicircle is the figure contained by a diameter and the part of the

circumference cut off by the diameter . 19 . A segment of a circle is the figure

contained ...

Side 116

1 . from K draw any

angle BKÁ м в — equal to the angle DEG , and the angle BKC equal to the angle

DFH ; [ I . 23 . and through the points A , B , C , draw the straight lines LAM , MBN

...

1 . from K draw any

**radius**KB ; at the point K , in the straight line KB , make theangle BKÁ м в — equal to the angle DEG , and the angle BKC equal to the angle

DFH ; [ I . 23 . and through the points A , B , C , draw the straight lines LAM , MBN

...

Side 253

... points , that we can produce a straight line to any length , and that we can

describe a circle from a given centre with a given distance as

sometimes stated that the postulates amount to requiring the use of a ruler and

compasses .

... points , that we can produce a straight line to any length , and that we can

describe a circle from a given centre with a given distance as

**radius**. It issometimes stated that the postulates amount to requiring the use of a ruler and

compasses .

Side 295

With centre A , and

describe a circle ; from B draw a straight line touching the circle 80 described at C

. Join AC and produce it to meet the circumference at D . Draw the

With centre A , and

**radius**equal to the difference of the radii of the given circles ,describe a circle ; from B draw a straight line touching the circle 80 described at C

. Join AC and produce it to meet the circumference at D . Draw the

**radius**BE ... Side 300

Draw two straight lines parallel to the given straight lines , at a distance from them

equal to the

centre of the given circle . Describe a circle touching the straight lines thus ...

Draw two straight lines parallel to the given straight lines , at a distance from them

equal to the

**radius**of the given circle , and on the sides of them remote from thecentre of the given circle . Describe a circle touching the straight lines thus ...

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The Elements of Euclid for the Use of Schools and Colleges Isaac Todhunter Uten tilgangsbegrensning - 1872 |

The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ... Isaac Todhunter Uten tilgangsbegrensning - 1880 |

The Elements of Euclid for the Use of Schools and Colleges: Comprising the ... Euclid,Isaac Todhunter Uten tilgangsbegrensning - 1867 |

### Vanlige uttrykk og setninger

ABCD AC is equal angle ABC angle BAC Axiom base bisected Book centre chord circle ABC circumference common Construction Corollary Definition demonstration describe a circle described diameter difference divided double draw drawn equal equal angles equiangular equilateral equimultiples Euclid extremities fall figure fixed formed four fourth given circle given point given straight line greater half Hypothesis inscribed intersect join less Let ABC magnitudes manner meet middle point multiple namely opposite sides parallel parallelogram pass perpendicular plane polygon PROBLEM produced proportionals Q.E.D. PROPOSITION quadrilateral radius ratio reason rectangle contained rectilineal figure remaining respectively right angles segment shew shewn sides similar square straight line drawn suppose taken tangent THEOREM third triangle ABC twice Wherefore whole

### Populære avsnitt

Side 264 - 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 73 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a Right Angle; and the straight line which stands on the other is called a Perpendicular to it.

Side 264 - To draw a straight line at right angles to a given straight line, from a given point in the same. Let AB be...

Side 184 - 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 10 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.

Side 300 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.

Side 60 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Side 62 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts in the point D ; The squares on AD and DB shall be together double of AD»+DB

Side 244 - Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied, so at length to become greater than AB.

Side 6 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.