## 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 |

### Inni boken

Resultat 1-5 av 27

Side 1

The

between its extreme points . 5 . A superficies is that which has only length and

breadth . 6 . The

that in ...

The

**extremities**of a line are points . 4 . A straight line is that which lies evenlybetween its extreme points . 5 . A superficies is that which has only length and

breadth . 6 . The

**extremities**of a superficies are lines . 7 . A plane superficies isthat in ...

Side 37

The straight lines which join the

parallel . Let AB and CD be equal and parallel straight lines , and let them be

joined towards the same parts by the straight lines AC and BD : AC and BD shall

...

The straight lines which join the

**extremities**of two are also themselves equal andparallel . Let AB and CD be equal and parallel straight lines , and let them be

joined towards the same parts by the straight lines AC and BD : AC and BD shall

...

Side 40

But straight lines which join the

towards the same parts are themselves equal and parallel . [ I . 33 . Therefore BE

, CH are both equal and parallel . Therefore EBCH is a parallelogram . [

Definition .

But straight lines which join the

**extremities**of equal and parallel straight linestowards the same parts are themselves equal and parallel . [ I . 33 . Therefore BE

, CH are both equal and parallel . Therefore EBCH is a parallelogram . [

Definition .

Side 72

An angle in a segment is the angle contained by two straight lines drawn from

any point in the circumference of the segment to the

which is the base of the segment . 9 . And an angle is said to insist or stand on

the ...

An angle in a segment is the angle contained by two straight lines drawn from

any point in the circumference of the segment to the

**extremities**of the straight linewhich is the base of the segment . 9 . And an angle is said to insist or stand on

the ...

Side 81

Definition 15 . the remainder KD is greater than the remainder GD , that is , GD is

less than KD . And because MLD is a triangle , and from the points M , D , the

within ...

Definition 15 . the remainder KD is greater than the remainder GD , that is , GD is

less than KD . And because MLD is a triangle , and from the points M , D , the

**extremities**of its side MD , the straight lines MK , DK are drawn to the point Kwithin ...

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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.