## 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 76

Side 13

triangle ; because AC is equal to AD , [ Hypothesis . the angle ACD is equal to the

angle ADC . [ I . 5 . But the angle ACD is greater than the angle BCD , [ AX .

**Join**CD . In the case in which the vertex of each triangle is without the othertriangle ; because AC is equal to AD , [ Hypothesis . the angle ACD is equal to the

angle ADC . [ I . 5 . But the angle ACD is greater than the angle BCD , [ AX .

Side 15

Take any point D in AB , and from AC cut off AE equal to AD ; [ I . 3 .

on DE , on the side remote from A , describe the equilateral triangle DEF . [ I . 1 .

...

Take any point D in AB , and from AC cut off AE equal to AD ; [ I . 3 .

**join**DE , andon DE , on the side remote from A , describe the equilateral triangle DEF . [ I . 1 .

**Join**AF . The straight line AF shall bisect the angle BAO . Because AD is equal to...

Side 17

Take any point Don the other side of AB , and from the centre C , at the distance

CD , describe the circle EGF , meeting AB at F and G . [ Postulate 3 . Bisect FG at

H , [ I . 10 . and

Take any point Don the other side of AB , and from the centre C , at the distance

CD , describe the circle EGF , meeting AB at F and G . [ Postulate 3 . Bisect FG at

H , [ I . 10 . and

**join**CH . The straight line CH drawn from the given point C shall ... Side 20

Bisect AC at E , [ I . 10 .

. and

AE , EB are equal to the two sides CE , EF , each to each ; and the angle AEB is ...

Bisect AC at E , [ I . 10 .

**join**BE and produce it to F , making EF equal to EB , [ I . 3. and

**join**FC . Because AE is equal to EC , and BE to EF ; [ Constr . the two sidesAE , EB are equal to the two sides CE , EF , each to each ; and the angle AEB is ...

Side 22

Because AC is greater than AB , make AD equal to AB , [ I . 3 . and

, because ADB is the exterior angle of the triangle BDC , it is greater than the

interior op - $ posite angle DCB . [ I . 16 . But the angle ADB is equal to the angle

...

Because AC is greater than AB , make AD equal to AB , [ I . 3 . and

**join**BD . Then, because ADB is the exterior angle of the triangle BDC , it is greater than the

interior op - $ posite angle DCB . [ I . 16 . But the angle ADB is equal to the angle

...

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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.