## 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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Resultat 1-5 av 28

Side 162

CF is to FD , ( Hypothesis . and that GK and LN are equimultiples of AE and CF ;

therefore GK is to EB as LN is to FD . [ V . 4 , Cor . But HO is equal to BE , and ...

**Suppose**that HO and MP are equal to BE and DF . Then , because AE is to EB asCF is to FD , ( Hypothesis . and that GK and LN are equimultiples of AE and CF ;

therefore GK is to EB as LN is to FD . [ V . 4 , Cor . But HO is equal to BE , and ...

Side 163

V . A . " " D - Again ,

Then , because AE is to EB as CF is to FD ; [ Hypothesis . and that GK and LN are

equimultiples of AE and CF , and HO and MP are equimultiples of EB and FD ...

V . A . " " D - Again ,

**suppose**that HO and MP are equimultiples of EB and FD .Then , because AE is to EB as CF is to FD ; [ Hypothesis . and that GK and LN are

equimultiples of AE and CF , and HO and MP are equimultiples of EB and FD ...

Side 255

For if not , one of them must be greater than the other ;

AC . Then the angle ACB is greater than the angle ABC , by I . 18 . But this is

impossible , hecause the angle ACB is equal to the angle ABC , EUCLID ' S ...

For if not , one of them must be greater than the other ;

**suppose**A B greater thanAC . Then the angle ACB is greater than the angle ABC , by I . 18 . But this is

impossible , hecause the angle ACB is equal to the angle ABC , EUCLID ' S ...

Side 261

Let A BC and DEF be two triangles ; let AB be equal to DE , and BC equal to EP ,

and the angle A equal to the angle D . First ,

angles . If the angle B be equal to the angle E , the triangles A BC , DEP are ...

Let A BC and DEF be two triangles ; let AB be equal to DE , and BC equal to EP ,

and the angle A equal to the angle D . First ,

**suppose**the angles C and F acuteangles . If the angle B be equal to the angle E , the triangles A BC , DEP are ...

Side 262

Next ,

similar to the above . Lastly ,

the angle C . If the angle B be not equal to the angle E , make the - G EL BK

angle ABG ...

Next ,

**suppose**the angles at C and F obtuse angles . The demonstration issimilar to the above . Lastly ,

**suppose**one of the angles a right angle , namely ,the angle C . If the angle B be not equal to the angle E , make the - G EL BK

angle ABG ...

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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.