## 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 52

Side 11

Axiom 3 . And it has also been shewn that the angle FBC is equal to the angle

GCB , which are the angles on the other side of the base . Wherefore , the angles

& c . Q . E . D .

Axiom 3 . And it has also been shewn that the angle FBC is equal to the angle

GCB , which are the angles on the other side of the base . Wherefore , the angles

& c . Q . E . D .

**Corollary**. Hence overy equilateral triangle is also equiangular . Side 12

Q . E . D .

PROPOSITION 7 . THEOREM . On the same base , and on the same side of it ,

there cannot be two triangles having their sides which are terminated at one

extremity of ...

Q . E . D .

**Corollary**. Hence every equiangular triangle is also equilateral .PROPOSITION 7 . THEOREM . On the same base , and on the same side of it ,

there cannot be two triangles having their sides which are terminated at one

extremity of ...

Side 16

Q . E . F .

lines cannot have a common segment . E If it be possible , let the two straight

lines ABC , ABD have the segment AB common to both of them . From the point B

...

Q . E . F .

**Corollary**. By the help of this problem it may be shewn that two straightlines cannot have a common segment . E If it be possible , let the two straight

lines ABC , ABD have the segment AB common to both of them . From the point B

...

Side 20

straight lines meeting at one point , are together equal to four right angles .

PROPOSITION 16 . THEOREM . If one side of a triangle be produced , the

exterior angle ...

**Corollary**2 . And consequently , that all the angles made by any number ofstraight lines meeting at one point , are together equal to four right angles .

PROPOSITION 16 . THEOREM . If one side of a triangle be produced , the

exterior angle ...

Side 35

But the angles ACD , ACB are together equal to two right angles ; [ 1 . 13 ,

therefore also the angles CBA , BAC , ACB are together equal to two right angles

. [ Axiom 1 . Wherefore , if a side of any triangle & c . Q . E . D . 36

.

But the angles ACD , ACB are together equal to two right angles ; [ 1 . 13 ,

therefore also the angles CBA , BAC , ACB are together equal to two right angles

. [ Axiom 1 . Wherefore , if a side of any triangle & c . Q . E . D . 36

**COROLLARY**1.

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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.