## 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 73

Side 3

A circle is a plane figure contained by one line , which is called the circumference

, and is such , that all straight lines

the circumference are equal to one another : 16 . And this point is called the ...

A circle is a plane figure contained by one line , which is called the circumference

, and is such , that all straight lines

**drawn**from a certain point within the figure tothe circumference are equal to one another : 16 . And this point is called the ...

Side 8

PROPOSITION 2 . PROBLEM . From a given point to

a given straight line . · Let A be the given point , and BC the given straight line : it

is required to

PROPOSITION 2 . PROBLEM . From a given point to

**draw**a straight line equal toa given straight line . · Let A be the given point , and BC the given straight line : it

is required to

**draw**from the point A a straight line equal to BC . From the point A ... Side 16

To

in the same . Let AB be the given ... The straight line CF

point C shall be at right angles to the given straight line AB . Because DC is equal

to ...

To

**draw**a straight line at right angles to a given straight line , from a given pointin the same . Let AB be the given ... The straight line CF

**drawn**from the givenpoint C shall be at right angles to the given straight line AB . Because DC is equal

to ...

Side 17

To

length , from a given point without it . Let AB be the ... The straight line CH

from the given point C shall be perpendicular to the given straight line AB . Join

CF ...

To

**draw**a straight line perpendicular to a given straight line of an unlimitedlength , from a given point without it . Let AB be the ... The straight line CH

**drawn**from the given point C shall be perpendicular to the given straight line AB . Join

CF ...

Side 67

In obtuse - angled triangles , if a perpendicular be

angles to the opposite side produced , the square on the side subtending the

obtuse angle is greater than the squares on the sides containing the obtuse

angle ...

In obtuse - angled triangles , if a perpendicular be

**drawn**from either of the acuteangles to the opposite side produced , the square on the side subtending the

obtuse angle is greater than the squares on the sides containing the obtuse

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.