## The Elements of Euclid |

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Resultat 1-5 av 15

Side 57

Let ABCD be a

which is not the centre ; let the centre be E ; of all the straight lines FB , FC , FG , &

c . that can be drawn from F to the circumference , FA is the greatest , and FD , the

...

Let ABCD be a

**circle**, and AD its diameter , in which let any point E be takenwhich is not the centre ; let the centre be E ; of all the straight lines FB , FC , FG , &

c . that can be drawn from F to the circumference , FA is the greatest , and FD , the

...

Side 61

One

the inside or outside . * For , if it be possible , let the

ABC in more points than one , and first on the inside , in the points B , D ; join BD

...

One

**circle**cannot touch another in more points than one , whether it touches it onthe inside or outside . * For , if it be possible , let the

**circle**EBF touch the**circle**ABC in more points than one , and first on the inside , in the points B , D ; join BD

...

Side 81

A

of the

line , equal to a given straight line not greater than the diameter of the

A

**circle**is said to be described about a rectilineal figure , when the circumferenceof the

**circle**passes through all the angular ... In a given**circle**to place a straightline , equal to a given straight line not greater than the diameter of the

**circle**. Side 87

in the alternate segment of the

therefore the whole angle BDA is equal to the two angles CDA , DAC ; but the

exterior angle BCD is equal ( 32 . 1 . ) to the angles CDA , DAC ; therefore also

BDA is ...

in the alternate segment of the

**circle**; to each of these add the angle CDA :therefore the whole angle BDA is equal to the two angles CDA , DAC ; but the

exterior angle BCD is equal ( 32 . 1 . ) to the angles CDA , DAC ; therefore also

BDA is ...

Side 89

Let ABCDE be the given equilateral and equiangular pentagon : it is required to

inscribe a

by the straight lines CF , DF , and from the point F , in which they meet , draw the

...

Let ABCDE be the given equilateral and equiangular pentagon : it is required to

inscribe a

**circle**in the pentagon ABCDE . Bisect ( 9 . 1 . ) the angles BCD , CDEby the straight lines CF , DF , and from the point F , in which they meet , draw the

...

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### Populære avsnitt

Side 36 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.

Side 145 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.

Side 65 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.

Side 248 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.

Side 11 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.

Side 121 - 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 21 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 14 - To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third (20.

Side 80 - 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. either the sides adjacent to the equal...

Side 133 - ... rectilineal figures are to one another in the duplicate ratio of their homologous sides.