## The Elements of Euclid |

### Inni boken

Resultat 1-5 av 12

Side 87

To inscribe an equilateral and

ABCDE be the given circle ; it is required to inscribe an equilateral and

triangle FGH ...

To inscribe an equilateral and

**equiangular**pentagon in a given circle . LetABCDE be the given circle ; it is required to inscribe an equilateral and

**equiangular**pentagon in the circle ABCDE . Describe ( 10 . 4 . ) an isoscelestriangle FGH ...

Side 89

It is also

that the angle HKL is double of the angle FKC , and KLM double of FLC , as was

before demonstrated , the angle HKL is equal to KLM : and in like manner it may

...

It is also

**equiangular**; for , since the angle FKC is equal to the angle FLC , andthat the angle HKL is double of the angle FKC , and KLM double of FLC , as was

before demonstrated , the angle HKL is equal to KLM : and in like manner it may

...

Side 90

To describe a circle about a given equilateral and

ABCDE be the given equilateral and

describe a circle about it . Bisect ( 9 . 1 . ) the angles BCD , CDE by the straight

lines CF ...

To describe a circle about a given equilateral and

**equiangular**pentagon . LetABCDE be the given equilateral and

**equiangular**pentagon ; it is required todescribe a circle about it . Bisect ( 9 . 1 . ) the angles BCD , CDE by the straight

lines CF ...

Side 92

PROB . To inscribe an equilateral and

circle . * Let ABCD be the given circle ; it is required to inscribe an equi . lateral

and

equilateral ...

PROB . To inscribe an equilateral and

**equiangular**quindecagon , in a givencircle . * Let ABCD be the given circle ; it is required to inscribe an equi . lateral

and

**equiangular**quindecagon in the circle ABCD . Let AC be the side of anequilateral ...

Side 129

... wherefore the remaining angle BAC is equal to the remaining angle EGF ( 32 .

1 . ) , and the triangle ABC is therefore

consequently they have their sides opposite to the в equal angles proportionals (

4 .

... wherefore the remaining angle BAC is equal to the remaining angle EGF ( 32 .

1 . ) , and the triangle ABC is therefore

**equiangular**to the triangle GEF ; andconsequently they have their sides opposite to the в equal angles proportionals (

4 .

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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.