## The Elements of Euclid |

### Inni boken

Resultat 1-5 av 19

Side 29

ABC , BCA , CAB , are together equal to two

draw CE parallel ( 31 . 1 . ) to the E straight line AB ; and because AB is parallel

to CE and AC meets them , the alternate angles BAC , ACE are equal ( 29 . 1 . ) ...

ABC , BCA , CAB , are together equal to two

**right angles**. Through the point Cdraw CE parallel ( 31 . 1 . ) to the E straight line AB ; and because AB is parallel

to CE and AC meets them , the alternate angles BAC , ACE are equal ( 29 . 1 . ) ...

Side 47

CE at

through E draw ( 31 . 1 . ) EF parallel to AB , and through D draw DF , parallel to

CE : and because the straight line EF meets the parallels EC , FD , the angles

CEF ...

CE at

**right angles**to AB : and make it equal to AC , or CB , and join AE , EB ;through E draw ( 31 . 1 . ) EF parallel to AB , and through D draw DF , parallel to

CE : and because the straight line EF meets the parallels EC , FD , the angles

CEF ...

Side 73

In a circle , the angle in a semicircle is a

greater than a semicircle is less than a ... to the two angles ABC , ACB ; therefore

the angle BAC is equal to the angle FAC , and each of them is therefore a right ...

In a circle , the angle in a semicircle is a

**right angle**; but the angle in a segmentgreater than a semicircle is less than a ... to the two angles ABC , ACB ; therefore

the angle BAC is equal to the angle FAC , and each of them is therefore a right ...

Side 89

angle FLC : and because KC is equal to CL , KL is double of KC : in the same

manner , it may be shown that HK is double of ... and the

C K D the

one ...

angle FLC : and because KC is equal to CL , KL is double of KC : in the same

manner , it may be shown that HK is double of ... and the

**right angle**FHC equal toC K D the

**right angle**FKC ; in the triangles FHC , FKC there are two angles ofone ...

Side 162

them is a

again , because A ... make

plane : but DC is in the plane passing through . E BD , DA , because all three are

in ...

them is a

**right angle**; therefore the base AD is equal ( 4 . 1 . ) to the base BE :again , because A ... make

**right angles**with every straight line meeting it in thatplane : but DC is in the plane passing through . E BD , DA , because all three are

in ...

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### Vanlige uttrykk og setninger

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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.