## Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement on the Quadrature of the Circle and the Geometry of Solids ... |

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Side 23

Ax . ) BG : But it has been shewn that BC is equal to BG ;

are each of them equal to BG ; and things that are equal to the same are equal to

one another ; therefore the straight line AL is equal to BC .

Ax . ) BG : But it has been shewn that BC is equal to BG ;

**wherefore**AL and BCare each of them equal to BG ; and things that are equal to the same are equal to

one another ; therefore the straight line AL is equal to BC .

**Wherefore**, from the ... Side 24

... the angle BAC is equal to the angle EDF ;

coincide with the point F , because AC is equal to DF : But the point B coincides

with the point E ;

def . 3. ) ...

... the angle BAC is equal to the angle EDF ;

**wherefore**also the point C shallcoincide with the point F , because AC is equal to DF : But the point B coincides

with the point E ;

**wherefore**the base BC shall coincide with the base EF ( cor .def . 3. ) ...

Side 25

remainder CG ; and FC was proved to be equal to GB , therefore the two sides BF

, FC are equal to the two CG , GB , each to each ; but the angle BFC is equal to

the angle CGB ;

remainder CG ; and FC was proved to be equal to GB , therefore the two sides BF

, FC are equal to the two CG , GB , each to each ; but the angle BFC is equal to

the angle CGB ;

**wherefore**the triangles BFC , CGB are equal ( 3. 1. ) , and their ... Side 27

... and likewise their sides terminated in the other extremity ; but this is impossible

( 7. 1. ) ; therefore , if the base BC coincides with the base EF , the sides BA , AC

cannot but coincide with the sides ED , DF ;

... and likewise their sides terminated in the other extremity ; but this is impossible

( 7. 1. ) ; therefore , if the base BC coincides with the base EF , the sides BA , AC

cannot but coincide with the sides ED , DF ;

**wherefore**likewise the angle BAC ... Side 30

Ax . ) to one another ; therefore the angles CBE , EBD are equal to the angles

DBA , ABC ; but CBE , EBD , are two right angles ; therefore DBA , ABC are

together equal to two right angles .

Q. E. D. upon ...

Ax . ) to one another ; therefore the angles CBE , EBD are equal to the angles

DBA , ABC ; but CBE , EBD , are two right angles ; therefore DBA , ABC are

together equal to two right angles .

**Wherefore**, ' when a straight line , & c .Q. E. D. upon ...

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Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1836 |

Elements of Geometry: Containing the First Six Books of Euclid : with a ... John Playfair Uten tilgangsbegrensning - 1837 |

Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1854 |

### Vanlige uttrykk og setninger

ABCD altitude angle ABC angle BAC arch base bisected Book called centre circle circle ABC circumference coincide common cosine cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular Euclid exterior extremity fall fore four fourth given given straight line greater half inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism produced PROP proportionals proposition proved Q. E. D. PROP radius ratio reason rectangle contained rectilineal figure right angles segment shewn sides similar sine solid square straight line taken tangent THEOR thing third touches triangle ABC wherefore whole

### Populære avsnitt

Side 153 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle...

Side 19 - 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 to the circumference, are equal to one another.

Side 33 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.

Side 292 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...

Side 308 - 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 36 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.

Side 18 - 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 78 - To draw a straight line from a given point, either without or in the circumference, which shall touch a given circle. First, let A be a given point without the given circle BCD : it is required to draw a straight line from A which shall touch the circle.

Side 77 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...

Side 39 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the too interior angles upon the same side together equal to two right angles.