## Euclid's plane geometry, practically applied; book i, with explanatory notes, by H. Green |

### Inni boken

Resultat 1-5 av 5

Side 11

... is the opening of two lines from their point of me that point being the vertex . ei

9 . A plane

inclination of two straight lines to one another , which meet together , but are not

in the ...

... is the opening of two lines from their point of me that point being the vertex . ei

9 . A plane

**rectilineal**angle ( reclus , straight , and linea , a thread ) , is theinclination of two straight lines to one another , which meet together , but are not

in the ...

Side 13

Trilateral figures , ( trilaterus , three sided ) , or Triangles ( triangulus , three

cornered ) , are bounded by three straight lines . All other

be ...

**Rectilineal**figures are those which are bounded by right or straight lines . 21 .Trilateral figures , ( trilaterus , three sided ) , or Triangles ( triangulus , three

cornered ) , are bounded by three straight lines . All other

**rectilineal**figures maybe ...

Side 35

... the first ; - - for equality of angles , according to Def . 1 , bk . vi . , is essential to

similarity of figure . PROP . 23 . - PROB . At a given point in a given line to make a

... the first ; - - for equality of angles , according to Def . 1 , bk . vi . , is essential to

similarity of figure . PROP . 23 . - PROB . At a given point in a given line to make a

**rectilineal**angle equal to a given**rectilineal**angle , Sol . - Pst . 1 , P . 22 . - DEM . Side 45

Wherefore , if a side of a triangle be produced , & c . Q . E . D ) COR . I . - All the

interior angles of any

twice as many rt . angles as the figure has sides . DEM . — P . 32 , P 15 , Cor .

Wherefore , if a side of a triangle be produced , & c . Q . E . D ) COR . I . - All the

interior angles of any

**rectilineal**figure , together with four rt . angles , are equal totwice as many rt . angles as the figure has sides . DEM . — P . 32 , P 15 , Cor .

Side 63

A few only of the properties of the circle are mentioned : those of the straight line

and

and all

A few only of the properties of the circle are mentioned : those of the straight line

and

**rectilineal**angle are subservient to the proof of the properties of the triangle ;and all

**rectilineal**figures are either triangles , or may be resolved into triangles .### Hva folk mener - Skriv en omtale

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### Vanlige uttrykk og setninger

ABCD added angle equal apply ascertain assumed Axioms base base BC bisected centre circle circumference coincide common Conc construct contained definition demonstration describe diagonal diameter distance divided draw drawn earth's equal Euclid extremity fall feet figure four Geometry given given point greater half height impossible inches inference intersect join length less line BC measure meet miles named object opposite parallel parallelogram perpendicular plane practical principle produced Prop proposition proved reason rectangle rectil rectilineal representative right angles scale sides square straight line suppose surface thing third triangle true truth units Wherefore whole

### Populære avsnitt

Side 36 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.

Side 17 - If a straight line meets 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 17 - Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same are equal to one another.

Side 41 - We assume that but one straight line can be drawn through a given point parallel to a given straight line.

Side 13 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.

Side 16 - LET it be granted that a straight line may be drawn from any one point to any other point.

Side 54 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Side 21 - If two angles of a triangle be equal to one another, the sides also which subtend, or are opposite to, the equal angles, shall be equal to one another.

Side 22 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base, equal to one another, and likewise those which are terminated in the other extremity.

Side 12 - 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.