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

### Inni boken

Resultat 1-5 av 5

Side 16

Two st . lines which

. line . " - PLAYFAIR . An illustration , will make the axiom plainer . I . The CGH

angles DGH and GHF are less than two right angles , and CD , EF meet in K . II .

Two st . lines which

**intersect**one another , cannot be both parallel to the same st. line . " - PLAYFAIR . An illustration , will make the axiom plainer . I . The CGH

angles DGH and GHF are less than two right angles , and CD , EF meet in K . II .

Side 27

The properties of the circle form the subject of the third book , but in the

construction for the 12th Prop . . the Lemma is borrowed from Prop . 2 , bk . ill . ,

that the circle will

indispensable to ...

The properties of the circle form the subject of the third book , but in the

construction for the 12th Prop . . the Lemma is borrowed from Prop . 2 , bk . ill . ,

that the circle will

**intersect**the line in two points . USE . - This problem isindispensable to ...

Side 41

The principle really assumed in the twelfth axiom is that two st . lines which

THEOR . — ( Converse of the 27th , and the 28th . ) If a line fall upon two parallel

st ...

The principle really assumed in the twelfth axiom is that two st . lines which

**intersect**each other cannot both be parallel to the same st . line . PROP . 29 . —THEOR . — ( Converse of the 27th , and the 28th . ) If a line fall upon two parallel

st ...

Side 42

The Twelfth Aciom may be expressed in any of the following ways : - Two

diverging rt . lines cannot be both parallel to the same rt . line ; or , If a rt . line

one rt . line ...

The Twelfth Aciom may be expressed in any of the following ways : - Two

diverging rt . lines cannot be both parallel to the same rt . line ; or , If a rt . line

**intersect**one of two parallel rt . lines , it must also**intersect**the other : or , Onlyone rt . line ...

Side 46

... and at A an angle CAD of 450 : the lines BC and AC

and a perpendicular from C to BE , namely CD , will represent the perpendicular

height of the mountain , Take CD in the compasses , and apply the distance to

the ...

... and at A an angle CAD of 450 : the lines BC and AC

**intersect**in the point C ;and a perpendicular from C to BE , namely CD , will represent the perpendicular

height of the mountain , Take CD in the compasses , and apply the distance to

the ...

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### 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.