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

### Inni boken

Resultat 1-5 av 5

Side 5

O

triangle . O circle . Oce circumference . A single capital letter , as A , or B , in

reference to a Diagram , denotes the point X , or the point B . Two capital letters ,

as ...

O

**rectangle**. 1 straight line . I perpendicular to . O parallelogram . 1 parallel to . Atriangle . O circle . Oce circumference . A single capital letter , as A , or B , in

reference to a Diagram , denotes the point X , or the point B . Two capital letters ,

as ...

Side 49

In the measurement of Surfaces or Areas , the unit of Surface is a

it is therefore necessary to convert all parallelograms which are not

into

In the measurement of Surfaces or Areas , the unit of Surface is a

**rectangle**; andit is therefore necessary to convert all parallelograms which are not

**rectangles**into

**rectangles**, in order to find their areas . The following method enables us to ... Side 56

Geometrically we say , a given

line BD , or its equal EH , 2 lineal feet ; how can we apply another

or EH measuring 2 lineal feet , so that the area of the required

Geometrically we say , a given

**rectangle**BC contains 12 square feet , - a givenline BD , or its equal EH , 2 lineal feet ; how can we apply another

**rectangle**to BDor EH measuring 2 lineal feet , so that the area of the required

**rectangle**may ... Side 58

LMNF is a

and is therefore equal in area to the triangle DHF . Η ΑΕ Prop . 46 . PROB . To

describe a square on a given st . line . SOL . . - P . 11 , P . 3 , P . 31 , Def . A . - -

DEM .

LMNF is a

**rectangle**of the same altitude as the triangle , and on half its base ,and is therefore equal in area to the triangle DHF . Η ΑΕ Prop . 46 . PROB . To

describe a square on a given st . line . SOL . . - P . 11 , P . 3 , P . 31 , Def . A . - -

DEM .

Side 62

36 , bk . iii . , the square of the tangent AB equals the

as in levelling the distances are usually small , AB ? = BL X EL nearly . When AB

is 1 mile , BL is f of 1 foot , or 8 inches ; , AB is 2 miles , BL is of 4 feet , or 32 , ...

36 , bk . iii . , the square of the tangent AB equals the

**rectangle**of BL into BÈ : andas in levelling the distances are usually small , AB ? = BL X EL nearly . When AB

is 1 mile , BL is f of 1 foot , or 8 inches ; , AB is 2 miles , BL is of 4 feet , or 32 , ...

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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.