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

### Inni boken

Resultat 1-5 av 5

Side 53

The area of a

parts in the side of the

inches , contains in its area 144

number is ...

The area of a

**square**is found numerically by multiplying the number of equalparts in the side of the

**square**by itself . Thus a**square**whose side is twelveinches , contains in its area 144

**square**inches . Hence in arithmetic , when anumber is ...

Side 58

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

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 59

In any right - angled triangle , the

subtending , or opposite to , the right angle , is equal to the squarcs described

upon the sides containing the right angle . Con . - - P . 46 , P . 31 , Pst . 1 - - DEM .

- - Def .

In any right - angled triangle , the

**square**which is described upon the sidesubtending , or opposite to , the right angle , is equal to the squarcs described

upon the sides containing the right angle . Con . - - P . 46 , P . 31 , Pst . 1 - - DEM .

- - Def .

Side 60

If the sides of a rt . angled a be given in numbers , its hypotenuse may be found :

for set the Os of the sides be added together , and the

will be the hypotenuse . ” Suppose AB the base , AC the perpendicular , BC the ...

If the sides of a rt . angled a be given in numbers , its hypotenuse may be found :

for set the Os of the sides be added together , and the

**square**root of their sumwill be the hypotenuse . ” Suppose AB the base , AC the perpendicular , BC the ...

Side 63

I In A ABC let the

then the < BAC is a rt . angle . C . 1 by P . 11 . At . A draw AD at rt . angles with AC

; 2 P . 3 & Pst . I make AD = AB , and join D , C , 3 Sol . then the BAC is a rt .

I In A ABC let the

**square**on BC = the sum of the squares on AB and AC ; 2 Conc .then the < BAC is a rt . angle . C . 1 by P . 11 . At . A draw AD at rt . angles with AC

; 2 P . 3 & Pst . I make AD = AB , and join D , C , 3 Sol . then the BAC is a rt .

### 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.