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

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Resultat 1-5 av 5

Side 10

The

that which lies evenly between its extreme points . “ A straight line is the shortest

distance between two points . " - ARCHIMEDES , adopted by LEGENDRE .

The

**Extremities**( extremus , outermost ) , of a line are points . 4 . A straight line isthat which lies evenly between its extreme points . “ A straight line is the shortest

distance between two points . " - ARCHIMEDES , adopted by LEGENDRE .

Side 23

... also be obtained by making an observation with a quadrant of altitude . SON

PROP . 7 . — THEOR . Upon the same base and upon the same side of it there

cannot be two triangles that have their sides which are terminated in one

... also be obtained by making an observation with a quadrant of altitude . SON

PROP . 7 . — THEOR . Upon the same base and upon the same side of it there

cannot be two triangles that have their sides which are terminated in one

**extremity**... Side 27

When the given point is at the

this proposition the Square is constructed , an instrument employed for

ascertaining the ...

When the given point is at the

**extremity**of a given line , the line from that**extremity**should be produced , and the rt . angle be then constructed . APP . - Bythis proposition the Square is constructed , an instrument employed for

ascertaining the ...

Side 60

... DE being each equal to AB , the square on AE is the multiple of the square on

AB . 39 . Let AB be the less , and AC the greater of the two lines ; at B the the

...

... DE being each equal to AB , the square on AE is the multiple of the square on

AB . 39 . Let AB be the less , and AC the greater of the two lines ; at B the the

**extremity**of the less , raise a perpendicular BG , and from A at the other**extremity**...

Side 61

... or links , & c . ; at one

other

, and the lines from A to C , and from A to B , are at rt . angles to each other .

... or links , & c . ; at one

**extremity**B , with 4 feet or links , draw an arc ; and at theother

**extremity**C , with three feet or links , another arc : the two arcs intersect in A, and the lines from A to C , and from A to B , are at rt . angles to each other .

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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.