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

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Resultat 1-5 av 5

Side 7

Direct Demonstration is when the very thing asserted is

Indirect Demonstration is when all other cases , or conditions , except the one in

question , are

thing ...

Direct Demonstration is when the very thing asserted is

**proved**to be true . :Indirect Demonstration is when all other cases , or conditions , except the one in

question , are

**proved**not to be true , and the inference is madetherefore the verything ...

Side 8

The Demonstrations in Euclid ' s Elements of Geometry consist of arguments by

which the assertions made in the propositions are

15th Prop . , bk . i . , the assertion is made that “ the opposite , or vertical angles ...

The Demonstrations in Euclid ' s Elements of Geometry consist of arguments by

which the assertions made in the propositions are

**proved**to be true . Thus , in the15th Prop . , bk . i . , the assertion is made that “ the opposite , or vertical angles ...

Side 9

... carried out completely , Inductive reasoning is that in which a universal

proposition is

Ls , A , B , C , and D are all the < s , in a certain figure ABCD ; we

rt .

... carried out completely , Inductive reasoning is that in which a universal

proposition is

**proved**by**proving**separately each of its particular cases : thus , theLs , A , B , C , and D are all the < s , in a certain figure ABCD ; we

**prove**that A is art .

Side 33

In like manner it may be

AB . 10 ' Conc . & R . Therefore any two sides of a triangle , & c . Q . E . D . OR ,

BN A c . ) by P . 9 . Let AE bisect _ BAC . D . 11 by P . 16 . : : : BEA is > _ EAC ,

and ...

In like manner it may be

**proved**that AB and BC are > AC , 9 , and BC and AC >AB . 10 ' Conc . & R . Therefore any two sides of a triangle , & c . Q . E . D . OR ,

BN A c . ) by P . 9 . Let AE bisect _ BAC . D . 11 by P . 16 . : : : BEA is > _ EAC ,

and ...

Side 39

Of the six parts of a triangle any three , except the three angles , being given

equal to one another , the equality of the other parts may be readily

. - 1 . The discovery of this Proposition is ascribed to THALES , who made use of

it ...

Of the six parts of a triangle any three , except the three angles , being given

equal to one another , the equality of the other parts may be readily

**proved**. APP. - 1 . The discovery of this Proposition is ascribed to THALES , who made use of

it ...

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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.