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

### Inni boken

Resultat 1-5 av 5

Side 6

An Axiom ( from axioma , a thing of worth ) , is a self - evident theorem , or the

assertion of a

soon as stated . A Proposition ( from proponere , to put forth ) , is something ...

An Axiom ( from axioma , a thing of worth ) , is a self - evident theorem , or the

assertion of a

**truth**, which does not need demonstration ; - it is worthy of credit assoon as stated . A Proposition ( from proponere , to put forth ) , is something ...

Side 8

... and the demonstration shows by argument , founded upon

admitted or proved , that the assertion itself ... things equal to the same thing are

equal to each other , ” - - this is one

the ...

... and the demonstration shows by argument , founded upon

**truths**alreadyadmitted or proved , that the assertion itself ... things equal to the same thing are

equal to each other , ” - - this is one

**truth**; “ the line AC equals the line AB , andthe ...

Side 9

... this mode of argument receives the name of a Syllogism ; ( from sullogismos , a

collection ) , for a Syllogism is a bringing together into one view the two steps of

the reasoning on which a

... this mode of argument receives the name of a Syllogism ; ( from sullogismos , a

collection ) , for a Syllogism is a bringing together into one view the two steps of

the reasoning on which a

**truth**depends , and the**truth**itself ; or , as Whately in ... Side 23

5 , is that in which we find intermediate steps , which proceed regularly to prove

the

when the predicate of it admits of an alternative , and one of them must be true ...

5 , is that in which we find intermediate steps , which proceed regularly to prove

the

**truth**of the proposition : the Indirect Method is only employed , as in Prop . 6 ,when the predicate of it admits of an alternative , and one of them must be true ...

Side 24

... or double Antecedent , in which the

the

antecedents ; and Whately , p . 72 , defines the true dilemma as “ a conditional

Syllogism ...

... or double Antecedent , in which the

**truth**of the one is impossible , if we admitthe

**truth**of the other . The dilemma may , however , have more than twoantecedents ; and Whately , p . 72 , defines the true dilemma as “ a conditional

Syllogism ...

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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.