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

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Resultat 1-5 av 5

Side 4

It is of great advantage to have stored in the memory the very words of the

to associate with the words the numbers , as

4 , 8 ...

It is of great advantage to have stored in the memory the very words of the

**Definitions**, Postulates and Axioms , and of the more important Propositions ; andto associate with the words the numbers , as

**Definition**15 , Axiom 8 , Proposition4 , 8 ...

Side 6

A

such of its properties as serve to distinguish it from all other things of the same

kind . 7 A Postulate ( from postulatum , a thing demanded ) , is a self - evident ...

A

**Definition**( from definire , to set bounds to ) , is a short description of a thing bysuch of its properties as serve to distinguish it from all other things of the same

kind . 7 A Postulate ( from postulatum , a thing demanded ) , is a self - evident ...

Side 8

The first kind of evidence is from the

triangle to be a figure bounded by three sides ; and if , of any figure placed before

us , we can affirm , that it has three sides exactly , the conclusion is inevitable ,

that ...

The first kind of evidence is from the

**definition**of the thing ; thus , we**define**atriangle to be a figure bounded by three sides ; and if , of any figure placed before

us , we can affirm , that it has three sides exactly , the conclusion is inevitable ,

that ...

Side 15

The least objectionable

solid , — that is , a magnitude which has length , breadth , and thickness , - in

order to understand aright the

The least objectionable

**definition**is that which , as Potts says ( p . ... to consider asolid , — that is , a magnitude which has length , breadth , and thickness , - in

order to understand aright the

**definitions**of a point , a line , and a superficies . Side 16

This Axiom is properly the

boundaries of one figure fall upon and cover all the parts and boundaries of

another figure , the two figures are equal . The name of Superposition is given to

this ...

This Axiom is properly the

**definition**of Geometrical equality . " If all the parts andboundaries of one figure fall upon and cover all the parts and boundaries of

another figure , the two figures are equal . The name of Superposition is given to

this ...

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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.