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

### Inni boken

Resultat 1-5 av 5

Side 49

11 Rec . Therefore ,

— 1 The equality denoted is equality of surface , or area , not equality of sides

and angles . APP . - In the measurement of Surfaces or Areas , the unit of Surface

is ...

11 Rec . Therefore ,

**Parallelograms**upon the same base , & c . Q . E . D . SCH .— 1 The equality denoted is equality of surface , or area , not equality of sides

and angles . APP . - In the measurement of Surfaces or Areas , the unit of Surface

is ...

Side 54

41 is , — If a

or equal bases upon the same straight line and towards the same parts ; they

shall be between the same parallels . APP . - The general method for finding the

...

41 is , — If a

**parallelogram**is double of a triangle , and they have the same base ,or equal bases upon the same straight line and towards the same parts ; they

shall be between the same parallels . APP . - The general method for finding the

...

Side 55

THEOR , The complements of the

any

1 Hyp . 1 . | Let ABCD be a O , and AC A HI its diameter , , 2 . EH and GF Os ...

THEOR , The complements of the

**parallelograms**which are about the diameter ofany

**parallelogram**, are equal to one another . DEM . — P . 34 , Ax . 2 , Ax . 8 . E .1 Hyp . 1 . | Let ABCD be a O , and AC A HI its diameter , , 2 . EH and GF Os ...

Side 56

Therefore , to the st . line AB the

proposition contains a kind of Geometrical Division . Arithmetically we can say , a

given triangle contains , for example , 20 square feet , - a given line 4 lineal feet ...

Therefore , to the st . line AB the

**parallelogram**, & c . Q . E . D ) . App . - Thisproposition contains a kind of Geometrical Division . Arithmetically we can say , a

given triangle contains , for example , 20 square feet , - a given line 4 lineal feet ...

Side 57

FG is in the same st . line with GL . 16 ) C . 2 & 3 ] And : : : KF | | HG , and HG | |

ML ; 17 P . 30 . 1 : KF is parallel to ML : 18 ! C . 2 & 3 ] Also KM is parallel to FL ;

19 Def . A . 1 . : . fig . KFLM is a

...

FG is in the same st . line with GL . 16 ) C . 2 & 3 ] And : : : KF | | HG , and HG | |

ML ; 17 P . 30 . 1 : KF is parallel to ML : 18 ! C . 2 & 3 ] Also KM is parallel to FL ;

19 Def . A . 1 . : . fig . KFLM is a

**parallelogram**. . 20 C . 2 & 3 And : A ABD = D HF...

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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.