## Euclid's Elements [book 1-6] with corrections, by J.R. Young |

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Side 137

When two magnitudes are compared together , in reference to the enquiry

whetber the first is contained in the second , or in a multiple of the second , the

former is called an antecedent , and the latter its

it is ...

When two magnitudes are compared together , in reference to the enquiry

whetber the first is contained in the second , or in a multiple of the second , the

former is called an antecedent , and the latter its

**consequent**. Such comparison ,it is ...

Side 138

A line and surface can never , therefore , stand in the relation of antecedent and

two , an antecedent cannot be contained in any multiple of its

...

A line and surface can never , therefore , stand in the relation of antecedent and

**consequent**. VII . Magnitudes are proportional when , being compared two andtwo , an antecedent cannot be contained in any multiple of its

**consequent**oftener...

Side 142

If in any proportion an antecedent and its

as an antecedent and its

antecedent and con . sequent of the one will , with the remaining antecedent and

...

If in any proportion an antecedent and its

**consequent**be respectively the sameas an antecedent and its

**consequent**in another proportion , the remainingantecedent and con . sequent of the one will , with the remaining antecedent and

...

Side 143

Consequently , C is contained in nD , a multiple of its

is contained in nB , a like multiple of its

impossible . Therefore , if mA be greater than nB , mC must be greater than nD ;

and in ...

Consequently , C is contained in nD , a multiple of its

**consequent**, oftener than Ais contained in nB , a like multiple of its

**consequent**, which ( def . 7 ) isimpossible . Therefore , if mA be greater than nB , mC must be greater than nD ;

and in ...

Side 147

In a proportion according as one antecedent is greater than , less than , or equal

to its

equal to its

In a proportion according as one antecedent is greater than , less than , or equal

to its

**consequent**, so will the other antecedent be greater than , less than , orequal to its

**consequent**. Let the proportion be A : B : : C : D . It has already been ...### Hva folk mener - Skriv en omtale

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Euclid's Elements [Book 1-6] with Corrections, by J.R. Young Euclides Ingen forhåndsvisning tilgjengelig - 2018 |

Euclid's Elements [Book 1-6] with Corrections, by J.R. Young Euclides Ingen forhåndsvisning tilgjengelig - 2015 |

### Vanlige uttrykk og setninger

ABCD alternate angle ABC angle ACB angle BAC antecedent base base BC bisected Book called centre circle circle ABC circumference common consequent Const demonstrated describe diameter difference divided double draw drawn equal angles equiangular equilateral equimultiples exterior angle extremity fall fore four Geometry given straight line greater half Hence inscribed join less Let ABC logarithm magnitudes manner measure meet multiple parallel parallelogram pass perpendicular PROB produced PROP proportion proposition proved radius reason rectangle contained rectilineal figure remaining remaining angle right angles segment sides similar sine square square of AC taken tangent term THEOR third touches the circle triangle ABC wherefore whole

### Populære avsnitt

Side 30 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.

Side 105 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.

Side 50 - 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 61 - If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.

Side 65 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Side 70 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.

Side 41 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 172 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Side 45 - TRIANGLES upon the same base, and between the same parallels, are equal to one another.

Side 38 - If a, straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles.