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

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Side 215

In order , therefore , actually to construct our angle , we have only to draw any

straight line AB for one of its sides , and from A , the point intended for the vertex ,

to describe with any

...

In order , therefore , actually to construct our angle , we have only to draw any

straight line AB for one of its sides , and from A , the point intended for the vertex ,

to describe with any

**radius**AB , a circle , and then to take BC equal to the twelfth...

Side 219

Thus , when the angle is 0 the sine is 0 ; and it increases with the angle till this

becomes 90° , when the sine attains its greatest value , and becomes equal to

the

gradually ...

Thus , when the angle is 0 the sine is 0 ; and it increases with the angle till this

becomes 90° , when the sine attains its greatest value , and becomes equal to

the

**radius**, or , in numbers , to unity . As the angle , becoming now obtuse ,gradually ...

Side 224

to it , and whose base ( the

tangent ( see fig . 1 , above , ) and for its hypothenuse the secant of the given

angle ; so that we must multiply the given base by the tangent of the given angle

to get ...

to it , and whose base ( the

**radius**) is unity , will bave for its perpendicular thetangent ( see fig . 1 , above , ) and for its hypothenuse the secant of the given

angle ; so that we must multiply the given base by the tangent of the given angle

to get ...

Side 227

If we take CD for our geometrical

, and DA the tangent of DCA ; therefore AB is the difference of those tangents .

But by referring to the table of natural tangents , we find that , to

...

If we take CD for our geometrical

**radius**, DB will be the tangent of the angle DCB, and DA the tangent of DCA ; therefore AB is the difference of those tangents .

But by referring to the table of natural tangents , we find that , to

**radius**1 , tan 56°...

Side 228

whereas , according to the scale

the length of that scale , we have the proportion •8433752 : 100 : : 1 : 118 . 57 =

CD . 2 . At the top of a castle which stood on a hill near the sea - shore , the angle

...

whereas , according to the scale

**radius**= CD , it is 100 ; hence , for determiningthe length of that scale , we have the proportion •8433752 : 100 : : 1 : 118 . 57 =

CD . 2 . At the top of a castle which stood on a hill near the sea - shore , the angle

...

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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.