## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, The Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfthMathew Carey, and sold by J. Conrad & Company, S. F. Bradford, Birch & Small, and Samuel Etheridge. Printed by T. & G. Palmer, 116, High-Street., 1806 - 518 sider |

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Resultat 1-5 av 6

Side 483

4 , 5 , 6 , 7. and NO the sine , OM the versed sine , MP the tangent , and BP the

secant of the arch MN , according to the same definitions . Since CD , NO , AE ,

MP are parallel , CD is to NO as the

...

4 , 5 , 6 , 7. and NO the sine , OM the versed sine , MP the tangent , and BP the

secant of the arch MN , according to the same definitions . Since CD , NO , AE ,

MP are parallel , CD is to NO as the

**radius**CB to the**radius**NB , and AE to MP as...

Side 484

I. FIG . 5 . IN a right angled plane triangle , if the hypothenuse be made

the sides become the sines of the angles opposite to them ; and if either side be

made

the ...

I. FIG . 5 . IN a right angled plane triangle , if the hypothenuse be made

**radius**,the sides become the sines of the angles opposite to them ; and if either side be

made

**radius**, the remaining side is the tangent of the angle opposite to it , andthe ...

Side 502

therefore AF is the tangent of the arch AČ ; and in the rectilineal triangle AEF ,

having a right angle at A , AE will be to the

angle AEF ( 1. Pl . Tr . ) ; but AE is the sine of the arch AB , and AF the tangent of

the ...

therefore AF is the tangent of the arch AČ ; and in the rectilineal triangle AEF ,

having a right angle at A , AE will be to the

**radius**as AF to the tangent of theangle AEF ( 1. Pl . Tr . ) ; but AE is the sine of the arch AB , and AF the tangent of

the ...

Side 504

And since by this proposition the co - sine of the hypothenuse BC is to the

as the co - tangent of the angle ABC to the tangent of the angle ACB . But as the

...

And since by this proposition the co - sine of the hypothenuse BC is to the

**radius**as the co - tangent of the angle ABC to the tangent of the angle ACB . But as the

**radius**is to the co - tangent of the angle ACB , so is the tangent of the same to the...

Side 512

IN right angled plain triangles , the hypothenuse is to the

the hypothenuse above either of the sides to the versed sine of the acute angle

adjacent to that side , or as the sum of the hypothenuse , and either of the sides ...

IN right angled plain triangles , the hypothenuse is to the

**radius**, as the excess ofthe hypothenuse above either of the sides to the versed sine of the acute angle

adjacent to that side , or as the sum of the hypothenuse , and either of the sides ...

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The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Robert Simson Ingen forhåndsvisning tilgjengelig - 2017 |

### Vanlige uttrykk og setninger

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### Populære avsnitt

Side 30 - Any two sides of a triangle are together greater than the third side.

Side 64 - 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 30 - IF, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle. Let...

Side 59 - PROP. VIII. THEOR. IF a straight line be divided into any two parts, tour 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 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.

Side 165 - 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 19 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.

Side 191 - In right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar, and similarly described figures upon the sides containing the right angle.

Side 39 - 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 sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.

Side 180 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.