## The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; 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 |

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Resultat 1-5 av 5

Side 481

The sine , versed sine , tangent , and secant , of any arch which is the measure of

any given angle ABC , is to the sine , versed sine , tangent , and secant , of any

other arch which is the measure of the same angle , as the

...

The sine , versed sine , tangent , and secant , of any arch which is the measure of

any given angle ABC , is to the sine , versed sine , tangent , and secant , of any

other arch which is the measure of the same angle , as the

**radius**of the first is to...

Side 482

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 500

therefore AF is the tangent of the arch AC ; 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 AC ; 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 502

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 503

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...

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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1825 |

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Euclid,Robert Simson Uten tilgangsbegrensning - 1838 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base centre circle circle ABCD circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples Euclid excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid Q. E. D. PROP radius reason rectangle rectangle contained rectilineal figure remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole

### Populære avsnitt

Side 9 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 81 - The angles in the same segment of a circle are equal to one another.

Side 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Side 33 - 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 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.

Side 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Side 155 - 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 22 - ANY two angles of a triangle are together less than two right angles.

Side 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.

Side 24 - Any two sides of a triangle are together greater than the third side.