## 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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Side 481

The

any given angle ABC , is to the

other arch which is the measure of the same angle , as the radius of the first is to

...

The

**sine**, versed**sine**, tangent , and secant , of any arch which is the measure ofany given angle ABC , is to the

**sine**, versed**sine**, tangent , and secant , of anyother arch which is the measure of the same angle , as the radius of the first is to

...

Side 503

And since by this proposition the co -

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

...

And since by this proposition the co -

**sine**of the hypothenuse BC is to the radiusas 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 508

18. the

at A ) as the

18. the

**sine**of the hypothenuse BC is to the radius ( or the**sine**of the right angleat A ) as the

**sine**of the side AC to the**sine**of the angle B. And in like manner , the**sine**of BC is to the**sine**of the angle A , as the**sine**of AB to the**sine**of the ... Side 509

For , by 22. the co -

angle D to the

For , by 22. the co -

**sine**of the angle B is to the**sine**of the angle BCA as ( the co -**sine**of the side AC is to the radius ; that is , by prop . 22. , as ) the co -**sine**of theangle D to the

**sine**of the angle DCA ; and , by permutation , the co -**sine**of the ... Side 513

BE or AE therefore is the

perpendicular to AC , and AF will be the versed

because of the similar triangles CAE , BAF , CA is to AE , as AB , that is , twice AE

, to AF ...

BE or AE therefore is the

**sine**of the arch DB or AD , the half of AB : let BF beperpendicular to AC , and AF will be the versed

**sine**of the arch BA ; but ,because of the similar triangles CAE , BAF , CA is to AE , as AB , that is , twice AE

, to AF ...

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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.