## The Elements of Euclid |

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Side 386

A straight line AE, touching the circle at A, one extremity of the arch AC, and

meeting the diameter BC passing through the other extremity C in E, is called the

the ...

A straight line AE, touching the circle at A, one extremity of the arch AC, and

meeting the diameter BC passing through the other extremity C in E, is called the

**Tangent**of the arch AC; or of the angle ABC. VII. The straight line BE, betweenthe ...

Side 387

given angle, will each contain a given number of these parts; and, by

trigonometrical tables, the length of the sine, versed sine,

any angle, may be found in parts of which the radius contains a given number;

and, vice ...

given angle, will each contain a given number of these parts; and, by

trigonometrical tables, the length of the sine, versed sine,

**tangent**, and secant, ofany angle, may be found in parts of which the radius contains a given number;

and, vice ...

Side 403

11); therefore AF is the

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

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

11); 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 the angleAEF (1. Pl. Tr.); but AE is the sine of the arch AB, and AF the

**tangent**of the arch ... Side 404

Let ABC be a spherical triangle, having a right angle at A; the co-sine of the

hypothenuse BC will be to the radius, as the co-

meet ...

Let ABC be a spherical triangle, having a right angle at A; the co-sine of the

hypothenuse BC will be to the radius, as the co-

**tangent**of the angle ABC to the**tangent**of the angle ACB. Describe the circle DE, of which B is the pole, and let itmeet ...

Side 411

For, by 17, the sine of BA is to the radius, as the

the angle B; and by 17, and inversion, the radius is to the sine of AD, ... THE co-

sines of the vertical angles are reciprocally proportional to the

sides.

For, by 17, the sine of BA is to the radius, as the

**tangent**of AC to the**tangent**ofthe angle B; and by 17, and inversion, the radius is to the sine of AD, ... THE co-

sines of the vertical angles are reciprocally proportional to the

**tangents**of thesides.

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

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

### Vanlige uttrykk og setninger

altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given point given ratio given straight line gles gnomon join less Let ABC meet multiple parallel parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third three plane angles triangle ABC triplicate ratio vertex wherefore

### Populære avsnitt

Side 45 - Ir 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 41 - 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 54 - Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle.

Side 18 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC.

Side 10 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line: it is required to draw from the point A a straight line equal to BC.

Side 8 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 256 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.

Side 129 - 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 23 - At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...

Side 20 - ANY two angles of a triangle are together less than two right angles.