## The Elements of Euclid |

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Side 386

The

DA of the diameter passing through A, one extremity of the arch AC, between the

The

**Sine**of a quadrant, or of a right angle, is equal to the radius. V The segmentDA of the diameter passing through A, one extremity of the arch AC, between the

**sine**CD and that extremity, is called the Versed**Sine**of the arch AC, or angle ... Side 403

Pl. Tr.); but AE is the

the angle AEF is the inclination of the planes CBD, ABD (6. des. 11.), or the

spherical angle ABC: therefore the

tangent ...

Pl. Tr.); but AE is the

**sine**of the arch AB, and AF the tangent of the arch AC, andthe angle AEF is the inclination of the planes CBD, ABD (6. des. 11.), or the

spherical angle ABC: therefore the

**sine**of the arch AB is to the radius, as thetangent ...

Side 405

In right angled spherical triangles, the co-

radius, as the co-

same construction remaining; in the triangle CEF, the

is to ...

In right angled spherical triangles, the co-

**sine**of either of the sides is to theradius, as the co-

**sine**of the hypothenuse is to the co-**sine**of the other side. Thesame construction remaining; in the triangle CEF, the

**sine**of the hypothenuse CFis to ...

Side 410

of BC is to the

wherefore (11. 5.) the

of AB to the

, ...

of BC is to the

**sine**of the angle A as the**sine**of AB to the**sine**of the angle C;wherefore (11. 5.) the

**sine**of the side AC is to the**sine**of the angle B, as the**sine**of AB to the

**sine**of the angle C. Secondly, Let BCD be an oblique angled triangle, ...

Side 411

For, by 17, the

the angle B; and by 17, and inversion, the radius is to the

tangent of D to the tangent of AC: therefore, ex æquo perturbate, the

to the ...

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, as thetangent of D to the tangent of AC: therefore, ex æquo perturbate, the

**sine**of BA isto the ...

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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1834 |

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.