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

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Page 456

The

The

**Sine**of a quadrant , or of a right angle , is equal to the radius . V. The segment DA 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 ... Page 457

The

The

**sine**, tangent , and secant of any angle ABC , are likewise the**sine**, tangent , and secant of its supplement CBF . It is manifest from def . 4. that CD is the**sine**of the angle CBF . Let CB be produced till it meet the circle again ... Page 458

Let HK be the tangent , CL or DB , which is equal to it , the

Let HK be the tangent , CL or DB , which is equal to it , the

**sine**, and BK the secant of CBH , the complement of ABC , according to def . 4. 6. 7. HK is called the cotangent , BD the cosine , and BK the cosecant , of the angle ABC . Page 459

1. for if the hypothenuse be made radius , the sides are the sines of the angles opposite to them , and the radius is the

1. for if the hypothenuse be made radius , the sides are the sines of the angles opposite to them , and the radius is the

**sine**of a right angle ( cor . to def . 4. ) which is opposite to the hypothenuse . In any oblique angled triangle ... Page 461

1. as radius to the

1. as radius to the

**sine**of BAD , which is the complement of the angle ABC ; that is , as radius to the cosine of ABC . PROP . VI . Fig . 11 . In any triangle ABC , whose two sides are AB , AC , and base BC , the rectangle contained by ...### What people are saying - Write a review

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The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid No preview available - 2018 |

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