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

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Page 456

Whatever be the

Whatever be the

**radius**of the circle of which the measure of a given angle is an arch , that arch will contain the same number of degrees , minutes , seconds , & c . as is manifest from Lemma 2 . III . Let AB be produced till it meet ... Page 457

4 . 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

4 . 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 the**radius**of ... Page 458

The

The

**radius**is a mean proportional between the tangent and cotangent . For , since HK , BA , are parallel , the angles HKB , ABC , will be equal , and the angles KHB , BAE , are right ; therefore the triangles BAE , KHB , are similar ... Page 459

1. for if the hypothenuse be made

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 460

... ( 1. of this ) FB being

... ( 1. of this ) FB being

**radius**, BE , BG , are the tangents of the angles EFR , BFG ; but it is manifest that EC is the sum of the sides BA , AC , and CF their difference ; and since BC , FG are parallel ( 2. 6. ) ...### 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 |

### Common terms and phrases

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