## The Elements of Euclid |

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Page 482

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 483

Since CD , NO , AE , MP are parallel , CD is to NO as the

Since CD , NO , AE , MP are parallel , CD is to NO as the

**radius**CB to the**radius**NB , and AE to MP as AB to BM , and BC or BA to BD as BN or BM to BO ; and , by conversion , DA to MO as AB to MB . Hence the corol . lary is manifest ... Page 484

IN a right angled plane triangle , if the hypothenuse be made

IN a right angled plane triangle , if the hypothenuse be made

**radius**, the sides become the sines of the angles opposite to them ; and if either side be made**radius**, the remaining side is the tangent of the angle opposite to it ... Page 485

... semicircle is a right angie ( 1. of this ) FB being

... semicircle is a right angie ( 1. of this ) FB being

**radius**, BE , BG , are the tangents of the angles EFB , 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. Page 486

And because BAD is a right angle , BA the less side is to AD or AC the greater , as the

And because BAD is a right angle , BA the less side is to AD or AC the greater , as the

**radius**is to the tangent of the angle ABD ; and because BGD is a right angle , BG is to GD or GF as the ...### What people are saying - Write a review

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### Other editions - View all

The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid No preview available - 2015 |

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Robert Simson,Robert Euclid No preview available - 2016 |

### Common terms and phrases

added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples 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 prisms produced PROP proportionals proposition pyramid radius reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole