## The Elements of Euclid |

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Page 482

“ A straight line CD drawn through C , one of the extremities of the arch AC perpendicular upon the diameter passing through the other extremity A , is called the

“ A straight line CD drawn through C , one of the extremities of the arch AC perpendicular upon the diameter passing through the other extremity A , is called the

**Sine**of the arch AC , or of the angle ABC , of which it is the measure . Page 483

The

The

**sine**, versed**sine**, tangent , and se .. cant , of any arch , which is the measure of any given angle ABC , is to the**sine**... CD the**sine**, DA the verged**sine**, AE the tangent and BE the secant of the arch AC , according to def . Page 484

Let ABC be a right angled triangle ; if the hypothenuse BC be made radius , either of the sides AC will be the

Let ABC be a right angled triangle ; if the hypothenuse BC be made radius , either of the sides AC will be the

**sine**of the angle ABC opposite to it ; and if either side BA be made ' radius , the other side AC will be the tangent of the ... Page 486

IN any triangle , twice the rectangle contained by any two sides is to the difference of the sum of the squares of these two sides , and the square of the base as the radius is to the co -

IN any triangle , twice the rectangle contained by any two sides is to the difference of the sum of the squares of these two sides , and the square of the base as the radius is to the co -

**sine**of the angle included by the two sides . Page 487

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 co -**sine**of ABC . PROP . VI . FIG . 11 : IN any triangle ABC , whose two sides are AB , AC , and base BC , the rectangle contained ...### 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