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

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Page 68

X. A sector of a circle is the figure contained by two straight lines drawn from the centre , and the circumference between them . XI .

X. A sector of a circle is the figure contained by two straight lines drawn from the centre , and the circumference between them . XI .

**Similar**segments of circles are those in which 68 EUCLID'S ELEMENTS . Page 69

**Similar**segments of circles are those in which the angles are equal , or which contain equal angles . PROP . I. PROB . # * 10.1 . * 11.1 . To find the centre of a given circle . Let ABC be the given circle ; it is required to find its ... Page 89

Upon the same straight line , and upon the same side of it , there cannot be two

Upon the same straight line , and upon the same side of it , there cannot be two

**similar**segments of circles , not coinciding with one another . If it be possible , upon the same straight line 13 BOOK III . 89 PROP . XXII . Page 90

If it be possible , upon the same straight line AB , and upon the same side of it , let there be two

If it be possible , upon the same straight line AB , and upon the same side of it , let there be two

**similar**segments of circles , ACB , ADB , not coinciding with one another . Then , because the circle ACB cuts the circle ADB in the ... Page 91

Wherefore

Wherefore

**similar**segments , + 8 Ax , & c . Q. E. D. * 10. 1 . PROP . XXV . PROB . A segment of a circle being given , to describe the circle of which it is the segment . Let ABC be the given segment of a circle ; it is required to ...### 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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altitude angle ABC angle BAC base base BC BC is equal centre circle ABCD circumference common cone Const contained cylinder demonstrated described diameter divided double draw drawn equal angles equiangular equilateral equimultiples extremities fall figure fore four fourth given given straight line greater half inscribed join less Let ABC likewise magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced PROP proportionals proved pyramid ratio reason rectangle contained rectilineal figure remaining angle right angles segment shown sides similar solid solid angle solid parallelopiped sphere square taken THEOR third touches triangle ABC vertex wherefore whole