## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Corrected |

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Side 15

Which was to be demonstrated . PROP . V.

isosceles triangle are equal to one another : and , if the equal sides be produced

, the angles upon the other side of the base shall be equal . Let ABC be ...

Which was to be demonstrated . PROP . V.

**THEOR**. Tue angles at the base of anisosceles triangle are equal to one another : and , if the equal sides be produced

, the angles upon the other side of the base shall be equal . Let ABC be ...

Side 16

subtend , or are opposite to , the equal angles , shall be equal to one another .

Let ABC be a triangle having the anglo ABC equal to the angle ACB ; the side AB

...

**THEOR**. Ir two angles of a triangle be equal to one another , the sides also whichsubtend , or are opposite to , the equal angles , shall be equal to one another .

Let ABC be a triangle having the anglo ABC equal to the angle ACB ; the side AB

...

Side 17

triangles that have their sides which are terminated in one extremity of the base

equal to one another , and likewise those which are terminated in the other ...

**THEOR**. UPON the same base , and on the same side of it , there cannot be twotriangles that have their sides which are terminated in one extremity of the base

equal to one another , and likewise those which are terminated in the other ...

Side 18

other , each to each , and have likewise their bases equal ; the angle which is

contained by the two sides of the one shall be equal to the angle contained by

the two ...

**THEOR**. 1 If two triangles have two sides of the one equal to two sides of theother , each to each , and have likewise their bases equal ; the angle which is

contained by the two sides of the one shall be equal to the angle contained by

the two ...

Side 23

And , in like manner , it may be demonstrated that no other can be in the same

straight line with it but BD , which therefore is in the same straight line with CB .

Wherefore , if at a point , & c . Q. E. D. PROP . XV .

And , in like manner , it may be demonstrated that no other can be in the same

straight line with it but BD , which therefore is in the same straight line with CB .

Wherefore , if at a point , & c . Q. E. D. PROP . XV .

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The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2015 |

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2016 |

The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2018 |

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added altitude angle ABC angle BAC base BC is given centre circle circle ABCD circumference common cone contained 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 prism produced PROP proportionals proposition pyramid Q. E. D. PROP 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