## The Elements of Euclid |

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Page iii

ALSO , " THE BOOK OF EUCLID'S DATA , IN LIKE

ALSO , " THE BOOK OF EUCLID'S DATA , IN LIKE

**MANNER**CORRECTED . BY ROBERT SIMSON , M.D. Emeritus Profesor of Mathematics in the University of Glasgow . TO THIS LDITION ARE ALSO AXNESED , ELEMENTS OF PLANE AND SPHERICAL TRIGONOMETRY . Page vi

... be made evident in the notes subjoined to these Elements . In like

... be made evident in the notes subjoined to these Elements . In like

**manner**, in the demonstration of the 26th prop . of the 11th book , it is taken for granted , that those solid angles are equal to one another which are contained by ... Page 23

1 . line , the angle CBE is equal to the angle EBA ; in the same

1 . line , the angle CBE is equal to the angle EBA ; in the same

**manner**, because ABD is straight line , the angle DBE is equal to the angle EBA ; where . fore the angle DBE is equal to the angle CBE , the less to the greater ; which is ... Page 25

And , in like

And , in like

**manner**, it may be demonstrated , that no other can be in the same straight line witn it but BD , which therefore is in the same straight line with CB . Wherefore , if at a point , & c . Q. E.D. PROP . XV . THEOR . Page 26

... each to each , to which the equal sides are opposite ; wherefore the angle BAE is equal to the angle ECF ; but the angle ECD is greater than the angle LCF ; therefore the angle ACD is greater than BAE : in the same

... each to each , to which the equal sides are opposite ; wherefore the angle BAE is equal to the angle ECF ; but the angle ECD is greater than the angle LCF ; therefore the angle ACD is greater than BAE : in the same

**manner**, if 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