The Elements of Euclid |
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Page 17
... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal each to each , viz . the angle ABC to ...
... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal each to each , viz . the angle ABC to ...
Page 18
... angle FBC is equal to the angle GCB , and the angle BCF to the angle CBG : and , since it has been demonstrated , that the whole angle ABG is equal to the whole ACF , the parts of which , the angles CBG , BCF are also equal ; the remaining ...
... angle FBC is equal to the angle GCB , and the angle BCF to the angle CBG : and , since it has been demonstrated , that the whole angle ABG is equal to the whole ACF , the parts of which , the angles CBG , BCF are also equal ; the remaining ...
Page 19
... equal to one another , and likewise their sides CB , DB , that are terminated in B. Join CD ; then , in the case in which the vertex of each of the tri- angles is without the other triangle , because AC is equal to AD , the angle ACD is ...
... equal to one another , and likewise their sides CB , DB , that are terminated in B. Join CD ; then , in the case in which the vertex of each of the tri- angles is without the other triangle , because AC is equal to AD , the angle ACD is ...
Page 21
... angle BAC coincides with the angle EDF , and is equal to it . Therefore if two b 8. Ax . triangles , & c . Q. E. D. ر PROP . IX . PROB . TO bisect a given rectilineal angle , that is , to di- vide it into two equal angles . Let BAC be ...
... angle BAC coincides with the angle EDF , and is equal to it . Therefore if two b 8. Ax . triangles , & c . Q. E. D. ر PROP . IX . PROB . TO bisect a given rectilineal angle , that is , to di- vide it into two equal angles . Let BAC be ...
Page 22
... angles DCF , ECF , d 10. Def . is a right angle . Wherefore , from the given point C , in the given straight line AB , FC has been drawn at right angles to AB . Which was to be done . 1 ... angle CBE is equal to the angle 22 THE ELEMENTS.
... angles DCF , ECF , d 10. Def . is a right angle . Wherefore , from the given point C , in the given straight line AB , FC has been drawn at right angles to AB . Which was to be done . 1 ... angle CBE is equal to the angle 22 THE ELEMENTS.
Other editions - View all
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Robert Simson,Robert Euclid No preview available - 2016 |
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Robert Simson,Euclid No preview available - 2015 |
Common terms and phrases
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Bibliographic information
| Title | The Elements of Euclid |
| Author | Euclid |
| Editor | Robert Simson |
| Publisher | Johnson and Warner, 1811 |
| Original from | University of Chicago |
| Digitized | 17 Jun 2013 |
| Length | 518 pages |
| Export Citation | BiBTeX EndNote RefMan |