The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 7
... triangle upon a given finite straight line . Let AB be the given straight line ; it is required to de- scribe an ... ABC shall be an equilateral triangle . Because the point A is the centre of the circle BCD , * * AC is equal to AB ; and ...
... triangle upon a given finite straight line . Let AB be the given straight line ; it is required to de- scribe an ... ABC shall be an equilateral triangle . Because the point A is the centre of the circle BCD , * * AC is equal to AB ; and ...
Page 9
... triangle ABC be applied to DEF , so that the point A may be on D , and the straight line AB upon DE ; the point B ... triangle ABC † 8 Ax . coincides with the whole triangle DEF , and is equal to it ; and the other angles of the one ...
... triangle ABC be applied to DEF , so that the point A may be on D , and the straight line AB upon DE ; the point B ... triangle ABC † 8 Ax . coincides with the whole triangle DEF , and is equal to it ; and the other angles of the one ...
Page 10
... ABC is equal + to the remaining angle ACB , which are the angles at the base of the triangle ABC : and it has also been proved that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base ...
... ABC is equal + to the remaining angle ACB , which are the angles at the base of the triangle ABC : and it has also been proved that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base ...
Page 12
... ABC , DEF be two triangles , having the two sides AB , AC , equal to the two sides DE , DF , each to each , viz . AB ... triangle ABC be applied to DEF , so that the point B may be on E , and the straight line BC upon B Ꭰ Ꮐ CE EF ; the ...
... ABC , DEF be two triangles , having the two sides AB , AC , equal to the two sides DE , DF , each to each , viz . AB ... triangle ABC be applied to DEF , so that the point B may be on E , and the straight line BC upon B Ꭰ Ꮐ CE EF ; the ...
Page 13
... triangle ABC , and * 1.1 . bisect * the angle ACB by the straight line CD . AB * 9.1 . shall be cut into two equal parts in the point D. Because AC is equal † to CB , and CD common to the two triangles ACD , BCD ; the two sides AC , CD ...
... triangle ABC , and * 1.1 . bisect * the angle ACB by the straight line CD . AB * 9.1 . shall be cut into two equal parts in the point D. Because AC is equal † to CB , and CD common to the two triangles ACD , BCD ; the two sides AC , CD ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson No preview available - 2019 |
Common terms and phrases
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected centre circle ABCD circumference common logarithm cone Constr cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali 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 logarithm multiple opposite parallel parallelogram AC perpendicular polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle contained rectilineal figure right angles segment shewn sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore