The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 10
... equiangular . PROP . VI . THEOR . If two angles of a triangle be equal to one another ; the sides also which subtend , or are opposite to , the equal angles , shall be equal to one another . Let ABC be a triangle having the angle ABC ...
... equiangular . PROP . VI . THEOR . If two angles of a triangle be equal to one another ; the sides also which subtend , or are opposite to , the equal angles , shall be equal to one another . Let ABC be a triangle having the angle ABC ...
Page 11
... equiangular triangle is also equilateral . PROP . VII . THEOR . Upon the same base , and on the same side of it , there can- See N. not be two triangles that have their sides which are ter- minated in one extremity of the base equal to ...
... equiangular triangle is also equilateral . PROP . VII . THEOR . Upon the same base , and on the same side of it , there can- See N. not be two triangles that have their sides which are ter- minated in one extremity of the base equal to ...
Page 86
... the diameter of the circle . Which was to be done . +1 Ax . PROP . II . PROB . In a given circle to inscribe a triangle equiangular to a given triangle . Let ABC be the given circle , and DEF the 86 EUCLID'S ELEMENTS .
... the diameter of the circle . Which was to be done . +1 Ax . PROP . II . PROB . In a given circle to inscribe a triangle equiangular to a given triangle . Let ABC be the given circle , and DEF the 86 EUCLID'S ELEMENTS .
Page 87
... equiangular to the triangle DEF . * H * 23. 1 . Draw the straight line GAH touching the circle in 17.3 . the point A ... equiangular to the triangle DEF , and it is inscribed in the circle ABC . Which was to be done . PROP . III . PROB ...
... equiangular to the triangle DEF . * H * 23. 1 . Draw the straight line GAH touching the circle in 17.3 . the point A ... equiangular to the triangle DEF , and it is inscribed in the circle ABC . Which was to be done . PROP . III . PROB ...
Page 88
... equiangular to the triangle DEF : and it is described about the circle ABC . Which was to be done . See N. * 9 . 1 . * 12.1 . † 11 Ax . * 26 . 1 . † 1 Ax . 16 , 3 . PROP . IV . PROB . To inscribe a circle in a given triangle . Let the ...
... equiangular to the triangle DEF : and it is described about the circle ABC . Which was to be done . See N. * 9 . 1 . * 12.1 . † 11 Ax . * 26 . 1 . † 1 Ax . 16 , 3 . PROP . IV . PROB . To inscribe a circle in a given triangle . Let the ...
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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