The Elements of EuclidJohnson and Warner, 1811 - 518 Seiten |
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Seite 16
... third sides , equal ; and the two triangles shall be equal ; and their other angles shall be equal , each to each , viz . those to which the equal sides are opposite . Let ABC , DEF be two triangles which have the two sides AB , AC ...
... third sides , equal ; and the two triangles shall be equal ; and their other angles shall be equal , each to each , viz . those to which the equal sides are opposite . Let ABC , DEF be two triangles which have the two sides AB , AC ...
Seite 28
... third side . Let ABC be a triangle ' ; any two sides of it together are greater than the third side , viz . the sides BA , AC greater than the side BC ; and AB , BC greater than AC ; and BC , GA greater than AB . Produce BA to the point ...
... third side . Let ABC be a triangle ' ; any two sides of it together are greater than the third side , viz . the sides BA , AC greater than the side BC ; and AB , BC greater than AC ; and BC , GA greater than AB . Produce BA to the point ...
Seite 29
... third " . Let A , B , C be the three given straight lines , of which any two whatever are greater than the third , viz . A and B greater than C ; A and C greater than B and B and C than A. It is required to make a triangle of which the ...
... third " . Let A , B , C be the three given straight lines , of which any two whatever are greater than the third , viz . A and B greater than C ; A and C greater than B and B and C than A. It is required to make a triangle of which the ...
Seite 32
... third angle of the other . D Let ABC , DEF be two triangles which have the angles ABC , BCA equal to the angles DEF ... third angle BAC to the third , angle EDF . For , if AB be not B C E equal to DE , one of them must be the greater ...
... third angle of the other . D Let ABC , DEF be two triangles which have the angles ABC , BCA equal to the angles DEF ... third angle BAC to the third , angle EDF . For , if AB be not B C E equal to DE , one of them must be the greater ...
Seite 33
... third angle BAC to the third angle EDF .. Next , let the sides A which are opposite to equal angles in each triangle be equal to one another , viz . AB to DE ; likewise in this case , the other sides shall be equal , AC to DF , and BC ...
... third angle BAC to the third angle EDF .. Next , let the sides A which are opposite to equal angles in each triangle be equal to one another , viz . AB to DE ; likewise in this case , the other sides shall be equal , AC to DF , and BC ...
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Häufige Begriffe und Wortgruppen
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