The Elements of EuclidJohnson and Warner, 1811 - 518 sider |
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Side vi
... demonstrated , and not assumed ; and , there- fore , though this were a true proposition , it ought to have been demonstrated . But , indeed , this proposition , which makes the 10th definition of the 11th book , is not true universally ...
... demonstrated , and not assumed ; and , there- fore , though this were a true proposition , it ought to have been demonstrated . But , indeed , this proposition , which makes the 10th definition of the 11th book , is not true universally ...
Side vii
... demonstrated since Theon's time hitherto . Besides , there are several other things which have nothing of Euclid's accura- cy , and which plainly show , that his Elements have been much corrupted by unskilful geometers ; and , though ...
... demonstrated since Theon's time hitherto . Besides , there are several other things which have nothing of Euclid's accura- cy , and which plainly show , that his Elements have been much corrupted by unskilful geometers ; and , though ...
Side 17
... demonstrated . PROP . V. THEOR . The angles at the base of an isosceles triangle are equal to one another ; and , if the equal sides be pro- duced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles ...
... demonstrated . PROP . V. THEOR . The angles at the base of an isosceles triangle are equal to one another ; and , if the equal sides be pro- duced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles ...
Side 18
... 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 ABC is therefore equal to the remaining angle ACB , which are the angles at the base of ...
... 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 ABC is therefore equal to the remaining angle ACB , which are the angles at the base of ...
Side 22
... demonstrated , that two straight lines can cannot have a common segment . If it be possible , let the two straight lines ABC , ABD have the segment AB common to both of them . From the poirt B draw BE at right angles to AB ; and because ...
... demonstrated , that two straight lines can cannot have a common segment . If it be possible , let the two straight lines ABC , ABD have the segment AB common to both of them . From the poirt B draw BE at right angles to AB ; and because ...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1806 |
Vanlige uttrykk og setninger
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