The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 28
... fore all the angles of the figure , together with four right angles , are equal to twice as many right angles as the figure has sides . COR . 2. All the exterior angles of any rectilineal figure are together equal to four right angles ...
... fore all the angles of the figure , together with four right angles , are equal to twice as many right angles as the figure has sides . COR . 2. All the exterior angles of any rectilineal figure are together equal to four right angles ...
Page 30
... fore the two triangles ABC , CBD have two angles ABC , BCA in the one , equal to two angles BCD , CBD in the other , each to each , and one side BC common to the two triangles , which is adjacent to their equal angles ; therefore their ...
... fore the two triangles ABC , CBD have two angles ABC , BCA in the one , equal to two angles BCD , CBD in the other , each to each , and one side BC common to the two triangles , which is adjacent to their equal angles ; therefore their ...
Page 31
... fore parallelograms upon the same base , & c . Q. E. D. PROP . XXXVI . THEOR . Parallelograms upon equal bases , and between the same parallels , are equal to one another . Let ABCD , EFGH , be parallel- ograms upon equal bases BC , FG ...
... fore parallelograms upon the same base , & c . Q. E. D. PROP . XXXVI . THEOR . Parallelograms upon equal bases , and between the same parallels , are equal to one another . Let ABCD , EFGH , be parallel- ograms upon equal bases BC , FG ...
Page 34
... fore ABCD is also double of the triangle EBC . Therefore , if a parallelogram , & c . Q. E. D. * PROP . XLII . PROB . To describe a parallelogram that shall be equal to a given triangle , and have one of its angles equal to a given ...
... fore ABCD is also double of the triangle EBC . Therefore , if a parallelogram , & c . Q. E. D. * PROP . XLII . PROB . To describe a parallelogram that shall be equal to a given triangle , and have one of its angles equal to a given ...
Page 42
... fore a straight line , & c . Q. E. D. PROP . III . THEOR . If a straight line be divided into any two parts , the rect- angle contained by the whole and one of the parts , is equal to the rectangle contained by the two parts , toge ...
... fore a straight line , & c . Q. E. D. PROP . III . THEOR . If a straight line be divided into any two parts , the rect- angle contained by the whole and one of the parts , is equal to the rectangle contained by the two parts , toge ...
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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