The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 5
... , the remainders are equal . IV . If equals be added to unequals , the wholes are unequal . V. If equals be taken from unequals , the remainders are unequal . VI . Things which are double of the same , BOOK I. - DEFINITIONS , & c . 5.
... , the remainders are equal . IV . If equals be added to unequals , the wholes are unequal . V. If equals be taken from unequals , the remainders are unequal . VI . Things which are double of the same , BOOK I. - DEFINITIONS , & c . 5.
Page 6
... double of the same , are equal to one another . VII . Things which are halves of the same , are equal to one another . VIII . Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one ...
... double of the same , are equal to one another . VII . Things which are halves of the same , are equal to one another . VIII . Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one ...
Page 30
... double * of the triangle BDC ; and they are therefore equal to one another . But , if the sides AD , EF , opposite to the base BC of the parallelograms ABCD , EBCF , be not termi- * * * 20r3 Ax . +34 . 1 . SO EUCLID'S ELEMENTS .
... double * of the triangle BDC ; and they are therefore equal to one another . But , if the sides AD , EF , opposite to the base BC of the parallelograms ABCD , EBCF , be not termi- * * * 20r3 Ax . +34 . 1 . SO EUCLID'S ELEMENTS .
Page 33
... . Q. E. D. PROP . XLI . THEOR . If a parallelogram and a triangle be upon the same base , and between the same parallels ; the parallelogram shall be double of the triangle . D * 37.1 . * 34. 1 . * 10. 1. BOOK I. PROP . XL . XLI . 33.
... . Q. E. D. PROP . XLI . THEOR . If a parallelogram and a triangle be upon the same base , and between the same parallels ; the parallelogram shall be double of the triangle . D * 37.1 . * 34. 1 . * 10. 1. BOOK I. PROP . XL . XLI . 33.
Page 34
... double of the triangle ABC , because the diameter AC divides it into two equal parts ; where- fore ABCD is also double of the triangle EBC . Therefore , if a parallelogram , & c . Q. E. D. * PROP . XLII . PROB . To describe a ...
... double of the triangle ABC , because the diameter AC divides it into two equal parts ; where- fore ABCD is also double of the triangle EBC . Therefore , if a parallelogram , & c . Q. E. D. * PROP . XLII . PROB . To describe a ...
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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