The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 29
... parallelograms are equal to one another , and the diameter bisects them , that is , divides them into two equal parts ... parallelogram , of which BC is a diameter : the opposite sides and angles of the figure shall be equal to one ...
... parallelograms are equal to one another , and the diameter bisects them , that is , divides them into two equal parts ... parallelogram , of which BC is a diameter : the opposite sides and angles of the figure shall be equal to one ...
Page 30
... parallelogram ACDB into two equal parts . Q. E. D. PROP . XXXV . THEOR . Parallelograms upon the same base , and between the same parallels , are equal to one another . Let the parallelograms ABCD , EBCF be upon the same base BC , and ...
... parallelogram ACDB into two equal parts . Q. E. D. PROP . XXXV . THEOR . Parallelograms upon the same base , and between the same parallels , are equal to one another . Let the parallelograms ABCD , EBCF be upon the same base BC , and ...
Page 31
... parallelogram * 3 Ax . ABCD is equal to the parallelogram EBCF . There- 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 ...
... parallelogram * 3 Ax . ABCD is equal to the parallelogram EBCF . There- 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 ...
Page 32
... parallelogram : and EBCA is equal to DBCF , because they are upon the same base BC , and between the same parallels BC , EF ; and the triangle ABC is the half of the parallelogram EBCA , because the dia- meter AB bisects * it ; and the ...
... parallelogram : and EBCA is equal to DBCF , because they are upon the same base BC , and between the same parallels BC , EF ; and the triangle ABC is the half of the parallelogram EBCA , because the dia- meter AB bisects * it ; and the ...
Page 33
... 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.
... 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.
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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