The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page vii
... prove acceptable to all lovers of accurate reasoning and of mathematical learning , to remove such blemishes , and restore the principal Books of the Ele- ments to their original accuracy , as far as I was able ; especially since these ...
... prove acceptable to all lovers of accurate reasoning and of mathematical learning , to remove such blemishes , and restore the principal Books of the Ele- ments to their original accuracy , as far as I was able ; especially since these ...
Page 7
... proved that CA is equal to AB ; therefore CA , CB , are each of them equal to AB : but things which are equal to the same thing are equal to one another ; 1st Ax- therefore CA is equal to CB : wherefore CA , AB , BC iom . are equal to ...
... proved that CA is equal to AB ; therefore CA , CB , are each of them equal to AB : but things which are equal to the same thing are equal to one another ; 1st Ax- therefore CA is equal to CB : wherefore CA , AB , BC iom . are equal to ...
Page 9
... proved to coincide with the point E : wherefore the base BC shall coincide with the base EF ; because , the point B coinciding with E , and C with F , if the base BC does not coincide with the base EF , two straight . lines would ...
... proved to coincide with the point E : wherefore the base BC shall coincide with the base EF ; because , the point B coinciding with E , and C with F , if the base BC does not coincide with the base EF , two straight . lines would ...
Page 10
... proved to be equal to GB ; therefore the two sides BF , FC are equal to the two CG , GB , each to each ; and the angle BFC was proved to be equal to the angle CGB , and the base BC is common to the two triangles BFC , CGB ; wherefore ...
... proved to be equal to GB ; therefore the two sides BF , FC are equal to the two CG , GB , each to each ; and the angle BFC was proved to be equal to the angle CGB , and the base BC is common to the two triangles BFC , CGB ; wherefore ...
Page 12
... proved to be greater than the same BCD ; which is impossible . The case in which the vertex of one tri- angle is upon a side of the other , needs no demon- stration . Therefore , upon the same base , and on the same side of it , there ...
... proved to be greater than the same BCD ; which is impossible . The case in which the vertex of one tri- angle is upon a side of the other , needs no demon- stration . Therefore , upon the same base , and on the same side of it , there ...
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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