Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth, Also the Book of Euclid's DataLongman, Rees, Orme, 1834 - 482 σελίδες |
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Σελίδα vi
... shew what things can be found out or known from those that by hypothesis are already known ; so that in the analysis ... shewn to be given , and so on , until that which was proposed to be found out in the problem is demonstrated to be ...
... shew what things can be found out or known from those that by hypothesis are already known ; so that in the analysis ... shewn to be given , and so on , until that which was proposed to be found out in the problem is demonstrated to be ...
Σελίδα vii
... of the problem . WHEREIN this edition differs from the Greek , and the rea- sons of the alterations from it , will be shewn in the Notes at the end of the Data . OF THE LIFE AND WRITINGS OF EUCLID , AND OF PREFACE TO THE DATA . vii.
... of the problem . WHEREIN this edition differs from the Greek , and the rea- sons of the alterations from it , will be shewn in the Notes at the end of the Data . OF THE LIFE AND WRITINGS OF EUCLID , AND OF PREFACE TO THE DATA . vii.
Σελίδα 7
... shewn , that BC is equal to BG ; wherefore AL and BC are each of them equal to BG : and things that are equal to the same thing are equal to one another ; therefore the straight line † 1 Ax . AL is equal to BC . Wherefore , from the ...
... shewn , that BC is equal to BG ; wherefore AL and BC are each of them equal to BG : and things that are equal to the same thing are equal to one another ; therefore the straight line † 1 Ax . AL is equal to BC . Wherefore , from the ...
Σελίδα 18
... shewn that it is not equal to AB : therefore AC is greater than AB . Wherefore , the greater angle , & c . Q. E. D. PROPOSITION XX . THEOR . - Any two sides of a triangle are together greater than the third side . Let ABC be a triangle ...
... shewn that it is not equal to AB : therefore AC is greater than AB . Wherefore , the greater angle , & c . Q. E. D. PROPOSITION XX . THEOR . - Any two sides of a triangle are together greater than the third side . Let ABC be a triangle ...
Σελίδα 19
... shewn that BA , AC are greater than BE , EC ; much more then are BA , AC greater than BD , DC . * 20. 1 . † 4 Ax . † 20. 1 . † 4 Ax . Again , because the exterior angle of a triangle * is greater * 16. 1 . than the interior and opposite ...
... shewn that BA , AC are greater than BE , EC ; much more then are BA , AC greater than BD , DC . * 20. 1 . † 4 Ax . † 20. 1 . † 4 Ax . Again , because the exterior angle of a triangle * is greater * 16. 1 . than the interior and opposite ...
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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 parallel parallelogram parallelogram AC perpendicular polygon prism Prop proportionals Q. E. D. PROPOSITION radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment shewn sides BA similar sine solid angle solid parallelopiped square of AC straight line AB straight line BC THEOR.-If third tiple triangle ABC triplicate ratio vertex wherefore