The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page vi
... similar solid figures are those which are contained by similar planes of the same number and magnitude . " Now this propo- sition is a Theorem , not a Definition ; because the equality of figures of any kind must be demonstrated , and ...
... similar solid figures are those which are contained by similar planes of the same number and magnitude . " Now this propo- sition is a Theorem , not a Definition ; because the equality of figures of any kind must be demonstrated , and ...
Page 55
... drawn from the cen- tre , and the circumference between them . XI . Similar segments of circles are those in which the angles are equal , or which contain equal angles . e See N. * 10. 1 . 11. 1 . + BOOK III . DEFINITIONS . 55.
... drawn from the cen- tre , and the circumference between them . XI . Similar segments of circles are those in which the angles are equal , or which contain equal angles . e See N. * 10. 1 . 11. 1 . + BOOK III . DEFINITIONS . 55.
Page 72
... similar to the segment ADB , and that similar seg- ments of circles contain * equal angles ; therefore the angle ACB is equal to the angle ADB , the exterior to the interior , which is impossible * . Therefore there cannot be two similar ...
... similar to the segment ADB , and that similar seg- ments of circles contain * equal angles ; therefore the angle ACB is equal to the angle ADB , the exterior to the interior , which is impossible * . Therefore there cannot be two similar ...
Page 73
... Similar segments of circles upon equal straight lines are See N. equal to one another . Let AEB , CFD be similar segments of circles upon the equal straight lines AB , CD : the segment AEB shall be equal to the segment CFD . E For if ...
... Similar segments of circles upon equal straight lines are See N. equal to one another . Let AEB , CFD be similar segments of circles upon the equal straight lines AB , CD : the segment AEB shall be equal to the segment CFD . E For if ...
Page 74
... similar to the segment EDF ; and they are upon equal straight lines BC , EF : but similar segments of circles + Hyp . * 4. 1 . † Hyp . * * * 24.3 . upon equal straight lines are equal to 74 EUCLID'S ELEMENTS .
... similar to the segment EDF ; and they are upon equal straight lines BC , EF : but similar segments of circles + Hyp . * 4. 1 . † Hyp . * * * 24.3 . upon equal straight lines are equal to 74 EUCLID'S ELEMENTS .
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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