The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner CorrectedT. Desilver and R. Desilver, 1825 - 516 sider |
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Side 15
... remaining angles of the other , and be equal to them , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . Therefore , if two trian- gles have two sides of the one equal to two sides of the other , each to each , and have ...
... remaining angles of the other , and be equal to them , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . Therefore , if two trian- gles have two sides of the one equal to two sides of the other , each to each , and have ...
Side 16
... remaining angles of the one are equal ( 4. 1. ) to the remaining angles of the other , each to each , to which the equal sides are opposite ; viz . the angle ACF to the angle ABG , and the angle AFC to the angle AGB ; and because the ...
... remaining angles of the one are equal ( 4. 1. ) to the remaining angles of the other , each to each , to which the equal sides are opposite ; viz . the angle ACF to the angle ABG , and the angle AFC to the angle AGB ; and because the ...
Side 23
... remaining angle CEA is equal ( 3. Ax . ) to the remaining angle DEB . In the same man- ner it can be demonstrated that the angles CEB , AED are equal . Therefore , if two straight lines , & c . Q. E. D. Cor . 1. From this it is manifest ...
... remaining angle CEA is equal ( 3. Ax . ) to the remaining angle DEB . In the same man- ner it can be demonstrated that the angles CEB , AED are equal . Therefore , if two straight lines , & c . Q. E. D. Cor . 1. From this it is manifest ...
Side 24
... remaining angles , each to each , to which the equal sides are opposite ; wherefore the angle BAE is equal to the angle ECF ; but the angle ECD is greater than the angle ECF ; therefore the angle ACD is greater than BAE : in the same ...
... remaining angles , each to each , to which the equal sides are opposite ; wherefore the angle BAE is equal to the angle ECF ; but the angle ECD is greater than the angle ECF ; therefore the angle ACD is greater than BAE : in the same ...
Side 33
... remaining angle AGH is equal to the remaining angle GHD ; and they are alternate angles therefore AB is parallel to CD . Wherefore , if a straight line , & c . Q. E. D. PROP . XXIX . THEOR . IF a straight line fall upon two parallel ...
... remaining angle AGH is equal to the remaining angle GHD ; and they are alternate angles therefore AB is parallel to CD . Wherefore , if a straight line , & c . Q. E. D. PROP . XXIX . THEOR . IF a straight line fall upon two parallel ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
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altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone 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 meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment 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