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 78
... drawn to them from the centre are equal ( 4. def . 3. ) therefore ABCD are equally distant from the centre . Next ... draw EH , EK perpen- K dicular to BC , FG , and join EB , EC , EF ; and because AE is equal to EB , and ED to EC , AD ...
... drawn to them from the centre are equal ( 4. def . 3. ) therefore ABCD are equally distant from the centre . Next ... draw EH , EK perpen- K dicular to BC , FG , and join EB , EC , EF ; and because AE is equal to EB , and ED to EC , AD ...
Side 79
... drawn at right angles to the diameter of a circle , from the extremity of it , falls without the cir- cle ; and no straight line can be drawn between that straight line and the circumference from the extremity , so as not to cut the ...
... drawn at right angles to the diameter of a circle , from the extremity of it , falls without the cir- cle ; and no straight line can be drawn between that straight line and the circumference from the extremity , so as not to cut the ...
Side 80
... drawn from the point A which does not cut the circle for , if possible , let FA be between them , and from the point D draw ( 12. 1. ) DG perpendicular to FA , and let it meet the circumference in H : and because AGD is a right an- gle ...
... drawn from the point A which does not cut the circle for , if possible , let FA be between them , and from the point D draw ( 12. 1. ) DG perpendicular to FA , and let it meet the circumference in H : and because AGD is a right an- gle ...
Side 81
... drawn from the centre ; but a straight line drawn from the extremity of a diameter , at right angles to it , touches the circle ( cor . 16. 3. ) : therefore AB touches the circle ; and it is drawn from the given point A. Which was to be ...
... drawn from the centre ; but a straight line drawn from the extremity of a diameter , at right angles to it , touches the circle ( cor . 16. 3. ) : therefore AB touches the circle ; and it is drawn from the given point A. Which was to be ...
Side 82
... drawn at right angles to the touching line , the centre of the circle shall be in that line . Let the straight line DE touch the circle ABC in C , and from C let CA be drawn at right angles to DE ; the centre of the circle is in CA. For ...
... drawn at right angles to the touching line , the centre of the circle shall be in that line . Let the straight line DE touch the circle ABC in C , and from C let CA be drawn at right angles to DE ; the centre of the circle is in CA. For ...
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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