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 16
... common to the two triangles AFC , AGB ; therefore the base FC is equal ( 4. 1. ) to the base GB , and the triangle AFC to the triangle AGB ; and the remaining angles of the one are equal ( 4. 1. ) to the remaining angles of the other ...
... common to the two triangles AFC , AGB ; therefore the base FC is equal ( 4. 1. ) to the base GB , and the triangle AFC to the triangle AGB ; and the remaining angles of the one are equal ( 4. 1. ) to the remaining angles of the other ...
Side 17
... common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the angle ACB ; therefore the base DC is equal to the base AB , and the triangle DBC is equal to the triangle ( 4. 1 ...
... common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the angle ACB ; therefore the base DC is equal to the base AB , and the triangle DBC is equal to the triangle ( 4. 1 ...
Side 19
... common to the two triangles DAF , EAF ; the two sides DA , AF , are equal to the two sides , EA , AF , each to each ; and the base DF is equal to the base EF ; there- fore the angle DAF is equal ( 8. 1. ) to the angle EAF ; wherefore ...
... common to the two triangles DAF , EAF ; the two sides DA , AF , are equal to the two sides , EA , AF , each to each ; and the base DF is equal to the base EF ; there- fore the angle DAF is equal ( 8. 1. ) to the angle EAF ; wherefore ...
Side 20
... common to the two triangles ACD , BCD ; the two sides AC , CD are equal to BC , CD , each to each ; and the angle ACD is equal to the angle BCD ; therefore the base AD is equal to the base ( 4. 1. ) DB and the straight line AB is ...
... common to the two triangles ACD , BCD ; the two sides AC , CD are equal to BC , CD , each to each ; and the angle ACD is equal to the angle BCD ; therefore the base AD is equal to the base ( 4. 1. ) DB and the straight line AB is ...
Side 21
... common segment . PROP . XII . PROB . E D B C C To draw a straight line perpendicular to a given straight line of an unlimited length , from a given point without it . Let AB be the given straight line , which may be produced to any ...
... common segment . PROP . XII . PROB . E D B C C To draw a straight line perpendicular to a given straight line of an unlimited length , from a given point without it . Let AB be the given straight line , which may be produced to any ...
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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