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
... base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite ... base BC shall coincide with the base EF , because the point B coinciding with E , and C with F , if the base BC does ...
... base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite ... base BC shall coincide with the base EF , because the point B coinciding with E , and C with F , if the base BC does ...
Side 16
... 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 , each to each , to which the equal sides are opposite ...
... 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 , each to each , to which the equal sides are opposite ...
Side 17
... base DC is equal to the base AB , and the triangle DBC is equal to the triangle ( 4. 1. ) ACB , the less to the great- er ; which is absurd . Therefore AB is not un- equal to AC , that is , it is equal to it . Where- fore , if two ...
... base DC is equal to the base AB , and the triangle DBC is equal to the triangle ( 4. 1. ) ACB , the less to the great- er ; which is absurd . Therefore AB is not un- equal to AC , that is , it is equal to it . Where- fore , if two ...
Side 18
... base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle ... base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one ...
... base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle ... base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one ...
Side 19
... base BC coincides with the base EF , but the sides BA , CA do not coincide with the sides ED , FD , but have a different situation , as EG , FG ; then upon the same base EF , and upon the same side of it , there can be two triangles ...
... base BC coincides with the base EF , but the sides BA , CA do not coincide with the sides ED , FD , but have a different situation , as EG , FG ; then upon the same base EF , and upon the same side of it , there can be two triangles ...
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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