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 Restored : Also the Book of Euclid's Data, in Like Manner CorrectedJ. Nourse, London, 1781 - 520 sider |
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Side 16
... fhall likewise have their bases , or third fides , equal ; and the two triangles fhall be equal ; and their other angles fhall be equal , each to each , viz . thofe to which the equal fides are oppofite . Let ABC , DEF be two triangles ...
... fhall likewise have their bases , or third fides , equal ; and the two triangles fhall be equal ; and their other angles fhall be equal , each to each , viz . thofe to which the equal fides are oppofite . Let ABC , DEF be two triangles ...
Side 17
... fhall coincide with the point E , because AB is equal to DE ; and AB coinciding with DE , AC fhall coincide with DF , be- cause the angle BAC is equal to the angle EDF ; wherefore alfo the point C fhall coincide with the point F ...
... fhall coincide with the point E , because AB is equal to DE ; and AB coinciding with DE , AC fhall coincide with DF , be- cause the angle BAC is equal to the angle EDF ; wherefore alfo the point C fhall coincide with the point F ...
Side 18
... fhall be equal to the angle ACB , and the angle CBD to the angle BCE . a 3. I. b 4. I. c 3. Ax . In BD take any point F , and from AE , the greater , cut off AG equal to AF , the lefs , and join FC , GB . A Because AF is equal to AG ...
... fhall be equal to the angle ACB , and the angle CBD to the angle BCE . a 3. I. b 4. I. c 3. Ax . In BD take any point F , and from AE , the greater , cut off AG equal to AF , the lefs , and join FC , GB . A Because AF is equal to AG ...
Side 20
... fhall be equal to the angle con- tained by the two fides equal to them , of the other . Let ABC , DEF be two triangles having the two fides AB , AC equal to the two fides DE , DF , each to each , viz . AB to DE , and AC to A DF ; and ...
... fhall be equal to the angle con- tained by the two fides equal to them , of the other . Let ABC , DEF be two triangles having the two fides AB , AC equal to the two fides DE , DF , each to each , viz . AB to DE , and AC to A DF ; and ...
Side 21
... fhall epincide with ED and DF ; for , if the bafe BC coin- cides with the bafe EF , but the fides BA , CA do not coin- cide with the fides ED , FD , but have a different fituation , as EG , FG ; then , upon the fame bafe EF , and upon ...
... fhall epincide with ED and DF ; for , if the bafe BC coin- cides with the bafe EF , but the fides BA , CA do not coin- cide with the fides ED , FD , but have a different fituation , as EG , FG ; then , upon the fame bafe EF , and upon ...
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The Elements of Euclid: Viz. The First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1793 |
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alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle bifected Book XI cafe centre circle ABCD circumference cone confequently conftruction cylinder defcribed demonftrated diameter drawn equal angles equiangular equimultiples Euclid excefs faid fame manner fame multiple fame ratio fame reafon fecond fegment fides BA fimilar fince firft firſt folid angle fome fore fphere fquare of AC ftraight line AB given angle given ftraight line given in fpecies given in magnitude given in pofition given magnitude given ratio gnomon greater join lefs leſs likewife line BC oppofite parallel parallelepipeds parallelogram perpendicular polygon prifm propofition proportionals pyramid Q. E. D. PROP rectangle contained rectilineal figure right angles ſquare thefe THEOR theſe triangle ABC vertex wherefore