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 15
... fore equilateral , and it is defcribed upon the given ftraight line AB . Which was required to be done . PROP . II . PROB . ROM a given point to draw a ftraight line equal to a given straight line . FR Let A be the given point , and BC ...
... fore equilateral , and it is defcribed upon the given ftraight line AB . Which was required to be done . PROP . II . PROB . ROM a given point to draw a ftraight line equal to a given straight line . FR Let A be the given point , and BC ...
Side 21
... fore if two triangles , & c . Q. E. D. T PROP . IX . PRO B. O bifect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle , it is required to bi- fect it . A b I. I. Take any ...
... fore if two triangles , & c . Q. E. D. T PROP . IX . PRO B. O bifect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle , it is required to bi- fect it . A b I. I. Take any ...
Side 24
... fore the angles CBE , EBD are equal to the three angles CBA , ABE , EBD . Again , becaufe the angle DBA is equal to the two angles DBE , EBA , add to these equals the angle ABC ; therefore the angles DBA , ABC are equal to the three ...
... fore the angles CBE , EBD are equal to the three angles CBA , ABE , EBD . Again , becaufe the angle DBA is equal to the two angles DBE , EBA , add to these equals the angle ABC ; therefore the angles DBA , ABC are equal to the three ...
Side 25
... fore BE is not in the fame ftraight line with BC . And , in like manner , it may be demonftrated , that no other can be in the fame ftraight line with it but BD , which therefore is in the fame ftraight line with CB . Wherefore , if at ...
... fore BE is not in the fame ftraight line with BC . And , in like manner , it may be demonftrated , that no other can be in the fame ftraight line with it but BD , which therefore is in the fame ftraight line with CB . Wherefore , if at ...
Side 28
... fore the fide AC is not less than AB ; and it has been hewn that it is not equal to AB ; therefore AC is greater than AB . Wherefore the greater angle , & c . Q. E. D. PROP . XX . THEOR . ANY two fides of a triangle are together greater ...
... fore the fide AC is not less than AB ; and it has been hewn that it is not equal to AB ; therefore AC is greater than AB . Wherefore the greater angle , & c . Q. E. D. PROP . XX . THEOR . ANY two fides of a triangle are together greater ...
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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