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
... greater of two given ftraight lines to cut off a part equal to the less . FR Let AB and C be the two gi ven straight lines , whereof AB is the greater . It is required to cut off from AB , the greater , a part equal to C the lefs . b EB ...
... greater of two given ftraight lines to cut off a part equal to the less . FR Let AB and C be the two gi ven straight lines , whereof AB is the greater . It is required to cut off from AB , the greater , a part equal to C the lefs . b EB ...
Side 19
... greater than a the other : Let AB be the greater , and from it cut off DB e- a 3. I. qual to AC , the lefs , and join DC ; there- fore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two fides DB ...
... greater than a the other : Let AB be the greater , and from it cut off DB e- a 3. I. qual to AC , the lefs , and join DC ; there- fore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two fides DB ...
Side 20
... greater than BCD ; much more then is the angle BDC greater than the angle BCD . Again , because CB is equal A to DB , the angle BDC is equal to the a angle BCD ; but BDC has been proved to be greater than the fame BCD ; which is ...
... greater than BCD ; much more then is the angle BDC greater than the angle BCD . Again , because CB is equal A to DB , the angle BDC is equal to the a angle BCD ; but BDC has been proved to be greater than the fame BCD ; which is ...
Side 26
... greater than the angle ECF ; therefore the angle ACD is greater than BAE : In the fame manner , if the fide BC be bifected , it may be demonstrated that the angle BCG , that is 4 , the angle ACD , is greater thari the angle ABC ...
... greater than the angle ECF ; therefore the angle ACD is greater than BAE : In the fame manner , if the fide BC be bifected , it may be demonstrated that the angle BCG , that is 4 , the angle ACD , is greater thari the angle ABC ...
Side 27
... greater than the angles ABC , ACB ; but ACD , ACB are to- gether equal b to two right angles ; therefore the angles ... greater fide of every triangle is oppofite to the greater angle . Let ABC be a triangle , of which the fide AC is ...
... greater than the angles ABC , ACB ; but ACD , ACB are to- gether equal b to two right angles ; therefore the angles ... greater fide of every triangle is oppofite to the greater angle . Let ABC be a triangle , of which the fide AC is ...
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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