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 18
... join FC , GB . A Because AF is equal to AG , and AB to AC , the two fides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG com- mon to the two triangles AFC , AGB ; therefore the bafe FC is e- qual to ...
... join FC , GB . A Because AF is equal to AG , and AB to AC , the two fides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG com- mon to the two triangles AFC , AGB ; therefore the bafe FC is e- qual to ...
Side 19
... join DC ; there- fore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two fides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the angle ACB ; therefore the ...
... join DC ; there- fore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two fides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the angle ACB ; therefore the ...
Side 21
... join DE , and upon it de- fcribe an equilateral triangle DEF ; then join AF ; the ftraight line AF bifects the angle BAC . Because AD is equal to AE , and AF is common to the two triangles DAF , EAF ; the two fides DA , AF , are equal ...
... join DE , and upon it de- fcribe an equilateral triangle DEF ; then join AF ; the ftraight line AF bifects the angle BAC . Because AD is equal to AE , and AF is common to the two triangles DAF , EAF ; the two fides DA , AF , are equal ...
Side 26
... join BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle AEB is equal to the angle CEF , be- cause ...
... join BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle AEB is equal to the angle CEF , be- cause ...
Side 28
... join DC . Because DA is equal to AC , the angle ADC is likewife equal b to ACD ; but the angle BCI is greater than the angle ACD ; therefore the angle BCD is great- B er than the angle ADC ; and be- D cause the angle BCD of the triangle ...
... join DC . Because DA is equal to AC , the angle ADC is likewife equal b to ACD ; but the angle BCI is greater than the angle ACD ; therefore the angle BCD is great- B er than the angle ADC ; and be- D cause the angle BCD of the triangle ...
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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