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
... Because the point A is the centre of the circle BCD , AC is equal to AB ; and because the point B is the centre of the c . 15th De- circle ACE , BC is equal to BA : But it has been proved that CA is equal to AB ; therefore CA , CB are ...
... Because the point A is the centre of the circle BCD , AC is equal to AB ; and because the point B is the centre of the c . 15th De- circle ACE , BC is equal to BA : But it has been proved that CA is equal to AB ; therefore CA , CB are ...
Side 17
... 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 , because the ftraight line AC is equal ...
... 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 , because the ftraight line AC is equal ...
Side 27
... Because AC is greater than AB , make AD equal to AB , and join BD ; and because ADB is the exterior angle of the tri- angle BDC , it is greater than B D a . 3. I. C b . 16. I. the interior and oppofite angle DCB ; but ADB is equal e to ...
... Because AC is greater than AB , make AD equal to AB , and join BD ; and because ADB is the exterior angle of the tri- angle BDC , it is greater than B D a . 3. I. C b . 16. I. the interior and oppofite angle DCB ; but ADB is equal e to ...
Side 39
... because the ftraight line BC meets the two ftraight lines b 4. I. AC , BD , and makes the alternate angles ACB , CBD equal to one another , AC is parallel to BD ; and it was fhown to be c 27.1 . equal to it . Therefore ftraight lines ...
... because the ftraight line BC meets the two ftraight lines b 4. I. AC , BD , and makes the alternate angles ACB , CBD equal to one another , AC is parallel to BD ; and it was fhown to be c 27.1 . equal to it . Therefore ftraight lines ...
Side 42
... because the diameter AB bifects e it ; and the triangle DBC is the half of the parallelo- gram DBCF , because the diameter DC bifects it : But the halves of equal things are equal d ; therefore the triangle ABC is equal to the triangle ...
... because the diameter AB bifects e it ; and the triangle DBC is the half of the parallelo- gram DBCF , because the diameter DC bifects it : But the halves of equal things are equal d ; therefore the triangle ABC is equal to 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