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 |
Inni boken
Resultat 1-5 av 100
Side 6
... fame Number and Magnitude . " Now , this Propofition is a Theorem , not a Definition ; because the equality of Figures of any kind must be demonftrated , and not affumed ; and , therefore , though this were a true Propo- fition , it ...
... fame Number and Magnitude . " Now , this Propofition is a Theorem , not a Definition ; because the equality of Figures of any kind must be demonftrated , and not affumed ; and , therefore , though this were a true Propo- fition , it ...
Side 13
... fame plane , and which , being produced ever fo far both ways , do not meet . Book I. LE POSTULATES . I. ET it be granted that a straight line may be drawn from any one point to any other point . II . That a terminated ftraight line may ...
... fame plane , and which , being produced ever fo far both ways , do not meet . Book I. LE POSTULATES . I. ET it be granted that a straight line may be drawn from any one point to any other point . II . That a terminated ftraight line may ...
Side 24
... fame three angles ; and things 1. Ax . that are equal to the fame are equal to one another ; therefore the angles CBE , EBD are equal to the angles DBA , ABC ; but CBE , EBD are two right angles ; therefore DBA , ABC are together equal ...
... fame three angles ; and things 1. Ax . that are equal to the fame are equal to one another ; therefore the angles CBE , EBD are equal to the angles DBA , ABC ; but CBE , EBD are two right angles ; therefore DBA , ABC are together equal ...
Side 25
... 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 a point , & c ...
... 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 a point , & c ...
Side 34
... fame fide ; or make the interior angles on the fame fide BGH , GHD together equal to two right angles ; AB is parallel to CD . E G -B D H Because the angle EGB is e qual to the angle GHD , and the angle C a Book I. a 15. I. angle EGB ...
... fame fide ; or make the interior angles on the fame fide BGH , GHD together equal to two right angles ; AB is parallel to CD . E G -B D H Because the angle EGB is e qual to the angle GHD , and the angle C a Book I. a 15. I. angle EGB ...
Andre utgaver - Vis alle
The Elements of Euclid: Viz. The First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1793 |
Vanlige uttrykk og setninger
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