The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 5
... called Trapeziums . XXXV . Parallel straight lines are such as are in the same plane , and which being produced ever so far both ways , do not meet . POSTULATES . I. LET it be granted , that a B 3 BOOK I. - DEFINITIONS . 5 XXX. ...
... called Trapeziums . XXXV . Parallel straight lines are such as are in the same plane , and which being produced ever so far both ways , do not meet . POSTULATES . I. LET it be granted , that a B 3 BOOK I. - DEFINITIONS . 5 XXX. ...
Page 6
... produced to any length in a straight line . III . And that a circle may be described from any centre , at any distance from that centre . AXIOMS . I. THINGS which are equal to the same thing , are equal to one another . II . If equals ...
... produced to any length in a straight line . III . And that a circle may be described from any centre , at any distance from that centre . AXIOMS . I. THINGS which are equal to the same thing , are equal to one another . II . If equals ...
Page 7
... produced , shall at length meet upon that side on which are the angles " which are less than two right angles . " See the notes on Prop . xxix . of Book 1. Oct. Ed . 66 Recal PROP . I. PROBLEM . To describe an equilateral triangle BOOK ...
... produced , shall at length meet upon that side on which are the angles " which are less than two right angles . " See the notes on Prop . xxix . of Book 1. Oct. Ed . 66 Recal PROP . I. PROBLEM . To describe an equilateral triangle BOOK ...
Page 8
... . angle DAB , and produce * the straight lines DA , DB , to E and F ; from the centre B , at the dis- * 3 Post . tance BC , describe * the circle CGH , and from the centre D , at the distance DG , describe 8 EUCLID'S ELEMENTS .
... . angle DAB , and produce * the straight lines DA , DB , to E and F ; from the centre B , at the dis- * 3 Post . tance BC , describe * the circle CGH , and from the centre D , at the distance DG , describe 8 EUCLID'S ELEMENTS .
Page 11
... produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles triangle , of which the side AB is equal to AC , and let the straight lines AB , AC be produced to D and E : the angle ABC shall be equal to ...
... produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles triangle , of which the side AB is equal to AC , and let the straight lines AB , AC be produced to D and E : the angle ABC shall be equal to ...
Other editions - View all
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid No preview available - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid No preview available - 2023 |
Common terms and phrases
AB is equal altitude angle ABC angle ACB angle BAC angle EDF base BC base DEF BC is equal bisected centre circle ABCD circle EFGH circumference cone Const cylinder described diameter draw equal angles equal to AC equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism PROB pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD solid parallelopiped sphere square of AC straight line AB straight line AC THEOR three plane angles tiple touches the circle triangle ABC triangle DEF triplicate ratio wherefore whole