The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth BooksMacmillan, 1886 - 400 Seiten |
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Seite ix
... take up Logic before Geometry ; and it seems therefore premature to devote space to a subject which will be altogether unsuitable to the majority of those who use a work like the present . After the notes will be found an Appendix ...
... take up Logic before Geometry ; and it seems therefore premature to devote space to a subject which will be altogether unsuitable to the majority of those who use a work like the present . After the notes will be found an Appendix ...
Seite 10
... ABC shall be equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE the greater cut off AG equal to AF the less , [ 1.3 . and join FC , GB . Because A Fis equal 10 EUCLID'S ELEMENTS .
... ABC shall be equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE the greater cut off AG equal to AF the less , [ 1.3 . and join FC , GB . Because A Fis equal 10 EUCLID'S ELEMENTS .
Seite 15
... Take any point D in AB , and from AC cut off AE equal to AD ; [ I. 3 . join DE , and on DE , on the side remote from A , describe the equi- lateral triangle DEF . [ I. 1 . B Join AF . The straight line AF shall bisect the angle BAC ...
... Take any point D in AB , and from AC cut off AE equal to AD ; [ I. 3 . join DE , and on DE , on the side remote from A , describe the equi- lateral triangle DEF . [ I. 1 . B Join AF . The straight line AF shall bisect the angle BAC ...
Seite 16
... Take any point D in AC , and make CE equal to CD . [ I. 3 , On DE describe the equilateral triangle DFE , and join CF. [ I. 1 . The straight line CF drawn from the given point C shall be at right angles to the given straight line AB ...
... Take any point D in AC , and make CE equal to CD . [ I. 3 , On DE describe the equilateral triangle DFE , and join CF. [ I. 1 . The straight line CF drawn from the given point C shall be at right angles to the given straight line AB ...
Seite 17
... Take any point D on the other side of AB , and from the centre C , at the distance CD , describe the circle EGF , meeting AB at F and G. [ Postulate 3 . Bisect FG at H , and join CH . [ I. 10 . H The straight line CH drawn from the ...
... Take any point D on the other side of AB , and from the centre C , at the distance CD , describe the circle EGF , meeting AB at F and G. [ Postulate 3 . Bisect FG at H , and join CH . [ I. 10 . H The straight line CH drawn from the ...
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Häufige Begriffe und Wortgruppen
ABCD angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC BC is equal bisects the angle centre chord circle ABC circle described circumference Construction Corollary describe a circle diameter double draw a straight equal angles equal to F equiangular equilateral equimultiples Euclid Euclid's Elements exterior angle given circle given point given straight line gnomon Hypothesis inscribed intersect isosceles triangle less Let ABC magnitudes middle point multiple opposite angles opposite sides parallelogram perpendicular plane polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION quadrilateral radius rectangle contained rectilineal figure remaining angle rhombus right angles right-angled triangle segment shew shewn side BC square on AC straight line &c straight line drawn tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vertex Wherefore