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 10
... angle 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 .
... angle 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
... 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 . Because AD is equal to AE , [ Construction . and AF is common to the two ...
... 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 . Because AD is equal to AE , [ Construction . and AF is common to the two ...
Seite 17
... join CH . [ I. 10 . H The straight line CH drawn from the given point C shall be perpendicular to the given straight line AB . Join CF , CG . Because FH is equal to HG , [ Construction . and HC is common to the two triangles FHC , GHC ...
... join CH . [ I. 10 . H The straight line CH drawn from the given point C shall be perpendicular to the given straight line AB . Join CF , CG . Because FH is equal to HG , [ Construction . and HC is common to the two triangles FHC , GHC ...
Seite 20
... join BE and produce it to F , making EF equal to EB , [ I. 3 . and join FC . Because AE is equal to EC , and BE to EF ; [ Constr . the two sides AE , EB are equal to the two sides CE , EF , each to each ; and the angle AEB is equal to ...
... join BE and produce it to F , making EF equal to EB , [ I. 3 . and join FC . Because AE is equal to EC , and BE to EF ; [ Constr . the two sides AE , EB are equal to the two sides CE , EF , each to each ; and the angle AEB is equal to ...
Seite 30
... join AH . [ I. 3 . H E Then because BH is equal to EF , and AB to DE ; [ Construction . [ Hypothesis . the two sides AB , BH are equal to the two sides DE , EF , each to each ; and the angle ABH is equal to the angle DEF ; [ Hypothesis ...
... join AH . [ I. 3 . H E Then because BH is equal to EF , and AB to DE ; [ Construction . [ Hypothesis . the two sides AB , BH are equal to the two sides DE , EF , each to each ; and the angle ABH is equal to the angle DEF ; [ Hypothesis ...
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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