Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Explanatory Notes .... the first six booksJ. W. Parker & son, 1860 - 361 sider |
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Side 9
... ( constr . ) and AB to AC ; ( hyp . ) the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG common to the two triangles AFC , AGB ; F A B C G D E therefore the base B 5 BOOK I. PROP . IV , V.
... ( constr . ) and AB to AC ; ( hyp . ) the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG common to the two triangles AFC , AGB ; F A B C G D E therefore the base B 5 BOOK I. PROP . IV , V.
Side 11
... BDC is both equal to , and greater than the angle BCD ; which is impossible . Secondly . Let the vertex D of the triangle ADB fall within the triangle ACB . E C F D A B Produce AC to E , and AD to F , BOOK I. PROP . VI , VII . 11.
... BDC is both equal to , and greater than the angle BCD ; which is impossible . Secondly . Let the vertex D of the triangle ADB fall within the triangle ACB . E C F D A B Produce AC to E , and AD to F , BOOK I. PROP . VI , VII . 11.
Side 17
... of the interior opposite angles CBA or BAC . F A. B G Bisect AC in E , ( 1. 10. ) and join BE ; produce BE to F , making EF equal to BE , ( 1. 3. ) and join FC . Because AE is equal to EC , and BE to BOOK I. PROP . XV , XVI . 17.
... of the interior opposite angles CBA or BAC . F A. B G Bisect AC in E , ( 1. 10. ) and join BE ; produce BE to F , making EF equal to BE , ( 1. 3. ) and join FC . Because AE is equal to EC , and BE to BOOK I. PROP . XV , XVI . 17.
Side 19
... than the third side . Let ABC be a triangle . Then any two sides of it together shall be greater than the third side , viz . the sides BĂ , AC greater than the side BC ; AB , BC greater than AC ; and BC , BOOK I. PROP . XVIII - XX . 19.
... than the third side . Let ABC be a triangle . Then any two sides of it together shall be greater than the third side , viz . the sides BĂ , AC greater than the side BC ; AB , BC greater than AC ; and BC , BOOK I. PROP . XVIII - XX . 19.
Side 23
... , that the angle BAC is not equal to the angle EDF : therefore the angle BAC is greater than the angle EDF . Wherefore , if two triangles , & c . Q.E.D. PROPOSITION XXVI . THEOREM . If two triangles have two BOOK I. PROP . XXIV , XXV . 23.
... , that the angle BAC is not equal to the angle EDF : therefore the angle BAC is greater than the angle EDF . Wherefore , if two triangles , & c . Q.E.D. PROPOSITION XXVI . THEOREM . If two triangles have two BOOK I. PROP . XXIV , XXV . 23.
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ... Robert Potts Uten tilgangsbegrensning - 1845 |
Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson with ... Euclid,Robert Potts Uten tilgangsbegrensning - 1847 |
Vanlige uttrykk og setninger
A₁ ABCD AC is equal Algebraically angle ABC angle ACB angle BAC Apply Euc axiom base BC chord circle ABC constr describe a circle diagonals diameter divided double draw equal angles equiangular equilateral triangle equimultiples Euclid Euclid's Elements exterior angle Geometrical given circle given line given point given straight line given triangle gnomon greater hypotenuse inscribed intersection isosceles triangle less Let ABC line AC lines be drawn meet the circumference multiple opposite angles parallelogram pentagon perpendicular porism problem produced Prop proportionals proved Q.E.D. PROPOSITION quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn similar similar triangles square on AC tangent THEOREM touch the circle trapezium triangle ABC twice the rectangle vertex vertical angle wherefore
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