Euclid's Elements of geometry, transl. To which are added, algebraic demonstrations to the second and fifth books; also deductions in the first six, eleventh and twelfth books, with notes, by G. Phillips. Part 1, containing book i-vi1826 |
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Σελίδα 6
... angle BAC equal to the angle EDF . Then is the base BC equal to the base EF , and the triangle ABC equal to the triangle DEF ; also the remaining angles equal to the remaining angles , R each to each , to which the equal ДА CE sides are ...
... angle BAC equal to the angle EDF . Then is the base BC equal to the base EF , and the triangle ABC equal to the triangle DEF ; also the remaining angles equal to the remaining angles , R each to each , to which the equal ДА CE sides are ...
Σελίδα 11
... angle BAC equal to the angle EDF . For the tri- angle ABC being applied to the triangle DEF , and the point в being put on E ; also the right line BC being applied to EF , the point c will coincide with A B D G CE Therefore BC the point ...
... angle BAC equal to the angle EDF . For the tri- angle ABC being applied to the triangle DEF , and the point в being put on E ; also the right line BC being applied to EF , the point c will coincide with A B D G CE Therefore BC the point ...
Σελίδα 12
... angle , that is , to divide it into two equal parts . Let BAC be the given rectilineal angle ; it is required to bisect it . Take any point D in a the right line AB , and from the line AC take AE equal to AD , and DE being joined ; upon ...
... angle , that is , to divide it into two equal parts . Let BAC be the given rectilineal angle ; it is required to bisect it . Take any point D in a the right line AB , and from the line AC take AE equal to AD , and DE being joined ; upon ...
Σελίδα 17
... angles . F . 15. 1 . E b 4. 1 . D E Let ABC be a triangle , and let one of its sides BC be produced to D. The exterior angle ACD is greater than either of the interior and opposite angles ; namely , the angles CBA and BAC . Bisect AC in ...
... angles . F . 15. 1 . E b 4. 1 . D E Let ABC be a triangle , and let one of its sides BC be produced to D. The exterior angle ACD is greater than either of the interior and opposite angles ; namely , the angles CBA and BAC . Bisect AC in ...
Σελίδα 18
... angle ABC ; add ACB ... BAC , ACB , and also CAB , ABC , are less than two right angles . Therefore two angles of every triangle , & c . Q. E. D. PROPOSITION XVIII . THEOREM . The greater side of every triangle subtends the greater angle ...
... angle ABC ; add ACB ... BAC , ACB , and also CAB , ABC , are less than two right angles . Therefore two angles of every triangle , & c . Q. E. D. PROPOSITION XVIII . THEOREM . The greater side of every triangle subtends the greater angle ...
Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal adjacent angles Algebra angle ABC angle ACB angle BAC angles equal base BC bisected centre circle ABC circumference diameter double draw equal angles equal circles equal right lines equal to F equi equiangular equimultiples Euclid EUCLID'S ELEMENTS exceed exterior angle fore four magnitudes fourth given circle given point given right line gnomon greater ratio hence inscribed isosceles triangle join less Let ABC multiple parallel parallelogram perpendicular polygon proportional Q. E. D. Deductions Q. E. D. PROPOSITION rectangle contained remaining angle right line AB right line AC right line drawn segment side AC similar and similarly square of AC subtending THEOREM three right lines tiple touches the circle triangle ABC triangle DEF whence whole
Δημοφιλή αποσπάσματα
Σελίδα xxx - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference. XVIII. A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter. XIX. "A segment of a circle is the figure contained by a straight line, and the circumference it cuts off.
Σελίδα 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Σελίδα 33 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Σελίδα 146 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 27 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB, therefore the whole angle ABD is equal to the whole angle ACD • (ax.
Σελίδα 2 - Things which are double of the same are equal to one another. 7. Things which are halves of the same are equal to one another.
Σελίδα 28 - Parallelograms upon the same base, and between the same parallels, are equal to one another.
Σελίδα 73 - DH ; (i. def. 15.) therefore DH is greater than DG, the less than the greater, which is impossible : therefore no straight line can be drawn from the point A, between AE and the circumference, which does not cut the circle : or, which amounts to the same thing, however great an acute angle a straight line makes with the diameter at the point A, or however small an angle it makes with AE, the circumference must pass between that straight line and the perpendicular AE.
Σελίδα 88 - From a given circle to cut off a segment, which shall contain an angle equal to a given rectilineal angle.
Σελίδα 95 - IN a given circle to inscribe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle; it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF. Draw (1 7. 3.) the straight line G AH touching the circle in the point A, and. at the point A, in the straight line AH, make (23.